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@string{annsens4 = {Ann. Sci. {\'E}cole Norm. Sup. (4)}}

@string{annyas = {Ann. N.Y. Acad. Sci.}}

@string{aphysa = {Appl. Phys. A: Mater. Sci. Process.}}

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@string{bioll = {Biol. Lett.}}

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@string{cmda = {Celestial Mech. Dynam. Astronom.}}

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@string{etna = {Electron. Trans. Numer. Anal.}}

@string{eurepl = {Europhys. Lett. EPL}}

@string{eurjp = {Eur. J. Phys.}}

@string{eurpl = {Europhys. Lett.}}

@string{eurpst = {Eur. Phys. J. Special Topics}}

@string{evcomp = {Evolutionary Comp.}}

@string{expma = {Experiment. Math.}}

@string{fcompm = {Found. Comput. Math.}}

@string{fieldsic = {Fields Inst. Comm.}}

@string{fneco = {Functional Ecology}}

@string{fused = {Fusion Eng. Design}}

@string{ie3tcsf = {IEEE Trans. Circuits Syst. I: Fund. Theor. Appl.}}

@string{ie3tm = {IEEE Trans. Magnetics}}

@string{ie3tns = {IEEE Trans. Nucl. Sci.}}

@string{ijbc = {Internat. J. Bifur. Chaos}}

@string{imajna = {IMA J. Numer. Anal.}}

@string{intjmpa = {Int. J. Modern Phys. A}}

@string{intjnt = {Int. J. Number Theory}}

@string{intjtp = {Internat. J. Theoret. Phys.}}

@string{invpr = {Inverse Problems}}

@string{iremtt = {IRE Microwave Theory Tech.}}

@string{isis = {Isis}}

@string{izvm = {Izv. Math.}}

@string{jbsci = {J. Biosci.}}

@string{jcompam = {J. Comput. Appl. Math}}

@string{jcompp = {J. Comput. Phys.}}

@string{jcompx = {J. Complexity}}

@string{jelas = {J. Elasticity}}

@string{jexpb = {J. Exp. Biol.}}

@string{jgeopr = {J. Geophys. Res.}}

@string{jmathb = {J. Math. Biol.}}

@string{jmathc = {J. Math. Chem.}}

@string{jmathp = {J. Math. Phys.}}

@string{jmatsj = {J. Math. Soc. Japan}}

@string{jphysa = {J. Phys. A: Math. Gen.}}

@string{jphyscs = {J. Phys.: Conf. Ser.}}

@string{jphysg = {J. Phys. G: Nucl. Part. Phys.}}

@string{jrnist = {J. Res. Natl. Inst. Stand. Technol.}}

@string{jrsif = {J. R. Soc. Interface}}

@string{jstatp = {J. Stat. Phys.}}

@string{jthbio = {J. Theoret. Biol.}}

@string{ledpm7 = {London Edinburgh Dublin Philos. Mag. J. Sci. (7)}}

@string{linaa = {Linear Algebra Appl.}}

@string{mathc = {Math. Comp.}}

@string{mathi = {Math. Intelligencer}}

@string{mathm = {Math. Mag.}}

@string{mathz = {Math. Z.}}

@string{molecp = {Molecular Phys.}}

@string{mulmo = {Multiscale Model. Simul.}}

@string{natma = {Nature Materials}}

@string{nature = {Nature}}

@string{newjp = {New J. Phys.}}

@string{nonli = {Nonlinearity}}

@string{notams = {Notices Amer. Math. Soc.}}

@string{nucim = {Nucl. Instrum. Methods}}

@string{nucima = {Nucl. Instrum. Methods Phys. Res., Sect. A}}

@string{nucimpr = {Nucl. Instrum. Methods Phys. Res.}}

@string{numalgo = {Numer. Algorithms}}

@string{numm = {Numer. Math.}}

@string{pacc = {Part. Accel.}}

@string{philm = {Philos. Mag.}}

@string{phtrrs = {Philos. Trans. R. Soc. Lond.}}

@string{phtrrsa = {Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci.}}

@string{phtrrsb = {Philos. Trans. R. Soc. Lond. Ser. B Biol. Sci.}}

@string{physbio = {Phys. Biol.}}

@string{physd = {Physica D}}

@string{physed = {Phys. Ed.}}

@string{physla = {Phys. Lett. A}}

@string{physlb = {Phys. Lett. B}}

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@string{physr = {Phys. Rep.}}

@string{physs = {Phys. Scr.}}

@string{physt = {Phys. Today}}

@string{ploscb = {PLoS Comput. Biol.}}

@string{pnasusa = {Proc. Nat. Acad. Sci. USA}}

@string{ppcf = {Plasma Phys. Control. Fusion}}

@string{pramana = {Pramana}}

@string{prev = {Phys. Rev.}}

@string{preva = {Phys. Rev. A}}

@string{prevb = {Phys. Rev. B}}

@string{prevc = {Phys. Rev. C}}

@string{prevd = {Phys. Rev. D}}

@string{preve = {Phys. Rev. E}}

@string{prevl = {Phys. Rev. Lett.}}

@string{procamm = {Proc. Appl. Math. Mech.}}

@string{procja = {Proc. Japan Acad.}}

@string{procjaa = {Proc. Japan Acad. Ser. A Math. Sci.}}

@string{procjab = {Proc. Japan Acad. Ser. B Phys. Biol. Sci.}}

@string{procrs = {Proc. R. Soc. Lond.}}

@string{procrsa = {Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci.}}

@string{procrsb = {Proc. R. Soc. Lond. Ser. B Biol. Sci.}}

@string{procrse = {Proc. R. Soc. Edinburgh}}

@string{prstab = {Phys. Rev. ST Accel. Beams}}

@string{regcd = {Regul. Chaotic Dyn.}}

@string{reppp = {Rep. Progr. Phys.}}

@string{revgp = {Rev. Geophys.}}

@string{revmp = {Rev. Modern Phys.}}

@string{revsi = {Rev. Sci. Instrum.}}

@string{rumaths = {Russian Math. Surveys}}

@string{sciam = {Sci. Amer.}}

@string{scien = {Science}}

@string{siamjads = {SIAM J. Appl. Dyn. Syst.}}

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@string{siamjma = {SIAM J. Math. Anal.}}

@string{siamjmax = {SIAM J. Matrix Anal. Appl.}}

@string{siamjna = {SIAM J. Numer. Anal.}}

@string{siamjsc = {SIAM J. Sci. Comput.}}

@string{siamjssc = {SIAM J. Sci. Stat. Comput.}}

@string{siamr = {SIAM Rev.}}

@string{statsci = {Statist. Sci.}}

@string{theco = {Theor. Ecol.}}

@string{trams = {Trans. Amer. Math. Soc.}}

@string{zekstf = {Zh. \`Eksper. Teoret. Fiz.}}

@string{zphysc = {Z. Phys. C}}


@proceedings{IPAC:2010,
	Booktitle = {Proceedings of the 1st International Particle Accelerator Conference, Kyoto, Japan, 23--28 May 2010},
	Date-Added = {2015-04-03 19:33:35 +0000},
	Date-Modified = {2015-04-03 19:33:35 +0000},
	Editor = {Noda, A. and Petit-Jean-Genaz, {\relax Ch}ristine and Schaa, V. and Shirai, T. and Shirakawa, A.},
	Title = {Proceedings of the 1st International Particle Accelerator Conference, Kyoto, Japan, 23--28 May 2010},
	Year = {2010}}

@proceedings{IPAC:2011,
	Booktitle = {Proceedings of the 2nd International Particle Accelerator Conference, San Sebastian, Spain, 4--9 September 2011},
	Date-Added = {2015-04-03 19:33:35 +0000},
	Date-Modified = {2015-04-03 19:33:35 +0000},
	Editor = {Petit-Jean-Genaz, Christine and Blanco, Angela and Etxebarria, Iker and Perez, Francis and Wolski, Andy and Schaa, Volker},
	Title = {Proceedings of the 2nd International Particle Accelerator Conference, San Sebastian, Spain, 4--9 September 2011},
	Year = {2011}}

@proceedings{IPAC:2013,
	Booktitle = {Proceedings of the 4th International Particle Accelerator Conference, Shanghai, China, 12--17 May 2013},
	Date-Added = {2015-04-03 19:32:52 +0000},
	Date-Modified = {2015-04-03 19:32:52 +0000},
	Editor = {Petit-Jean-Genaz, Christine and others},
	Title = {Proceedings of the 4th International Particle Accelerator Conference, Shanghai, China, 12--17 May 2013},
	Year = {2013}}

@article{Burov:2002:CircModes,
	Author = {Burov, Alexey V. and Nagaitsev, Sergei and Derbenev, {\relax Ya}roslav S.},
	Date-Added = {2015-04-03 19:31:12 +0000},
	Date-Modified = {2015-04-03 19:31:12 +0000},
	Doi = {10.1103/PhysRevE.66.016503},
	Journal = preve,
	Month = jul,
	Number = {1},
	Pages = {016503},
	Title = {Circular modes, beam adapters, and their applications in beam optics},
	Volume = {66},
	Year = {2002},
	Abstract = {In the optics of charged particle beams, circular transverse modes can be introduced; they provide an adequate basis for rotation-invariant transformations.  A group of these transformations is shown to be identical to a group of the canonical angular momentum preserving mappings.  These mappings and the circular modes are parametrized similar to the Courant-Snyder forms for the conventional uncoupled, or planar, case.  The planar-to-circular and reverse transformers (beam adapters) are introduced in terms of the circular and planar modes; their implementation on the basis of skew quadrupole blocks is described.  Various kinds of matching for beams, adapters and solenoids are considered.  Applications of the planar-to-circular, circular-to-planar and circular-to-circular transformers are discussed.  A range of applications includes round beams at the interaction region of circular colliders, flat beams for linear colliders, relativistic electron cooling, and ionization cooling.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevE.66.016503}}

@article{Danilov:2010:NLAccelLatt,
	Author = {Danilov, V. and Nagaitsev, Sergei},
	Date-Added = {2015-04-03 19:31:12 +0000},
	Date-Modified = {2015-04-03 19:31:12 +0000},
	Doi = {10.1103/PhysRevSTAB.13.084002},
	Journal = {Phys. Rev. ST Accel. Beams},
	Keywords = {accelerator beam dynamics},
	Month = aug,
	Number = {8},
	Pages = {084002},
	Title = {Nonlinear accelerator lattices with one and two analytic invariants},
	Volume = {13},
	Year = {2010},
	Abstract = {Integrable systems appeared in physics long ago at the onset of classical dynamics with examples being Kepler's and other famous problems. Unfortunately, the majority of nonlinear problems turned out to be nonintegrable. In accelerator terms, any 2D nonlinear nonintegrable mapping produces chaotic motion and a complex network of stable and unstable resonances. Nevertheless, in the proximity of an integrable system the full volume of such a chaotic network is small. Thus, the integrable nonlinear motion in accelerators has the potential to introduce a large betatron tune spread to suppress instabilities and to mitigate the effects of space charge and magnetic field errors. To create such an accelerator lattice, one has to find magnetic and electric field combinations leading to a stable integrable motion. This paper presents families of lattices with one invariant where bounded motion can be easily created in large volumes of the phase space. In addition, it presents three families of integrable nonlinear accelerator lattices, realizable with longitudinal-coordinate-dependent magnetic or electric fields with the stable nonlinear motion, which can be solved in terms of separable variables.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevSTAB.13.084002}}

@inproceedings{Danilov:2012:OnQuantumIntegrable,
	Author = {Danilov, Viatcheslav V. and Nagaitsev, Sergei},
	Crossref = {IPAC:2012},
	Date-Added = {2015-04-03 19:31:12 +0000},
	Date-Modified = {2015-04-03 19:31:12 +0000},
	Pages = {1392--1394},
	Title = {On quantum integrable systems},
	Abstract = {Many quantum integrable systems are obtained using an accelerator physics technique known as Ermakov (or normalized variables) transformation. This technique was used to create classical nonlinear integrable lattices for accelerators and nonlinear integrable plasma traps. Now, all classical results are carried over to a nonrelativistic quantum case.}}

@article{Danilov:2014:AcceleratorNBody,
	Author = {Danilov, V. and Nagaitsev, S.},
	Date-Added = {2015-04-03 19:31:12 +0000},
	Date-Modified = {2015-04-03 19:31:12 +0000},
	Doi = {10.1103/PhysRevSTAB.17.124402},
	Journal = prstab,
	Month = dec,
	Number = {12},
	Pages = {124402},
	Title = {Accelerator-feasible {$N$}-body nonlinear integrable system},
	Volume = {17},
	Year = {2014},
	Abstract = {Nonlinear $N$-body integrable Hamiltonian systems, where $N$ is an arbitrary number, have attracted the attention of mathematical physicists for the last several decades, following the discovery of some number of these systems. This paper presents a new integrable system, which can be realized in facilities such as particle accelerators. This feature makes it more attractive than many of the previous such systems with singular or unphysical forces.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevSTAB.17.124402}}

@misc{Nagaitsev:2011:NLIntegrIonTraps,
	Author = {Nagaitsev, Sergei and Danilov, Viatcheslav V.},
	Date-Added = {2015-04-03 19:31:12 +0000},
	Date-Modified = {2015-04-03 19:31:12 +0000},
	Howpublished = {Eprint \url{http://arxiv.org/abs/1111.1260}},
	Month = nov,
	Title = {Nonlinear Integrable Ion Traps},
	Year = {2011},
	Abstract = {Quadrupole ion traps can be transformed into nonlinear traps with integrable motion by adding special electrostatic potentials. This can be done with both stationary potentials (electrostatic plus a uniform magnetic field) and with time-dependent electric potentials. These potentials are chosen such that the single particle Hamilton-Jacobi equations of motion are separable in some coordinate systems. The electrostatic potentials have several free adjustable parameters allowing for a quadrupole trap to be transformed into, for example, a double-well or a toroidal-well system. The particle motion remains regular, non-chaotic, integrable in quadratures, and stable for a wide range of parameters. We present two examples of how to realize such a system in case of a time-independent (the Penning trap) as well as a time-dependent (the Paul trap) configuration.}}

@article{Webb:2011:3DModSSFEL,
	Author = {Webb, Stephen and Wang, Gang and Litvinenko, Vladimir N.},
	Date-Added = {2015-04-03 19:30:28 +0000},
	Date-Modified = {2015-04-03 19:30:28 +0000},
	Doi = {10.1103/PhysRevSTAB.14.051003},
	Journal = prstab,
	Keywords = {free electron laser},
	Month = may,
	Number = {5},
	Pages = {051003},
	Title = {Three-dimensional model of small signal free-electron lasers},
	Volume = {14},
	Year = {2011},
	Abstract = {Coherent electron cooling is an ultrahigh-bandwidth form of stochastic cooling which utilizes the charge perturbation from Debye screening as a seed for a free-electron laser. The amplified and frequency-modulated signal that results from the free-electron laser process is then used to give an energy-dependent kick on the hadrons in a bunch. In this paper, we present a theoretical description of a high-gain free-electron laser with applications to a complete theoretical description of coherent electron cooling.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevSTAB.14.051003}}

@misc{Webb:2011:FELGrowModes,
	Author = {Webb, Stephen and Wang, Gang and Litvinenko, Vladimir N.},
	Date-Added = {2015-04-03 19:30:28 +0000},
	Date-Modified = {2015-04-03 19:30:28 +0000},
	Howpublished = {Eprint \url{http://arxiv.org/abs/1105.0412}},
	Month = may,
	Title = {On Free-Electron Laser Growing Modes and their Bandwidth},
	Year = {2011}}

@article{Webb:2012:FELGrowingModes,
	Author = {Webb, Stephen and Litvinenko, Vladimir N. and Wang, Gang},
	Date-Added = {2015-04-03 19:30:28 +0000},
	Date-Modified = {2015-04-03 19:30:28 +0000},
	Doi = {10.1103/PhysRevSTAB.15.080701},
	Journal = {Phys. Rev. ST Accel. Beams},
	Keywords = {free electron laser},
	Month = aug,
	Number = {8},
	Pages = {080701},
	Title = {Free-electron laser growing modes and their bandwidths},
	Volume = {15},
	Year = {2012},
	Abstract = {The behavior of free-electron laser amplification in the small signal linear regime can be understood by studying the dispersion relation derived from the electron energy distribution. A thorough understanding of the growth modes in this regime is of great value in understanding numerical results obtained using simulations. In this paper we show that for a typical bell-shape energy distribution in the electron beam there is not more than one growing mode. We also derive an analytical expression, which determines the bandwidth of the free-electron laser. We also discuss the limitation on the number of growing modes for the case of beam energy distributions with multiple peaks.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevSTAB.15.080701}}

@article{Sonnad:2004:NLIntegLatt,
	Author = {Sonnad, Kiran G. and Cary, John R.},
	Date-Added = {2015-04-03 19:29:31 +0000},
	Date-Modified = {2015-04-03 19:29:31 +0000},
	Doi = {10.1103/PhysRevE.69.056501},
	Journal = preve,
	Keywords = {accelerator beam dynamics},
	Month = may,
	Number = {5},
	Pages = {056501},
	Title = {Finding a nonlinear lattice with improved integrability using {L}ie transform perturbation theory},
	Volume = {69},
	Year = {2004},
	Abstract = {A condition for improved dynamic aperture for nonlinear, alternating gradient transport systems is derived using Lie transform perturbation theory. The Lie transform perturbation method is used here to perform averaging over fast oscillations by canonically transforming to slowly oscillating variables. This is first demonstrated for a linear sinusoidal focusing system. This method is then employed to average the dynamics over a lattice period for a nonlinear focusing system, provided by the use of higher order poles such as sextupoles and octupoles along with alternate gradient quadrupoles. Unlike the traditional approach, the higher order focusing is not treated as a perturbation. The Lie transform method is particularly advantageous for such a system where the form of the Hamiltonian is complex. This is because the method exploits the property of canonical invariance of Poisson brackets so that the change of variables is accomplished by just replacing the old ones with the new. The analysis shows the existence of a condition in which the system is azimuthally symmetric in the transformed, slowly oscillating frame. Such a symmetry in the time averaged frame renders the system nearly integrable in the laboratory frame. This condition leads to reduced chaos and improved confinement when compared to a system that is not close to integrability. Numerical calculations of single-particle trajectories and phase space projections of the dynamic aperture performed for a lattice with quadrupoles and sextupoles confirm that this is indeed the case.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevE.69.056501}}

@article{Sonnad:2005:CtrlBmHalo,
	Author = {Sonnad, Kiran G. and Cary, John R.},
	Date-Added = {2015-04-03 19:29:31 +0000},
	Date-Modified = {2015-04-03 19:29:31 +0000},
	Doi = {10.1103/PhysRevSTAB.8.064202},
	Journal = {Phys. Rev. ST Accel. Beams},
	Keywords = {accelerator beam dynamics},
	Month = jun,
	Number = {6},
	Pages = {064202},
	Title = {Control of beam halo formation through nonlinear damping and collimation},
	Volume = {8},
	Year = {2005},
	Abstract = {This paper demonstrates that transverse beam halos can be controlled by combining nonlinear focusing and collimation. The study relies on one-dimensional, constant focusing particle-in-cell (PIC) simulations and a particle-core model. Beams with linear and nonlinear focusing are studied. Calculations with linear focusing confirm previous findings that the extent and density of the halo depend strongly upon the initial mismatch of the beam. Calculations with nonlinear focusing are used to study damping in the beam oscillations caused by the mismatch. Although the nonlinear force damps the beam oscillations, it is accompanied by emittance growth. This process is very rapid and happens within the first 2--3 envelope oscillations. After this, when the halo is collimated using a system of four collimators, further evolution of the beam shows that the halo is not regenerated. The elimination of the beam halo could allow either a smaller physical aperture for the transport system or it could allow a beam of higher current in a system with the same physical aperture. This advantage compensates for the loss of particles due to collimation.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevSTAB.8.064202}}

@article{Cary:1986:AdiabaticInvar,
	Author = {Cary, John R. and Escande, Dominique F. and Tennyson, J. L.},
	Date-Added = {2015-04-03 19:28:48 +0000},
	Date-Modified = {2015-04-03 19:28:48 +0000},
	Doi = {10.1103/PhysRevA.34.4256},
	Journal = preva,
	Month = nov,
	Number = {5},
	Pages = {4256--4275},
	Title = {Adiabatic-invariant change due to separatrix crossing},
	Volume = {34},
	Year = {1986},
	Abstract = {A slowly varying Hamiltonian with one degree of freedom and nearly closed orbits has an adiabatic invariant. This adiabatic invariant is conserved to all orders in $\epsilon$, the slowness parameter, except for orbits that cross a separatrix.  The present work discusses the change of the adiabatic invariant during this crossing process through order $\epsilon$.  First, a calculation of the change of the adiabatic invariant is presented.  This calculation is general and, hence, encompasses previous results for specific cases.  The change in the adiabatic invariant is shown to depend on a maximum of five parameters, which are functions of the Hamiltonian of interest.  Second, the statistics of this process are derived.  Finally, these results are applied to the motion of a particle in a wave with changing amplitude and phase velocity.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevA.34.4256}}

@article{Chow:1994:IntegNLAccel,
	Author = {Chow, Carson C. and Cary, John R.},
	Date-Added = {2015-04-03 19:28:06 +0000},
	Date-Modified = {2015-04-03 19:28:06 +0000},
	Doi = {10.1103/PhysRevLett.72.1196},
	Journal = {Phys. Rev. Lett.},
	Keywords = {accelerator beam dynamics},
	Month = feb,
	Number = {8},
	Pages = {1196--1199},
	Title = {Integrable nonlinear accelerator lattices},
	Volume = {72},
	Year = {1994},
	Abstract = {A method for creating integrable nonlinear accelerator lattices is presented. Fixed points for the two-dimensional return map corresponding to the lattice are found. Minimizing the residues (an indicator of the size of the associated island) of these fixed points by varying lattice parameters eliminates large islands and regions of chaos. The resulting nonlinear systems have larger dynamical apertures and are more stable to perturbations induced by, for example, error fields.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevLett.72.1196}}

@article{Chapman:2015:MathFaradayCage,
	Author = {Chapman, S. Jonathan and Hewett, David P. and Trefethen, Lloyd N.},
	Date-Added = {2015-04-03 19:26:38 +0000},
	Date-Modified = {2015-04-03 19:26:38 +0000},
	Journal = siamr,
	Title = {Mathematics of the {F}araday Cage},
	Year = {2015}}

@article{Chapman:2011:FourBugs,
	Author = {Chapman, S. Jonathan and Lottes, James and Trefethen, Lloyd N.},
	Date-Added = {2015-04-03 19:17:56 +0000},
	Date-Modified = {2015-04-03 19:17:56 +0000},
	Doi = {10.1098/rspa.2010.0506},
	Journal = procrsa,
	Month = mar,
	Number = {2127},
	Pages = {881--896},
	Title = {Four Bugs on a Rectangle},
	Volume = {467},
	Year = {2011},
	Abstract = {The idealized mathematical problem of four bugs in cyclic pursuit starting from a 2-by-1 rectangle is considered, and asymptotic formulas are derived to describe the motion. In contrast to the famous case of four bugs on a square, here the trajectories quickly freeze to essentially one dimension. After the first rotation about the centre point, the scale of the configuration has shrunk by a factor of $10^{427907250}$, and this number is then exponentiated four more times with each successive cycle. Relations to Knuth's double-arrow notation and level-index arithmetic are discussed.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1098/rspa.2010.0506}}

@article{Driscoll:1998:PotentialToMatrixIter,
	Author = {Driscoll, Tobin A. and Toh, Kim-Chuan and Trefethen, Lloyd N.},
	Date-Added = {2015-04-03 19:17:56 +0000},
	Date-Modified = {2015-04-03 19:17:56 +0000},
	Doi = {10.1137/S0036144596305582},
	Journal = siamr,
	Number = {3},
	Pages = {547--578},
	Title = {From Potential Theory to Matrix Iterations in Six Steps},
	Volume = {40},
	Year = {1998},
	Abstract = {The theory of the convergence of Krylov subspace iterations for linear systems of equations (conjugate gradients, biconjugate gradients, GMRES, QMR, Bi-CGSTAB, and so on) is reviewed. For a computation of this kind, an estimated asymptotic convergence factor $\rho \le 1$ can be derived by solving a problem of potential theory or conformal mapping. Six approximations are involved in relating the actual computation to this scalar estimate. These six approximations are discussed in asystematic way and illustrated by a sequence of examples computed with tools of numerical conformal mapping and semidefinite programming.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1137/S0036144596305582}}

@article{Gonnet:2011:RobustRatInterp,
	Author = {Gonnet, Pedro and Pach\'on, Ricardo and Trefethen, Lloyd N.},
	Date-Added = {2015-04-03 19:17:56 +0000},
	Date-Modified = {2015-04-03 19:17:56 +0000},
	Journal = etna,
	Keywords = {interpolation},
	Pages = {146--167},
	Title = {Robust rational interpolation and least-squares},
	Volume = {38},
	Year = {2011},
	Abstract = {An efficient and robust algorithm and a Matlab code \texttt{ratdisk} are presented for rational interpolation or linearized least-squares approximation of a function based on its values at points equally spaced on a circle. The use of the singular value decomposition enables the detection and elimination of spurious poles or Froissart doublets that commonly complicate such fits without contributing to the quality of the approximation. As an application, the algorithm leads to a method for the stable computation of certain radial basis function interpolants in the difficult case of smoothness parameter $\varepsilon$ close to zero.}}

@article{Gonnet:2013:RobustPadeSVD,
	Author = {Gonnet, Pedro and G{\"u}ttel, Stefan and Trefethen, Lloyd N.},
	Date-Added = {2015-04-03 19:17:56 +0000},
	Date-Modified = {2015-04-03 19:17:56 +0000},
	Doi = {10.1137/110853236},
	Journal = siamr,
	Number = {1},
	Pages = {101--117},
	Title = {Robust {P}ad{\'e} Approximation via {SVD}},
	Volume = {55},
	Year = {2013},
	Abstract = {Pad{\'e} approximation is considered from the point of view of robust methods of numerical linear algebra, in particular, the singular value decomposition. This leads to an algorithm for practical computation that bypasses most problems of solution of nearly-singular systems and spurious pole-zero pairs caused by rounding errors, for which a MATLAB code is provided. The success of this algorithm suggests that there might be variants of Pad{\'e} approximation that are pointwise convergent as the degrees of the numerator and denominator increase to $\infty$, unlike traditional Pad{\'e} approximants, which converge only in measure or capacity.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1137/110853236}}

@article{Hale:2008:CompMxFn,
	Author = {Hale, Nicholas and Higham, Nicholas J. and Trefethen, Lloyd N.},
	Date-Added = {2015-04-03 19:17:56 +0000},
	Date-Modified = {2015-04-03 19:17:56 +0000},
	Doi = {10.1137/070700607},
	Journal = siamjna,
	Keywords = {Cauchy integral, conformal map, contour integral, matrix function, quadrature, rational approximation, trapezoid rule},
	Number = {5},
	Pages = {2505--2523},
	Title = {Computing $A^\alpha$, $\log(A)$, and Related Matrix Functions by Contour Integrals},
	Volume = {46},
	Year = {2008},
	Abstract = {New methods are proposed for the numerical evaluation of $f(\mathbf{A})$ or $f(\mathbf{A}) b$, where $f(\mathbf{A})$ is a function such as $\mathbf{A}^{1/2}$ or $\log(\mathbf{A})$ with singularities in $(-\infty,0]$ and $\mathbf{A}$ is a matrix with eigenvalues on or near $(0,\infty)$.  The methods are based on combining contour integrals evaluated by the periodic trapezoid rule with conformal maps involving Jacobi elliptic functions.  The convergence is geometric, so that the computation of $f(\mathbf{A})b$ is typically reduced to one or two dozen linear system solves, which can be carried out in parallel.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1137/070700607}}

@article{Hale:2008:NewQuadrature,
	Author = {Hale, Nicholas and Trefethen, Lloyd N.},
	Date-Added = {2015-04-03 19:17:56 +0000},
	Date-Modified = {2015-04-03 19:17:56 +0000},
	Doi = {10.1137/07068607X},
	Journal = siamjna,
	Keywords = {Gauss quadrature, Clenshaw--Curtis quadrature, spectral methods, conformal mapping},
	Number = {2},
	Pages = {930--948},
	Title = {New Quadrature Formulas from Conformal Maps},
	Volume = {46},
	Year = {2008},
	Abstract = {Gauss and Clenshaw--Curtis quadrature, like Legendre and Chebyshev spectral methods, make use of grids strongly clustered at boundaries.  From the viewpoint of polynomial approximation this seems necessary and indeed in certain respects optimal.  Nevertheless such methods may ``waste'' a factor of $\pi/2$ with respect to each space dimension.  We propose new nonpolynomial quadrature methods that avoid this effect by conformally mapping the usual ellipse of convergence to an infinite strip or another approximately straight-sided domain.  The new methods are compared with related ideas of Bakhvalov, Kosloff and Tal-Ezer, Rokhlin and Alpert, and others.  An advantage of the conformal mapping approach is that it leads to theorems guaranteeing geometric rates of convergence for analytic integrands.  For example, one of the formulas presented is proved to converge $50\%$ faster than Gauss quadrature for functions analytic in an $\varepsilon$-neighborhood of $[-1,1]$.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1137/07068607X}}

@article{Hale:2009:ConfMapsMSlit,
	Author = {Hale, Nicholas and Tee, T. Wynn},
	Date-Added = {2015-04-03 19:17:56 +0000},
	Date-Modified = {2015-04-03 19:17:56 +0000},
	Doi = {10.1137/080738325},
	Journal = siamjsc,
	Number = {4},
	Pages = {3195--3215},
	Title = {Conformal Maps to Multiply Slit Domains and Applications},
	Volume = {31},
	Year = {2009},
	Abstract = {By exploiting conformal maps to vertically slit regions in the complex plane, a recently developed rational spectral method [T.W. Tee and L.N. Trefethen, \textit{SIAM J.\ Sci.\ Comput.}, 28 (2006), pp.\,1798--1811] is able to solve PDEs with interior layer-like behavior using significantly fewer collocation points than traditional spectral methods. The conformal maps are chosen to ``enlarge the region of analyticity'' in the solution: an idea which can be extended to other numerical methods based upon global polynomial interpolation. Here we show how such maps can be rapidly computed in both periodic and nonperiodic geometries and apply them to some challenging differential equations.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1137/080738325}}

@article{Javed:2014:TrapezoidRuleError,
	Author = {Javed, Mohsin and Trefethen, Lloyd N.},
	Date-Added = {2015-04-03 19:17:16 +0000},
	Date-Modified = {2015-04-03 19:17:16 +0000},
	Doi = {10.1098/rspa.2013.0571},
	Journal = procrsa,
	Month = jan,
	Number = {2161},
	Pages = {20130571},
	Title = {A trapezoidal rule error bound unifying the {E}uler--{M}aclaurin formula and geometric convergence for periodic functions},
	Volume = {470},
	Year = {2014},
	Abstract = {The error in the trapezoidal rule quadrature formula can be attributed to discretization in the interior and non-periodicity at the boundary. Using a contour integral, we derive a unified bound for the combined error from both sources for analytic integrands. The bound gives the Euler--Maclaurin formula in one limit and the geometric convergence of the trapezoidal rule for periodic analytic functions in another. Similar results are also given for the midpoint rule.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1098/rspa.2013.0571}}

@article{Platte:2011:ImpossFastStableApprox,
	Author = {Platte, Rodrigo B. and Trefethen, Lloyd N. and Kuijlaars, Arno B. J.},
	Date-Added = {2015-04-03 19:17:00 +0000},
	Date-Modified = {2015-04-03 19:17:00 +0000},
	Doi = {10.1137/090774707},
	Journal = siamr,
	Keywords = {interpolation},
	Number = {2},
	Pages = {308--318},
	Title = {Impossibility of Fast Stable Approximation of Analytic Functions from Equispaced Samples},
	Volume = {53},
	Year = {2011},
	Abstract = {It is shown that no stable procedure for approximating functions from equally spaced samples can converge exponentially for analytic functions. To avoid instability, one must settle for root-exponential convergence. The proof combines a Bernstein inequality of 1912 with an estimate due to Coppersmith and Rivlin in 1992.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1137/090774707}}

@article{VanDeun:2011:RobustImpCF,
	Author = {Van Deun, Joris and Trefethen, Lloyd N.},
	Date-Added = {2015-04-03 19:16:36 +0000},
	Date-Modified = {2015-04-03 19:16:36 +0000},
	Doi = {10.1007/s10543-011-0331-7},
	Journal = bitnm,
	Month = dec,
	Number = {4},
	Pages = {1039--1050},
	Title = {A robust implementation of the {C}arath{\'e}odory-{F}ej{\'e}r method for rational approximation},
	Volume = {51},
	Year = {2011},
	Abstract = {Best rational approximations are notoriously difficult to compute. However, the difference between the best rational approximation to a function and its Carath{\'e}odory-Fej{\'e}r (CF) approximation is often so small as to be negligible in practice, while CF approximations are far easier to compute. We present a robust and fast implementation of this method in the Chebfun software system and illustrate its use with several examples. Our implementation handles both polynomial and rational approximation and substantially improves upon earlier published software.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10543-011-0331-7}}

@article{Trefethen:1982:GrpVelFDSchemes,
	Author = {Trefethen, Lloyd N.},
	Date-Added = {2015-04-03 19:15:13 +0000},
	Date-Modified = {2015-04-03 19:15:13 +0000},
	Doi = {10.1137/1024038},
	Journal = siamr,
	Number = {2},
	Pages = {113--136},
	Title = {Group Velocity in Finite Difference Schemes},
	Volume = {24},
	Year = {1982},
	Abstract = {The relevance of group velocity to the behavior of finite difference models of time-dependent partial differential equations is surveyed and illustrated. Applications involve the propagation of wave packets in one and two dimensions, numerical dispersion, the behavior of parasitic waves, and the stability analysis of initial boundary value problems.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1137/1024038}}

@article{Trefethen:2006:TalbotQuadRat,
	Author = {Trefethen, Lloyd N. and Weideman, J. A. C. and Schmelzer, Thomas},
	Date-Added = {2015-04-03 19:15:13 +0000},
	Date-Modified = {2015-04-03 19:15:13 +0000},
	Doi = {10.1007/s10543-006-0077-9},
	Journal = bitnm,
	Month = sep,
	Number = {3},
	Pages = {653--670},
	Title = {Talbot quadratures and rational approximations},
	Volume = {46},
	Year = {2006},
	Abstract = {Many computational problems can be solved with the aid of contour integrals containing $e^z$ in the integrand: examples include inverse Laplace transforms, special functions, functions of matrices and operators, parabolic PDEs, and reaction-diffusion equations. One approach to the numerical quadrature of such integrals is to apply the trapezoid rule on a Hankel contour defined by a suitable change of variables. Optimal parameters for three classes of such contours have recently been derived: (a) parabolas, (b) hyperbolas, and (c) cotangent contours, following Talbot in 1979. The convergence rates for these optimized quadrature formulas are very fast: roughly $O(3^{-N})$, where $N$ is the number of sample points or function evaluations. On the other hand, convergence at a rate apparently about twice as fast, $O(9.28903^{-N})$, can be achieved by using a different approach: best supremum-norm rational approximants to $e^z$ for $z\elem(-\infty,0]$, following Cody, Meinardus and Varga in 1969. (All these rates are doubled in the case of self-adjoint operators or real integrands.) It is shown that the quadrature formulas can be interpreted as rational approximations and the rational approximations as quadrature formulas, and the strengths and weaknesses of the different approaches are discussed in the light of these connections. A MATLAB function is provided for computing Cody-Meinardus-Varga approximants by the method of Carath{\'e}odory-Fej{\'e}r approximation.
},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10543-006-0077-9}}

@article{Trefethen:2008:GaussVClenshawCurtis,
	Author = {Trefethen, Lloyd N.},
	Date-Added = {2015-04-03 19:15:13 +0000},
	Date-Modified = {2015-04-03 19:15:13 +0000},
	Doi = {10.1137/060659831},
	Journal = siamr,
	Number = {1},
	Pages = {67--87},
	Title = {Is {G}auss Quadrature Better than {C}lenshaw--{C}urtis?},
	Volume = {50},
	Year = {2008},
	Abstract = {We compare the convergence behavior of Gauss quadrature with that of its younger brother, Clenshaw--Curtis. Seven-line MATLAB codes are presented that implement both methods, and experiments show that the supposed factor-of-2 advantage of Gauss quadrature is rarely realized. Theorems are given to explain this effect. First, following O'Hara and Smith in the 1960s, the phenomenon is explained as a consequence of aliasing of coefficients in Chebyshev expansions. Then another explanation is offered based on the interpretation of a quadrature formula as a rational approximation of $\log((z+1)/(z-1))$ in the complex plane. Gauss quadrature corresponds to Pad{\'e} approximation at $z=\infty$. Clenshaw--Curtis quadrature corresponds to an approximation whose order of accuracy at $z=\infty$ is only half as high, but which is nevertheless equally accurate near $[-1,1]$.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1137/060659831}}

@book{Trefethen:2013:ApproxThPract,
	Address = {Philadelphia, PA},
	Author = {Trefethen, Lloyd N.},
	Booktitle = {Approximation Theory and Approximation Practice},
	Date-Added = {2015-04-03 19:15:13 +0000},
	Date-Modified = {2015-04-03 19:15:13 +0000},
	Publisher = {SIAM},
	Title = {Approximation Theory and Approximation Practice},
	Year = {2013}}

@article{Trefethen:2014:ExpConvTrapRule,
	Author = {Trefethen, Lloyd N. and Weideman, J. A. C.},
	Date-Added = {2015-04-03 19:15:13 +0000},
	Date-Modified = {2015-04-03 19:15:13 +0000},
	Doi = {10.1137/130932132},
	Journal = siamr,
	Note = {A preprint version is available at \url{http://people.maths.ox.ac.uk/~trefethen/trefethen_weideman.pdf}},
	Number = {3},
	Pages = {385--458},
	Title = {The exponentially convergent trapezoidal rule},
	Volume = {56},
	Year = {2014},
	Abstract = {It is well known that the trapezoidal rule converges geometrically when applied to analytic functions on periodic intervals or the real line. The mathematics and history of this phenomenon are reviewed, and it is shown that far from being a curiosity, it is linked with computational methods all across scientific computing, including algorithms related to inverse Laplace transforms, special functions, complex analysis, rational approximation, integral equations, and the computation of functions and eigenvalues of matrices and operators.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1137/130932132}}

@article{Webb:2012:StabBarycentric,
	Author = {Webb, Marcus and Trefethen, Lloyd N. and Gonnet, Pedro},
	Date-Added = {2015-04-03 19:14:28 +0000},
	Date-Modified = {2015-04-03 19:14:28 +0000},
	Doi = {10.1137/110848797},
	Journal = siamjsc,
	Number = {6},
	Pages = {A3009--A3015},
	Title = {Stability of Barycentric Interpolation Formulas for Extrapolation},
	Volume = {34},
	Year = {2012},
	Abstract = {The barycentric interpolation formula defines a stable algorithm for evaluation at points in $[-1,1]$ of polynomial interpolants through data on Chebyshev grids. Here it is shown that for evaluation at points in the complex plane outside $[-1,1]$, the algorithm becomes unstable and should be replaced by the alternative modified Lagrange or ``first barycentric'' formula dating to Jacobi in 1825. This difference in stability confirms the theory published by N.J. Higham in 2004 [\textit{IMA J.\ Numer.\ Anal.}, \textbf{24} (2004), pp.~547--556] and has practical consequences for computation with rational functions.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1137/110848797}}

@article{Tee:2006:RatSpectralCollocation,
	Author = {Tee, T. Wynn and Trefethen, Lloyd N.},
	Date-Added = {2015-04-03 19:13:55 +0000},
	Date-Modified = {2015-04-03 19:13:55 +0000},
	Doi = {10.1137/050641296},
	Journal = siamjsc,
	Number = {5},
	Pages = {1798--1811},
	Title = {A Rational Spectral Collocation Method with Adaptively Transformed {C}hebyshev Grid Points},
	Volume = {28},
	Year = {2006},
	Abstract = {A spectral collocation method based on rational interpolants and adaptive grid points is presented. The rational interpolants approximate analytic functions with exponential accuracy by using prescribed barycentric weights and transformed Chebyshev points. The locations of the grid points are adapted to singularities of the underlying solution, and the locations of these singularities are approximated by the locations of poles of Chebyshev-Pad{\'e} approximants. Numerical experiments on two time-dependent problems, one with finite time blow-up and one with a moving front, indicate that the method far outperforms the standard Chebyshev spectral collocation method for problems whose solutions have singularities in the complex plane close to $[-1,1]$.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1137/050641296}}

@article{Trefethen:2007:CompNumFns,
	Author = {Trefethen, Lloyd N.},
	Date-Added = {2015-04-03 19:13:55 +0000},
	Date-Modified = {2015-04-03 19:13:55 +0000},
	Doi = {10.1007/s11786-007-0001-y},
	Journal = mathcs,
	Month = dec,
	Number = {1},
	Pages = {9--19},
	Title = {Computing Numerically with Functions Instead of Numbers},
	Volume = {1},
	Year = {2007},
	Abstract = {Symbolic computation with functions of a real variable suffers from combinatorial explosion of memory and computation time. The alternative chebfun system for such computations is described, based on Chebyshev expansions and barycentric interpolation.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s11786-007-0001-y}}

@article{Pachon:2009:BarycentricRemez,
	Author = {Pach\'on, Ricardo and Trefethen, Lloyd N.},
	Date-Added = {2015-04-03 19:12:53 +0000},
	Date-Modified = {2015-04-03 19:12:53 +0000},
	Doi = {10.1007/s10543-009-0240-1},
	Journal = bitnm,
	Month = dec,
	Number = {4},
	Pages = {721--741},
	Title = {Barycentric-{R}emez algorithms for best polynomial approximation in the chebfun system},
	Volume = {49},
	Year = {2009},
	Abstract = {The Remez algorithm, 75~years old, is a famous method for computing minimax polynomial approximations. Most implementations of this algorithm date to an era when tractable degrees were in the dozens, whereas today, degrees of hundreds or thousands are not a problem. We present a 21st-century update of the Remez ideas in the context of the chebfun software system, which carries out numerical computing with functions rather than numbers. A crucial feature of the new method is its use of chebfun global rootfinding to locate extrema at each iterative step, based on a recursive algorithm combining ideas of Specht, Good, Boyd, and Battles. Another important feature is the use of the barycentric interpolation formula to represent the trial polynomials, which points the way to generalizations for rational approximations. We comment on available software for minimax approximation and its scientific context, arguing that its greatest importance these days is probably for fundamental studies rather than applications.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10543-009-0240-1}}

@misc{Sadiq:2011:BarycentricHermiteInterp,
	Author = {Sadiq, Burhan and Viswanath, Divakar},
	Date-Added = {2015-04-03 19:12:35 +0000},
	Date-Modified = {2015-04-03 19:12:35 +0000},
	Howpublished = {Eprint \url{http://arxiv.org/abs/1105.3466}},
	Month = may,
	Title = {Barycentric {H}ermite Interpolation},
	Year = {2011},
	Abstract = {Let $z_1,\dotsc,z_K$ be distinct grid points. If $f_{k,0} is the prescribed value of a function at the grid point $z_k$, and $f_{k,r}$ the prescribed value of the $r^\text{th}$ derivative, for $1 \leq r \leq n_k-1$, the Hermite interpolant is the unique polynomial of degree $N-1$ ($N = n_1 + \dotsb + n_K$) which interpolates the prescribed function values and function derivatives. We obtain another derivation of a method for Hermite interpolation recently proposed by Butcher et al. [\emph{Numerical Algorithms, vol.~56 (2011), p. 319-347}]. One advantage of our derivation is that it leads to an efficient method for updating the barycentric weights. If an additional derivative is prescribed at one of the interpolation points, we show how to update the barycentric coefficients using only $\mathcal{O}(N)$ operations. Even in the context of confluent Newton series, a comparably efficient and general method to update the coefficients appears not to be known. If the method is properly implemented, it computes the barycentric weights with fewer operations than other methods and has very good numerical stability even when derivatives of high order are involved. We give a partial explanation of its numerical stability.
}}

@article{Salzer:1972:LagrangInterpChep,
	Author = {Salzer, H. E.},
	Date-Added = {2015-04-03 19:12:35 +0000},
	Date-Modified = {2015-04-03 19:12:35 +0000},
	Doi = {10.1093/comjnl/15.2.156},
	Journal = compj,
	Month = may,
	Number = {2},
	Pages = {156--159},
	Title = {Lagrangian Interpolation at the {C}hebyshev Points $x_{n,\nu}=\cos(\nu\pi/n)$, $\nu=0(1)n$; some Unnoted Advantages},
	Volume = {15},
	Year = {1972},
	Abstract = {Besides many applications of the Chebyshev points $x_{n,\nu}=\cos(\nu\pi/n)$, $\nu=0(1)n$, in approximation, interpolation by Chebyshev series, numerical integration and numerical differentiation, there are advantages in their use in the barycentric form of the Lagrange interpolation formula and in checking by divided differences. When $n=2m$, we obtain $X_{2m,\nu}$ with less than half the number of square roots that are required to find the other Chebyshev points $X'_{2m,\nu}=\cos[(2\nu-1)\pi/2^{m+1}]$, $\nu=1(1)2^m$. Also, the barycentric interpolation formula may be applied to the solution of a near-minimax problem so as to avoid extensive calculation of auxiliary polynomials, and in a numerical differentiation procedure that conveniently by-passes direct differentiation of the interpolation polynomial.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1093/comjnl/15.2.156}}

@article{Hale:2012:ChebfunNumQuad,
	Author = {Hale, Nicholas and Trefethen, Lloyd N.},
	Date-Added = {2015-04-03 19:11:23 +0000},
	Date-Modified = {2015-04-03 19:11:23 +0000},
	Doi = {10.1007/s11425-012-4474-z},
	Journal = scichm,
	Number = {9},
	Pages = {1749--1760},
	Title = {Chebfun and numerical quadrature},
	Volume = {55},
	Year = {2012},
	Abstract = {Chebfun is a Matlab-based software system that overloads Matlab's discrete operations for vectors and matrices to analogous continuous operations for functions and operators. We begin by describing Chebfun's fast capabilities for Clenshaw-Curtis and also Gauss-Legendre, -Jacobi, -Hermite, and -Laguerre quadrature, based on algorithms of Waldvogel and Glaser, Liu and Rokhlin. Then we consider how such methods can be applied to quadrature problems including 2D integrals over rectangles, fractional derivatives and integrals, functions defined on unbounded intervals, and the fast computation of weights for barycentric interpolation.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s11425-012-4474-z}}

@misc{Desbrun:2005:DiscreteExteriorCalculus,
	Author = {Desbrun, Mathieu and Hirani, Anil N. and Leok, Melvin and Marsden, Jerrold E.},
	Date-Added = {2015-04-03 19:10:50 +0000},
	Date-Modified = {2015-04-03 19:10:50 +0000},
	Howpublished = {Eprint \url{http://arxiv.org/abs/math/0508341}},
	Month = aug,
	Title = {Discrete Exterior Calculus},
	Year = {2005},
	Abstract = {We present a theory and applications of discrete exterior calculus on simplicial complexes of arbitrary finite dimension. This can be thought of as calculus on a discrete space. Our theory includes not only discrete differential forms but also discrete vector fields and the operators acting on these objects. This allows us to address the various interactions between forms and vector fields (such as Lie derivatives) which are important in applications. Previous attempts at discrete exterior calculus have addressed only differential forms. We also introduce the notion of a circumcentric dual of a simplicial complex. The importance of dual complexes in this field has been well understood, but previous researchers have used barycentric subdivision or barycentric duals. We show that the use of circumcentric duals is crucial in arriving at a theory of discrete exterior calculus that admits both vector fields and forms.}}

@inproceedings{Furman:1987:EffectSCatLE,
	Author = {Furman, Miguel A.},
	Crossref = {PAC:1987},
	Date-Added = {2015-04-03 19:09:26 +0000},
	Date-Modified = {2015-04-03 19:09:26 +0000},
	Pages = {1034--1036},
	Title = {Effect of the space-charge force on tracking at low energy}}

@article{Furman:1994:CompactComplex2DSC,
	Author = {Furman, Miguel A.},
	Date-Added = {2015-04-03 19:09:26 +0000},
	Date-Modified = {2015-04-03 19:09:26 +0000},
	Doi = {10.1119/1.17674},
	Journal = ajp,
	Month = dec,
	Number = {12},
	Pages = {1134--1140},
	Title = {Compact complex expressions for the electric field of two-dimensional elliptical charge distributions},
	Volume = {62},
	Year = {1994},
	Abstract = {We present a formula for the analytic calculation of the electric field in complex form for two-dimensional charge distributions with elliptical contours, in the absence of boundary conditions except at infinity. The formula yields compact and practical expressions for a significant class of distributions. The fact that the electric field vanishes inside an elliptical shell follows as a straightforward consequence of Cauchy's theorem. The known expressions for the field inside and outside a uniformly charged ellipse are recovered in simple, concise form. Similarly, the expression for the field of a Gaussian distribution is found in a straightforward way as a special case of the more general formula. We also present a brief discussion of more complicated distributions.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1119/1.17674}}

@article{Furman:2002:ProbModelSEE,
	Author = {Furman, Miguel A. and Pivi, M. T. F.},
	Date-Added = {2015-04-03 19:09:26 +0000},
	Date-Modified = {2015-04-03 19:09:26 +0000},
	Doi = {10.1103/PhysRevSTAB.5.124404},
	Journal = prstab,
	Month = dec,
	Note = {Erratum at \doi{10.1103/PhysRevSTAB.16.069901}},
	Number = {12},
	Pages = {124404},
	Title = {Probabilistic model for the simulation of secondary electron emission},
	Volume = {5},
	Year = {2002},
	Abstract = {We provide a detailed description of a model and its computational algorithm for the secondary electron emission process. The model is based on a broad phenomenological fit to data for the secondary-emission yield and the emitted-energy spectrum. We provide two sets of values for the parameters by fitting our model to two particular data sets, one for copper and the other one for stainless steel.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevSTAB.5.124404},
	Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevSTAB.16.069901}}

@article{Furman:2007:EField2DEllipse,
	Author = {Furman, Miguel A.},
	Date-Added = {2015-04-03 19:09:26 +0000},
	Date-Modified = {2015-04-03 19:09:26 +0000},
	Doi = {10.1103/PhysRevSTAB.10.081001},
	Journal = prstab,
	Month = aug,
	Number = {8},
	Pages = {081001},
	Title = {Electric field of a 2{D} elliptical charge distribution inside a cylindrical conductor},
	Volume = {10},
	Year = {2007},
	Abstract = {By combining the method of images with calculus of complex variables, we provide a simple expression for the electric field of a two-dimensional (2D) static elliptical charge distribution inside a perfectly conducting circular cylinder. The charge distribution need not be concentric with the cylinder.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevSTAB.10.081001}}

@book{Flanders:1989:DiffForms,
	Address = {Mineola, NY},
	Author = {Flanders, Harley},
	Date-Added = {2015-04-03 19:08:00 +0000},
	Date-Modified = {2015-04-03 19:08:00 +0000},
	Note = {Unabridged and amended republication of the work first published in 1963 by Academic Press, Inc., New York.},
	Publisher = {Dover Publications, Inc.},
	Title = {Differential Forms with Applications to the Physical Sciences},
	Year = {1989}}

@article{Fischer:2012:Impact3DPol,
	Author = {Fischer, Wolfram and Bazilevsky, Alexander},
	Date-Added = {2015-04-03 19:07:18 +0000},
	Date-Modified = {2015-04-03 19:07:18 +0000},
	Doi = {10.1103/PhysRevSTAB.15.041001},
	Journal = prstab,
	Month = apr,
	Number = {4},
	Pages = {041001},
	Title = {Impact of three-dimensional polarization profiles on spin-dependent measurements in colliding beam experiments},
	Volume = {15},
	Year = {2012},
	Abstract = {We derive the effect of 3-dimensional polarization profiles on the measured polarization in polarimeters, as well as the observed polarization and the polarization-weighted luminosity (figure of merit) in single and double spin measurements in colliding beam experiments. Applications to RHIC are discussed.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevSTAB.15.041001}}

@article{Ferrel:1977:ForcedHarmonic,
	Author = {Ferrel, Richard A.},
	Date-Added = {2015-04-03 19:06:23 +0000},
	Date-Modified = {2015-04-03 19:06:23 +0000},
	Journal = ajp,
	Month = may,
	Number = {5},
	Pages = {468--469},
	Title = {Forced harmonic oscillator in the interaction picture},
	Volume = {45},
	Year = {1977},
	Abstract = {The interaction picture of quantum mechanics is used to calculate the unitary time development operator for a harmonic oscillator subject to an arbitrary time-dependent force.  The result is identical to that obtained from the more usual method of the Heisenberg equations of motion, except for a phase factor which the Heisenberg picture method is unable to determine.  A simplified derivation of the phase factor is given in the adiabatic limit, as well as a discussion of some possible physical effects which would depend upon the phase factor.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1119/1.10822}}

@article{Ferraro:2010:AppExterCalcWvguides,
	Author = {Ferraro, Rafael},
	Date-Added = {2015-04-03 19:06:16 +0000},
	Date-Modified = {2015-04-03 19:06:16 +0000},
	Doi = {10.1119/1.3265544},
	Journal = ajp,
	Keywords = {electromagnetic fields, exterior calculus},
	Month = mar,
	Number = {3},
	Pages = {264--269},
	Title = {Application of exterior calculus to waveguides},
	Volume = {78},
	Year = {2010},
	Abstract = {Exterior calculus is a powerful tool for finding solutions to the electromagnetic field equations. Its strength can be better appreciated when applied to nontrivial configurations. We show how to exploit this tool to obtain the TM and TE modes in hollow cylindrical waveguides. The use of exterior calculus and Lorentz boosts leads straightforwardly to the solutions and their respective power transmitted along the waveguide.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1119/1.3265544}}

@book{Erdelyi:1953:HTF1,
	Address = {Malabar, FL},
	Date-Added = {2015-04-03 19:05:06 +0000},
	Date-Modified = {2015-04-03 19:05:06 +0000},
	Editor = {Erd{\'e}lyi, Arthur},
	Note = {Reprint of the work published in 1953 by McGraw-Hill Book Company, Inc.},
	Publisher = {Robert E. Krieger Publishing Co.},
	Title = {Higher Transcendental Functions},
	Volume = {I},
	Year = {1985}}

@book{Erdelyi:1953:HTF2,
	Address = {Malabar, FL},
	Date-Added = {2015-04-03 19:05:06 +0000},
	Date-Modified = {2015-04-03 19:05:06 +0000},
	Editor = {Erd{\'e}lyi, Arthur},
	Note = {Reprint of the work published in 1953 by McGraw-Hill Book Company, Inc.},
	Publisher = {Robert E. Krieger Publishing Co.},
	Title = {Higher Transcendental Functions},
	Volume = {II},
	Year = {1985}}

@book{Erdelyi:1955:HTF3,
	Address = {Malabar, FL},
	Date-Added = {2015-04-03 19:05:06 +0000},
	Date-Modified = {2015-04-03 19:05:06 +0000},
	Editor = {Erd{\'e}lyi, Arthur},
	Note = {Reprint of the work published in 1955 by McGraw-Hill Book Company, Inc.},
	Publisher = {Robert E. Krieger Publishing Co.},
	Title = {Higher Transcendental Functions},
	Volume = {III},
	Year = {1987}}

@article{Enge:1964:ExtendFringe,
	Author = {Enge, Harald A.},
	Date-Added = {2015-04-03 19:04:43 +0000},
	Date-Modified = {2015-04-03 19:04:43 +0000},
	Doi = {10.1063/1.1718806},
	Journal = revsi,
	Month = mar,
	Number = {3},
	Pages = {278--287},
	Title = {Effect of Extended Fringing Fields on Ion-Focusing Properties of Deflecting Magnets},
	Volume = {35},
	Year = {1964},
	Abstract = {This paper presents the result of calculations on ion deflection and focusing in magnets that have realistic, extended fringing fields rather than sharply cutoff fringing fields.  The most important effects of the change from sharp cutoff to extended fringing fields are (a) displacements of the beam center line at entrance and exit (a ``zeroth-order'' effect), and (b) reduction of first-order z-direction (``vertical'') focusing.  When the pole boundaries are curved or an effective curvature is caused by the proximity of pole-piece corners, there are further first-order effects on the trajectories.  These effects can be minimized, and in practice made negligible, by correct centering of the beam relative to the pole-piece corners at entrance and exit.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.1718806}}

@book{Elmore:1969:PhysicsWaves,
	Address = {New York, NY},
	Author = {Elmore, William C. and Heald, Mark A.},
	Date-Added = {2015-04-03 19:04:19 +0000},
	Date-Modified = {2015-04-03 19:04:19 +0000},
	Publisher = {McGraw-Hill Book Company, Inc.},
	Title = {The Physics of Waves},
	Year = {1969}}

@misc{Ellison:2013:PlanarUndulator,
	Author = {Ellison, James A. and Heinemann, Klaus and Vogt, Mathias and Gooden, Matthew},
	Date-Added = {2015-04-03 19:03:43 +0000},
	Date-Modified = {2015-04-03 19:03:43 +0000},
	Howpublished = {http://arxiv.org/abs/1303.5797},
	Month = mar,
	Title = {Planar undulator motion excited by a fixed traveling wave: Quasiperiodic averaging, normal forms and the {FEL} pendulum},
	Year = {2013},
	Abstract = {We present a mathematical analysis of planar motion of energetic electrons moving through a planar dipole undulator, excited by a fixed planar polarized plane wave Maxwell field in the X-Ray Free Electron Laser (FEL) regime. Our starting point is the 6D Lorentz system, which allows planar motions, and we examine this dynamical system as the wavelength of the traveling wave varies. By scalings and transformations the 6D system is reduced, without approximation, to a 2D system in a form for a rigorous asymptotic analysis using the Method of Averaging (MoA), a long time perturbation theory. The two dependent variables are a scaled energy deviation and a generalization of the so-called ponderomotive phase. As the wavelength varies the system passes through resonant and nonresonant (NR) zones and we develop NR and near-to-resonant (NtoR) normal form approximations. For a special initial condition and on resonance, the NtoR normal form reduces to the well-known FEL pendulum system. We then state and prove NR and NtoR first-order averaging theorems which give near optimal error bounds for the MoA approximations. The proofs are novel in that they do not use a near identity transformation and they use a system of differential inequalities. The NR case is an example of quasiperiodic averaging where the small divisor problem enters in the simplest possible way. To our knowledge the planar problem has not been analyzed with the generality we aspire to here nor has the standard FEL pendulum system been derived with associated error bounds as we do here.}}

@article{Ellison:2013:PlanarUndulatorMotion,
	Author = {Ellison, James A. and Heinemann, Klaus and Vogt, Mathias and Gooden, Matthew},
	Date-Added = {2015-04-03 19:03:43 +0000},
	Date-Modified = {2015-04-03 19:03:43 +0000},
	Doi = {10.1103/PhysRevSTAB.16.090702},
	Journal = prstab,
	Month = sep,
	Number = {9},
	Pages = {090702},
	Title = {Planar undulator motion excited by a fixed traveling wave: Quasiperiodic averaging, normal forms, and the free electron laser pendulum},
	Volume = {16},
	Year = {2013},
	Abstract = {We present a mathematical analysis of planar motion of energetic electrons moving through a planar dipole undulator, excited by a fixed planar polarized plane wave Maxwell field in the x-ray free electron laser (FEL) regime. Our starting point is the 6D Lorentz system, which allows planar motions, and we examine this dynamical system as the wavelength $\lambda$ of the traveling wave varies. By scalings and transformations the 6D system is reduced, without approximation, to a 2D system in a form for a rigorous asymptotic analysis using the method of averaging (MoA), a long-time perturbation theory. The two dependent variables are a scaled energy deviation and a generalization of the so-called ponderomotive phase. As $\lambda$ varies the system passes through resonant and nonresonant (NonR) intervals and we develop NonR and near-to-resonant (NearR) MoA normal form approximations to the exact equations. The NearR normal forms contain a parameter which measures the distance from a resonance. For the planar motion, with the special initial condition that matches into the undulator design trajectory, and on resonance, the NearR normal form reduces to the well-known FEL pendulum system. We then state and prove NonR and NearR first-order averaging theorems which give explicit error bounds for the normal form approximations. We prove the theorems in great detail, giving the interested reader a tutorial on mathematically rigorous perturbation theory in a context where the proofs are easily understood. The proofs are novel in that they do not use a near-identity transformation and they use a system of differential inequalities. The NonR case is an example of quasiperiodic averaging where the small divisor problem enters in the simplest possible way. To our knowledge the planar problem has not been analyzed with the generality we aspire to here nor has the standard FEL pendulum system been derived with associated error bounds as we do here. We briefly discuss the low gain theory in light of our NearR normal form. Our mathematical treatment of the noncollective FEL beam dynamics problem in the framework of dynamical systems theory sets the stage for our mathematical investigation of the collective high gain regime.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevSTAB.16.090702}}

@article{Heinemann:2001:SpinTransport,
	Author = {Heinemann, Klaus A. and Barber, Desmond P.},
	Date-Added = {2015-04-03 19:02:08 +0000},
	Date-Modified = {2015-04-03 19:02:08 +0000},
	Doi = {10.1016/S0168-9002(01)00276-5},
	Journal = nucima,
	Keywords = {spin dynamics},
	Month = may,
	Number = {1--2},
	Pages = {62--67},
	Title = {Spin transport, spin diffusion and {B}loch equations in electron storage rings},
	Volume = {463},
	Year = {2001},
	Abstract = {We show how, beginning with the Fokker--Planck equation for electrons emitting synchrotron radiation in a storage ring, the corresponding equation for spin motion can be constructed. This is an equation of the Bloch type for the polarisation density.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/S0168-9002(01)00276-5}}

@phdthesis{Heinemann:2010:PhDthesis,
	Address = {Albuquerque, NM},
	Author = {Heinemann, Klaus A.},
	Date-Added = {2015-04-03 19:02:08 +0000},
	Date-Modified = {2015-04-03 19:02:08 +0000},
	Month = may,
	School = {University of New Mexico},
	Title = {Two Topics in Particle Accelerator Beams},
	Type = {{PhD} dissertation},
	Year = {2010},
	Abstract = {This thesis has two parts. In the first part I present results from my studies of the Vlasov-Maxwell system which was developed, together with a code, in collaboration with Bassi, Ellison and Warnock. The emphasis is on the link between the theory and the self-consistent numerical computations performed by the code. The Vlasov-Maxwell system models electron beams, typically in synchrotron light sources. In the second part I present results from my studies of the dynamics of spin polarized beams. Here the emphasis is on improvements of the theoretical basis of beam simulations by using topological methods.}}

@misc{Heinemann:2014:UnifyingSDBP,
	Author = {Heinemann, Klaus A. and Ellison, James A. and Barber, Desmond P. and Vogt, Mathias},
	Date-Added = {2015-04-03 19:02:08 +0000},
	Date-Modified = {2015-04-03 19:02:08 +0000},
	Howpublished = {Eprint \url{http://arxiv.org/abs/1409.4373}},
	Month = sep,
	Title = {A New and Unifying Approach to Spin Dynamics and Beam Polarization in Storage Rings},
	Year = {2014},
	Abstract = {With this paper we extend our studies on polarized beams by distilling tools from the theory of principal bundles. Four major theorems are presented, one which ties invariant fields with the notion of normal form, one which allows one to compare different invariant fields, and two that relate the existence of invariant fields to the existence of certain invariant sets and relations between them. We then apply the theory to the dynamics of spin-1/2 and spin-1 particles and their density matrices describing statistically the particle-spin content of bunches. Our approach thus unifies the spin-vector dynamics from the T-BMT equation with the spin-tensor dynamics and other dynamics. This unifying aspect of our approach relates the examples elegantly and uncovers relations between the various underlying dynamical systems in a transparent way.}}

@misc{Heinemann:2015:InformalSummary,
	Author = {Heinemann, Klaus and Barber, Desmond P. and Ellison, James A. and Vogt, Mathias},
	Date-Added = {2015-04-03 19:02:08 +0000},
	Date-Modified = {2015-04-03 19:02:08 +0000},
	Howpublished = {Eprint \url{http://arxiv.org/abs/1502.00538}},
	Month = feb,
	Title = {An Informal Summary of a New Formalism for Classifying Spin-Orbit Systems Using Tools Distilled from the Theory of Bundles},
	Year = {2015},
	Abstract = {We give an informal summary of ongoing work which uses tools distilled from the theory of fibre bundles to classify and connect invariant fields associated with spin motion in storage rings. We mention four major theorems. One ties invariant fields with the notion of normal form, the second allows comparison of different invariant fields and the two others tie the existence of invariant fields to the existence of certain invariant sets. We explain how the theorems apply to the spin dynamics of spin-1/2 and spin-1 particles. Our approach elegantly unifies the spin-vector dynamics from the T-BMT equation with the spin-tensor dynamics and other dynamics and suggests an avenue for addressing the question of the existence of the invariant spin field.}}

@misc{Heinemann:2015:UnifyinSDBPx,
	Author = {Heinemann, Klaus A. and Barber, Desmond P. and Ellison, James A. and Vogt, Mathias},
	Date-Added = {2015-04-03 19:02:08 +0000},
	Date-Modified = {2015-04-03 19:02:08 +0000},
	Howpublished = {Eprint \url{http://arxiv.org/abs/1501.02747}},
	Month = jan,
	Title = {A detailed and unified treatment of spin-orbit systems using tools distilled from the theory of bundles},
	Year = {2015},
	Abstract = {We return to our study \cite{BEH} of invariant spin fields and spin tunes for polarized beams in storage rings but in contrast to the continuous-time treatment in \cite{BEH}, we now employ a discrete-time formalism, beginning with the Poincar{\'e} maps of the continuous time formalism. We then substantially extend our toolset and generalize the notions of invariant spin field and invariant frame field. We revisit some old theorems and prove several theorems believed to be new. In particular we study two transformation rules, one of them known and the other new, where the former turns out to be an SO(3)-gauge transformation rule. We then apply the theory to the dynamics of spin-1/2 and spin-1 particle bunches and their density matrix functions, describing semiclassically the particle-spin content of bunches. Our approach thus unifies the spin-vector dynamics from the T-BMT equation with the spin-tensor dynamics and other dynamics. This unifying aspect of our approach relates the examples elegantly and uncovers relations between the various underlying dynamical systems in a transparent way. As in \cite{BEH}, the particle motion is integrable but we now allow for nonlinear particle motion on each torus. Since this work is inspired by notions from the theory of bundles, we also provide insight into the underlying bundle-theoretic aspects of the well-established concepts of invariant spin field, spin tune and invariant frame field. Since we neglect, as is usual, the Stern-Gerlach force, the underlying principal bundle is of product formso that we can present the theory in a fashion which does not use bundle theory. Nevertheless we occasionally mention the bundle-theoretic meaningof our concepts and we also mention the similarities with the geometrical approach to Yang-Mills Theory.}}

@unpublished{Barber:2010:COSYResStrength,
	Author = {Barber, Desmond P.},
	Date-Added = {2015-04-03 19:00:01 +0000},
	Date-Modified = {2015-04-03 19:00:01 +0000},
	Keywords = {spin dynamics, resonance},
	Month = aug,
	Note = {Private communication},
	Title = {Spin resonance strengths, spin-orbit tracking and invariant spin fields with the {SLIM} formalism in storage rings with oscillating external magnetic fields},
	Year = {2010},
	Abstract = {As shown in [several references] spin resonance strengths associated with synchro-betatron motion in storage rings can be calculated by a simple adaptation of the SLIM formalism. Here I show how to extend this approach to the case when magnets with oscillating fields are used to flip spins. The method can be used for rings of arbitrary geometry, arbitrary distortion and for linear coupling in 6-dimensional phase space. The algorithm is illustrated for the flipping of proton and deuteron spins in the COSY ring.}}

@article{Barber:2011:PolLHeC,
	Author = {Barber, Desmond P. and Wienands, H.-U. and Fitterer, M. and Burkhardt, H.},
	Date-Added = {2015-04-03 19:00:01 +0000},
	Date-Modified = {2015-04-03 19:00:01 +0000},
	Doi = {10.1088/1742-6596/295/1/012145},
	Journal = jphyscs,
	Keywords = {spin dynamics},
	Pages = {012145},
	Title = {The possibility of polarisation in the {LHeC} ring-ring scenario},
	Volume = {295},
	Year = {2011},
	Abstract = {A proposal to add 60-GeV electron and positron beams to the LHC at CERN (LHeC) is currently being prepared. The provision of electron and positron longitudinal polarisation is an important component of the proposal and we are examining the feasibility of Sokolov-Ternov self-polarisation at energies up to 60 GeV in a storage ring in the LHC tunnel. But at this energy the attainable polarisation can be very strongly limited by depolarising effects. This paper summarises first calculations of the attainable polarisation including estimates of the efficacy of Siberian Snakes for weakening synchrotron sideband resonances.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1088/1742-6596/295/1/012145}}

@article{Barber:2011:PreExistBetatron,
	Author = {Barber, Desmond P.},
	Date-Added = {2015-04-03 19:00:01 +0000},
	Date-Modified = {2015-04-03 19:00:01 +0000},
	Doi = {10.1088/1742-6596/295/1/012135},
	Journal = jphyscs,
	Keywords = {spin dynamics},
	Pages = {012135},
	Title = {Pre-existing betatron motion and spin flipping with {RF} fields in storage rings},
	Volume = {295},
	Year = {2011},
	Abstract = {It seems to be a common perception that pre-existing, non-spin-resonant, vertical, betatron motion in storage rings has little influence on spin-flipping with external, resonant, radio-frequency, magnetic fields. While this is often the case, care is needed, and useful insights are obtained by studying the geometry of the invariant spin field (ISF). I illustrate this by numerical means for protons in the COSY ring and I suggest a test that could be carried out at COSY.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1088/1742-6596/295/1/012135}}

@article{Abell:2003:FastSymp,
	Author = {Abell, Dan T. and McIntosh, Eric and Schmidt, Frank},
	Date-Added = {2015-04-03 18:58:42 +0000},
	Date-Modified = {2015-04-03 18:58:42 +0000},
	Doi = {10.1103/PhysRevSTAB.6.064001},
	Journal = prstab,
	Month = jun,
	Number = {6},
	Pages = {064001},
	Title = {Fast symplectic map tracking for the {CERN} {L}arge {H}adron {C}ollider},
	Volume = {6},
	Year = {2003},
	Abstract = {Tracking simulations remain the essential tool for evaluating how multipolar imperfections in ring magnets restrict the domain of stable phase-space motion.  In the Large Hadron Collider (LHC) at CERN, particles circulate at the injection energy, when multipole errors are most significant, for more than $10^7$ turns, but systematic tracking studies are limited to a small fraction of this total time---even on modern computers.  A considerable speedup is expected by replacing element-by-element tracking with the use of a symplectified one-turn map.  We have applied this method to the realistic LHC lattice, version 6, and report here our results for various map orders, with special emphasis on precision and speed.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevSTAB.6.064001}}

@article{Abell:2015:AccurEffSpinInteg,
	Author = {Abell, Dan T. and Meiser, Dominic and Ranjbar, Vahid H. and Barber, Desmond P.},
	Date-Added = {2015-04-03 18:58:00 +0000},
	Date-Modified = {2015-04-03 18:58:00 +0000},
	Doi = {10.1103/PhysRevSTAB.18.024001},
	Journal = prstab,
	Month = feb,
	Number = {2},
	Pages = {024001},
	Title = {Accurate and Efficient Spin Integration for Particle Accelerators},
	Volume = {18},
	Year = {2015},
	Abstract = {Accurate spin tracking is a valuable tool for understanding spin dynamics in particle accelerators and can help improve the performance of an accelerator. In this paper, we present a detailed discussion of the integrators in the spin tracking code gpuSpinTrack. We have implemented orbital integrators based on drift-kick, bend-kick, and matrix-kick splits. On top of the orbital integrators, we have implemented various integrators for the spin motion. These integrators use quaternions and Romberg quadratures to accelerate both the computation and the convergence of spin rotations. We evaluate their performance and accuracy in quantitative detail for individual elements as well as for the entire RHIC lattice. We exploit the inherently data-parallel nature of spin tracking to accelerate our algorithms on graphics processing units.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevSTAB.18.024001}}

@techreport{Forest:2008:AvgFokkerPlanck,
	Address = {Tsukuba, Japan},
	Author = {Forest, {\'E}tienne},
	Date-Added = {2015-04-03 18:53:23 +0000},
	Date-Modified = {2015-04-03 18:53:23 +0000},
	Institution = {KEK},
	Keywords = {accelerator beam dynamics},
	Month = feb,
	Number = {2007-80},
	Title = {The Averaged {F}okker-{P}lanck Equation, Ergodic Averages over Invariant Tori and Synchrotron Integrals},
	Type = {KEK Report},
	Year = {2008},
	Abstract = {In this paper we study the Fokker-Planck equation applied to a nonlinear integrable accelerator. We show that the equilibrium distribution obtained from a Fokker-Planck equation in the case of a system submitted to small damping can be expressed by a quadrature when the underlying symplectic system is fully normalizable into circles. For the time being we will restrict ourselves to stochastic fluctuations which are not phase-space dependent. These results, within the context of the Fokker-Planck approximation, are a near complete extension of the Chao synchrotron integral formalism to nonlinear systems. Our results will depend on an ergodic theorem analogous to the Fluctuation-Dissipation theorem. We also discuss, in an appendix, the links between the Beam Envelope theory, Chao's Synchrotron Integrals and Sands' Integrals in the light of Ripken-like invariant lattice functions.}}

@techreport{Forest:2010:AvegFokkerPlanckQL,
	Address = {Tsukuba, Japan},
	Author = {Forest, {\'E}tienne},
	Date-Added = {2015-04-03 18:53:23 +0000},
	Date-Modified = {2015-04-03 18:53:23 +0000},
	Institution = {KEK},
	Keywords = {accelerator beam dynamics},
	Month = oct,
	Number = {2010-36},
	Title = {The Averaged {F}okker-{P}lanck Equation and Quantum Lifetime},
	Type = {KEK Report},
	Year = {2010},
	Abstract = {This paper completes the work of reference [1]. Here we study the Fokker-Planck equation applied to a nonlinear integrable system in the limit of small damping. These results, within the context of the Fokker-Planck approximation, are a near complete extension of the Chao synchrotron integral formalism to nonlinear systems. We show that the averaged Fokker-Planck equation can be put into a simpler form consistent with a reduced dimensionality by one half. Our proof depends on a simple lemma, which amongst other things, is closely connected to the fact that the divergence of the phase space velocity is zero in each individual canonical plane. We also derive in one degree of freedom an expression for the quantum lifetime which is valid if the aperture is located in a region which is approximately integrable, i.e., foliated by KAM curves centred around the origin.}}

@techreport{Forest:2010:OrbitalSpinFPP,
	Address = {Tsukuba, Japan},
	Author = {Forest, {\'E}tienne},
	Date-Added = {2015-04-03 18:53:23 +0000},
	Date-Modified = {2015-04-03 18:53:23 +0000},
	Institution = {KEK},
	Keywords = {accelerator beam dynamics, normal form},
	Month = nov,
	Number = {2010-39},
	Title = {Orbital and Spin Normal Forms in {FPP} \emph{or} {P}ropaganda in Mathematical Physics},
	Type = {KEK Report},
	Year = {2010},
	Abstract = {This paper is about normal form for spin as it is implemented in FPP (and also PTC). I want to express my gratitude to Dr.~Desmond Barber for teaching me the microscopic amount of spin knowledge necessary for this project. The work was also checked by Dr.~Sateesh Mane and published on KEK's WEB site.}}

@techreport{Forest:2010:UniViewLatticeFns,
	Address = {Tsukuba, Japan},
	Author = {Forest, {\'E}tienne},
	Date-Added = {2015-04-03 18:53:23 +0000},
	Date-Modified = {2015-04-03 18:53:23 +0000},
	Institution = {KEK},
	Keywords = {accelerator beam dynamics, normal form},
	Month = nov,
	Number = {2010-38},
	Title = {Unified View of Lattice Functions as Representations of Complex Numbers---{B}onus: {C}hao falls out of {S}ands---{B}onus: {D}ragt's Quadratic Kinematic Invariants fall out},
	Type = {KEK Report},
	Year = {2010}}

@techreport{Forest:2011:ReconstructingPS,
	Address = {Tsukuba, Japan},
	Author = {Forest, {\'E}tienne and Molodozhentsev, Alexander Y.},
	Date-Added = {2015-04-03 18:53:23 +0000},
	Date-Modified = {2015-04-03 18:53:23 +0000},
	Institution = {KEK},
	Keywords = {accelerator beam dynamics},
	Month = jul,
	Number = {20110-4},
	Title = {Reconstructing Phase Space from {BPM} data using approximate partially inverted {T}aylor Maps},
	Type = {KEK Report},
	Year = {2011},
	Abstract = {The work presented here are applications of the TPSA tools of Martin Berz and Lingyun Yang of BNL. It simply uses the fact that if one has a partial Taylor inverter at one's disposal, then the four-dimensional phase space can be inverted at one monitor using monitors from a known section of the lattice, i.e., monitors as close to each other as possible. It should be pointed out that this theory can be modified to use up-stream or down-stream BPMs. The theory here uses up-stream BPMs. This is important in the analysis of a mysterious element, for example a strong wiggler, to be able to do both can give us a knowledge of the mysterious element.

In the second part of the part of the paper, we remind the reader that quadratic beam envelopes are dual to quadratic Lie operators and thus we can also compute lattice functions from the reconstructed BPM phase space.

Finally the method is applied to (pre-earthquake) experimental data from J-PARC which used 177 beam position monitors (BPMs). Each monitor recorded data in the horizontal and vertical planes.}}

@book{Forest:2015:TrkCodeToAnalysis,
	Author = {Forest, {\'E}tienne},
	Booktitle = {Perturbation Theory in Tracking Codes: A hierarchical Courant-Snyder theory based on the primacy of codes},
	Date-Added = {2015-04-03 18:53:23 +0000},
	Date-Modified = {2015-04-03 18:56:52 +0000},
	Publisher = {Springer},
	Title = {From Tracking Code to Analysis: Generalised Courant-Snyder theory for realistic accelerator models},
	Year = {2015}}

@techreport{Barber:1991:Canon8DSpin,
	Address = {Hamburg, Germany},
	Author = {Barber, Desmond P. and Heinemann, Klaus A. and Ripken, Gerhard},
	Date-Added = {2010-03-30 16:12:07 -0600},
	Date-Modified = {2010-03-30 16:12:07 -0600},
	Institution = {Deutsches Elektronen-Synchrotron},
	Keywords = {spin dynamics},
	Month = may,
	Number = {DESY 91-047},
	Title = {A Canonical eight-dimensional formalism for linear and nonlinear classical spin orbit motion in storage rings},
	Year = {1991},
	Abstract = {In the following report we begin to reformulate work by Derbenev on the behaviour of coupled quantised spin-orbit motion. To this end we present a classical symplectic treatment of linear and non-linear spin-orbit motion for storage rings using a fully coupled eight-dimensional formalism which generalizes earlier investigations of coupled synchro-betatron oscillations by introducing two additional canonical spin variables which behave, in a small-angle limit, like those already used in linearised spin theory. Thus in addition to the usual $x$-$z$-$s$ couplings, both the spin to orbit and orbit to spin coupling are described canonically. Since the spin Hamiltonian can be expanded in a Taylor series in canonical variables, the formalism is convenient for use in 8-dimensional symplectic tracking calculations with the help, for example, of Lie algebra or differential algebra, for the study of chaotic spin motion, for construction of spin normal forms and for studying the effect of Stern-Gerlach forces.}}

@techreport{Barber:1993:NLCanonSpin,
	Address = {Hamburg, Germany},
	Author = {Barber, Desmond P. and Heinemann, Klaus A. and Ripken, Gerhard},
	Date-Added = {2010-03-30 16:12:07 -0600},
	Date-Modified = {2010-03-30 16:12:07 -0600},
	Institution = {Deutsches Elektronen-Synchrotron},
	Keywords = {spin dynamics},
	Month = mar,
	Number = {DESY 93-031},
	Title = {Nonlinear canonical spin: Orbit dynamics in storage rings: Normal forms and the {$\vec{n}$}-axis},
	Year = {1993},
	Abstract = {The two real canonical spin variables $\alpha$ and $\beta$ introduced in an earlier paper are combined with the six canonical variables of coupled synchro-betatron motion to form a system of eight canonical spin-orbit variables in which spin and orbital motion are treated on the same level. In these variables one-turn maps are origin preserving and the usual techniques of canonical perturbation theory can be applied. By writing the Hamiltonian in normal form the spin detuning terms as well as the so called $\vec{n}$-axis which is needed in the theory of radiative polarization can be constructed. The equations derived are valid for arbitrary velocity of the particles (below and above transition energy).}}

@article{Barber:1994:SpinI,
	Author = {Barber, Desmond P. and Heinemann, Klaus A. and Ripken, Gerhard},
	Date-Added = {2010-03-30 16:12:07 -0600},
	Date-Modified = {2010-03-30 16:12:07 -0600},
	Doi = {10.1007/BF01557243},
	Journal = zphysc,
	Month = mar,
	Number = {1},
	Pages = {117--142},
	Title = {A canonical 8-dimensional formalism for classical spin-orbit motion in storage rings: I. {A} new pair of canonical spin variables},
	Volume = {64},
	Year = {1994},
	Abstract = {In this paper we present a classical symplectic treatment of linear and nonlinear spin-orbit motion for storage rings using a fully coupled eight-dimensional formalism which generalizes earlier investigations of coupled synchro-betatron oscillations by introducing two new real canonical spin variables which behave, in a small-angle limit, like those already used in linearised spin theory. Thus in addition to the usual $x$-$z$-$s$ couplings, both the spin to orbit and orbit to spin coupling are described canonically. Since the spin Hamiltonian can be expanded in a Taylor series in canonical variables, the formalism is convenient for use in 8-dimensional symplectic tracking calculations with the help, for example, of Lie algebra or differential algebra, for the study of chaotic spin motion, for construction of spin normal forms and for studying the effect of Stern-Gerlach forces.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/BF01557243}}

@article{Barber:1994:SpinII,
	Author = {Barber, Desmond P. and Heinemann, Klaus A. and Ripken, Gerhard},
	Date-Added = {2010-03-30 16:12:07 -0600},
	Date-Modified = {2010-03-30 16:12:07 -0600},
	Doi = {10.1007/BF01557244},
	Journal = zphysc,
	Month = mar,
	Number = {1},
	Pages = {143--167},
	Title = {A canonical 8-dimensional formalism for classical spin-orbit motion in storage rings: {II}. {N}ormal forms and the $n$-axis},
	Volume = {64},
	Year = {1994},
	Abstract = {The two real canonical spin variables $\alpha$ and $\beta$ introduced in an earlier paper to describe spin motion in storage rings are combined with the six canonical variables of coupled synchro-betatron motion to form a system of eight canonical spin-orbit variables in which spin and orbital motion are treated on the same level. In these variables, one-turn maps are origin-preserving, and the usual techniques of canonical perturbation theory can be applied. By writing the Hamiltonian in normal form, one may construct the spin detuning terms as well as the so called $\mathbf{n}$-axis, the semi-classical spin axis which is needed in the theory of radiative polarization. The equations derived are valid for arbitrary particle velocity (below and above transition energy).},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/BF01557244}}

@article{Nash:2006:EqBmDist,
	Author = {Nash, Boaz and Wu, Juhao and Chao, Alexander W.},
	Date-Added = {2010-01-25 09:51:55 -0700},
	Date-Modified = {2010-01-25 09:51:55 -0700},
	Doi = {10.1103/PhysRevSTAB.9.032801},
	Journal = prstab,
	Month = mar,
	Number = {3},
	Pages = {032801},
	Title = {Equilibrium beam distribution in an electron storage ring near linear synchrobetatron coupling resonances},
	Volume = {9},
	Year = {2006},
	Abstract = {Linear dynamics in a storage ring can be described by the one-turn map matrix.  In the case of a resonance where two of the eigenvalues of this matrix are degenerate, a coupling perturbation causes a mixing of the uncoupled eigenvectors.  A perturbation formalism is developed to find eigenvalues and eigenvectors of the one-turn map near such a linear resonance.  Damping and diffusion due to synchrotron radiation can be obtained by integrating their effects over one turn, and the coupled eigenvectors can be used to find the coupled damping and diffusion coefficients.  Expressions for the coupled equilibrium emittances and beam distribution moments are then derived.  In addition to the conventional instabilities at the sum, integer, and half-integer resonances, it is found that the coupling can cause an instability through antidamping near a sum resonance even when the symplectic dynamics are stable.  As one application of this formalism, the case of linear synchrobetatron coupling is analyzed where the coupling is caused by dispersion in the rf cavity, or by a crab cavity.  Explicit closed-form expressions for the sum/difference resonances are given along with the integer/half-integer resonances.  The integer and half-integer resonances caused by coupling require particular care.  We find an example of this with the case of a crab cavity for the integer resonance of the synchrotron tune.  Whether or not there is an instability is determined by the value of the horizontal betatron tune, a unique feature of these coupling-caused integer or half-integer resonances.  Finally, the coupled damping and diffusion coefficients along with the equilibrium invariants and projected emittances are plotted as a function of the betatron and synchrotron tunes for an example storage ring based on PEP-II.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevSTAB.9.032801}}

@article{Wolski:2006:AltGenLinOptics,
	Author = {Wolski, Andrzej},
	Date-Added = {2010-01-21 10:12:49 -0700},
	Date-Modified = {2010-01-21 10:12:49 -0700},
	Doi = {10.1103/PhysRevSTAB.9.024001},
	Journal = prstab,
	Keywords = {accelerator beam dynamics},
	Month = feb,
	Number = {2},
	Pages = {024001},
	Title = {Alternative approach to general coupled linear optics},
	Volume = {9},
	Year = {2006},
	Abstract = {The Twiss parameters provide a convenient description of beam optics in uncoupled linear beam lines. For coupled beam lines, a variety of approaches are possible for describing the linear optics; here, we propose an approach and notation that naturally generalizes the familiar Twiss parameters to the coupled case in 3 degrees of freedom. Our approach is based on an eigensystem analysis of the matrix of second-order beam moments, or alternatively (in the case of a storage ring) on an eigensystem analysis of the linear single-turn map. The lattice functions that emerge from this approach have an interpretation that is conceptually very simple: in particular, the lattice functions directly relate the beam distribution in phase-space to the invariant emittances. To emphasize the physical significance of the coupled lattice functions, we develop the theory from first principles, using only the assumption of linear symplectic transport. We also give some examples of the application of this approach, demonstrating its advantages of conceptual and notational simplicity.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevSTAB.9.024001}}

@inproceedings{Chao:2008:SLIMrevisted,
	Author = {Chao, Alexander Wu},
	Crossref = {EPAC:2008},
	Date-Added = {2010-01-21 10:11:41 -0700},
	Date-Modified = {2010-01-21 10:11:41 -0700},
	Pages = {2963--2967},
	Title = {{SLIM}---{A}n early work revisited}}

@inproceedings{Forest:2000:MapCrxnAnalysis,
	Author = {Forest, {\'E}tienne and Schmidt, Frank},
	Crossref = {EPAC:2000},
	Date-Added = {2010-01-03 14:55:44 -0700},
	Date-Modified = {2010-01-03 14:56:10 -0700},
	Pages = {1399--1401},
	Title = {Map Creation and Analysis via Overloaded Tools in {FORTRAN} 90},
	Abstract = {In tracking codes there is the need to obtain, at runtime, various machine quantities which depend parametrically on things such as momentum or quadrupole strength. To this end we have overloaded (in FORTRAN90) Berz's DA-package[1] as well as the analysis library LieLib [2,3] which is based on this package and we have created polymorphic types. Runtime polymorphism is not interpretation as in COSY-INFINITY [4] and is more appropriate to large ring tracking codes. Consequently we have applied these tools to the code SixTrack [6].}}

@article{BouRabee:2004:TippeTop,
	Author = {Bou-Rabee, Nawaf M. and Marsden, Jerrold E. and Romero, Louis A.},
	Date-Added = {2009-11-24 15:54:03 -0700},
	Date-Modified = {2010-03-30 17:30:03 -0600},
	Doi = {10.1137/030601351},
	Journal = siamjads,
	Number = {3},
	Pages = {352--377},
	Title = {Tippe Top Inversion as a Dissipation-Induced Instability},
	Volume = {3},
	Year = {2004},
	Abstract = {By treating tippe top inversion as a dissipation-induced instability, we explain tippe top inversion through a system we call the modified Maxwell--Bloch equations.  We revisit previous work done on this problem and follow Or's mathematical model [\textit{SIAM J.\ Appl.\ Math.}, \textbf{54} (1994), pp. 597--609].  A linear analysis of the equations of motion reveals that only the equilibrium points correspond to the inverted and noninverted states of the tippe top and that the modified Maxwell--Bloch equations describe the linear/spectral stability of these equilibria.  We supply explicit criteria for the spectral stability of these states.  A nonlinear global analysis based on energetics yields explicit criteria for the existence of a heteroclinic connection between the noninverted and inverted states of the tippe top.  This criteria for the existence of a heteroclinic connection turns out to agree with the criteria for spectral stability of the inverted and noninverted states.  Throughout the work we support the analysis with numerical evidence and include simulations to illustrate the nonlinear dynamics of the tippe top.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1137/030601351}}

@article{BouRabee:2009:StochVarInteg,
	Author = {Bou-Rabee, Nawaf M. and Owhad, Houman},
	Date-Added = {2009-11-24 15:54:03 -0700},
	Date-Modified = {2009-11-24 15:54:03 -0700},
	Doi = {10.1093/imanum/drn018},
	Journal = imajna,
	Month = apr,
	Number = {2},
	Pages = {421--443},
	Title = {Stochastic variational integrators},
	Volume = {29},
	Year = {2009},
	Abstract = {This paper presents a continuous and discrete Lagrangian theory for stochastic Hamiltonian systems on manifolds, akin to the Ornstein--Uhlenbeck theory of Brownian motion in a force field.  The main result is to derive governing SDEs for such systems from a critical point of a stochastic action.  Using this result, the paper derives Langevin-type equations for constrained mechanical systems and implements a stochastic analogue of Lagrangian reduction.  These are easy consequences of the fact that the stochastic action is intrinsically defined.  Stochastic variational integrators (SVIs) are developed using a discrete variational principle.  The paper shows that the discrete flow of an SVI is almost surely symplectic and in the presence of symmetry almost surely momentum-map preserving.  A first-order mean-squared convergent SVI for mechanical systems on Lie groups is introduced.  As an application of the theory, SVIs are exhibited for multiple, randomly forced and torqued rigid bodies interacting via a potential.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1093/imanum/drn018}}

@article{Dayton:1954:Meas2DMag,
	Author = {Dayton, I. E. and Shoemaker, F. C. and Mozley, R. F.},
	Date-Added = {2009-11-24 14:29:25 -0700},
	Date-Modified = {2009-11-24 14:29:25 -0700},
	Doi = {10.1063/1.1771107},
	Journal = revsi,
	Keywords = {magnet measurement},
	Month = may,
	Number = {5},
	Pages = {485--489},
	Title = {Measurement of Two-Dimensional Fields. {P}art {II}: Study of a Quadrupole Magnet},
	Volume = {25},
	Year = {1954},
	Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.1771105}}

@article{Elmore:1954:Meas2DMag,
	Author = {Elmore, William C. and Garrett, M. W.},
	Date-Added = {2009-11-24 14:23:13 -0700},
	Date-Modified = {2009-11-24 14:30:10 -0700},
	Doi = {10.1063/1.1771105},
	Journal = revsi,
	Keywords = {magnet measurement},
	Month = may,
	Number = {5},
	Pages = {480--485},
	Title = {Measurement of Two-Dimensional Fields. {P}art {I}: Theory},
	Volume = {25},
	Year = {1954},
	Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.1771105}}

@inproceedings{Ryne:1987:GenMap,
	Author = {Ryne, Robert D. and Dragt, Alex J.},
	Crossref = {PAC:1987},
	Date-Added = {2009-11-24 14:11:59 -0700},
	Date-Modified = {2009-11-24 14:11:59 -0700},
	Pages = {1081--1083},
	Title = {Numerical Computation of Transfer Maps Using {L}ie Algebraic Methods},
	Abstract = {These transfer maps can then be used in conjunction with a Lie algebraic beam transport code, such as MARYLIE 3.0.  Together, these codes are expected to have many applications in the study of charged particle optical systems with fringe fields.}}

@article{Yokoya:1982:SpinChrom,
	Author = {Yokoya, Kaoru},
	Date-Added = {2009-11-24 14:08:25 -0700},
	Date-Modified = {2009-11-24 14:08:25 -0700},
	Journal = pacc,
	Note = {Also available as KEK Preprint 82-28.},
	Pages = {85--93},
	Title = {Spin Chromaticity For Higher Order Synchrotron Resonances},
	Volume = {13},
	Year = {1983},
	Abstract = {An explicit representation of spin chromaticity which is a crucial quantity to estimate diffusive electron depolarization is derived for general machines, with taking into account linear effects of betatron oscillations and spin phase modulation due to synchrotron oscillation.}}

@techreport{Yokoya:1986:SpinVars,
	Author = {Yokoya, Kaoru},
	Date-Added = {2009-11-24 14:08:25 -0700},
	Date-Modified = {2009-11-24 14:08:25 -0700},
	Institution = {Deutsches Elektronen-Synchrotron},
	Month = jun,
	Number = {DESY 86-057},
	Title = {The Action-Angle Variables of Classical Spin Motion in Circular Accelerators},
	Year = {1986},
	Abstract = {A general formalism is presented which shows how to rewrite a given Hamiltonian involving classical spin motion in an action-angle variable representation.  The canonical transformation is made usng the Lie transformation technique.}}

@article{Yokoya:1987:LieCalcPol,
	Author = {Yokoya, Kaoru},
	Date-Added = {2009-11-24 14:08:25 -0700},
	Date-Modified = {2009-11-24 14:08:25 -0700},
	Journal = nucima,
	Month = aug,
	Number = {2},
	Pages = {149--160},
	Title = {Calculation Of The Equilibrium Polarization Of Stored Electron Beams Using Lie Algebra},
	Volume = {258},
	Year = {1987},
	Abstract = {An algorithm is presented for calculating the spin-quantization axis n, introduced by Derbenev and Kondratenko, up to arbitrarily high orders including nonlinear orbital motion.  It can be used to evaluate the expected degree of equilibrium polarization in electron storage rings.}}

@techreport{Yokoya:1992:Nonpertalc,
	Address = {Tsukuba, Japan},
	Author = {Yokoya, Kaoru},
	Date-Added = {2009-11-24 14:08:25 -0700},
	Date-Modified = {2009-11-24 14:08:25 -0700},
	Institution = {KEK},
	Month = may,
	Number = {92-6},
	Title = {Nonperturbative calculation of equilibrium polarization of stored electron beams},
	Type = {KEK Report},
	Year = {1992}}

@techreport{Yokoya:1999:SpinTune,
	Address = {Hamburg, Germany},
	Author = {Yokoya, Kaoru},
	Date-Added = {2009-11-24 14:08:25 -0700},
	Date-Modified = {2009-11-24 14:08:25 -0700},
	Institution = {Deutsches Elektronen-Synchrotron},
	Month = jan,
	Number = {DESY 99-006},
	Title = {An Algorithm for Calculating the Spin Tune in Circular Accelerators},
	Year = {1999},
	Abstract = {A new algorithm for calculating the spin tune and the $\mathbf{n}$-axis for circular accelerators is presented.  The method resembles the one employed in the existing program code SODOM in that one-turn numerical spin maps at equally spaced orbit angle variables are used but it is more efficient than the latter.  Furthermore, it is applicable at large openning angles of the $\mathbf{n}$-axis, whereas the existing SODOM only converges for small angles.}}

@article{Yoshida:1990:ConstrHiOrder,
	Author = {Yoshida, Haruo},
	Date-Added = {2009-11-24 14:08:25 -0700},
	Date-Modified = {2009-11-24 14:08:25 -0700},
	Journal = physla,
	Month = nov,
	Number = {5--7},
	Pages = {262--268},
	Title = {Construction of higher order symplectic integrators},
	Volume = {150},
	Year = {1990},
	Abstract = {For Hamiltonian systems of the form $H = T(p) + V(q)$ a method is shown to construct explicit and time reversible symplectic integrators of higher order.  For any even order there exists at least one symplectic integrator with exact coefficients.  The simplest one is the 4th order integrator which agrees with one found by Forest and by Neri.  For 6th and 8th orders, symplectic integrators with fewer steps are obtained, for which the coefficients are given by solving a set of simultaneous algebraic equations numerically.}}

@article{Yoshida:1993:RecSympInt,
	Author = {Yoshida, Haruo},
	Date-Added = {2009-11-24 14:08:25 -0700},
	Date-Modified = {2009-11-24 14:08:25 -0700},
	Journal = cmda,
	Month = mar,
	Number = {1--2},
	Pages = {27--43},
	Title = {Recent progress in the theory and application of symplectic integrators},
	Volume = {56},
	Year = {1993},
	Abstract = {In this paper various aspect of symplectic integrators are reviewed.  Symplectic integrators are numerical integration methods for Hamiltonian systems which are designed to conserve the symplectic structure exactly as the original flow.  There are explicit symplectic schemes for systems of the form $H=T(p)+V(q)$, and implicit schemes for general Hamiltonian systems.  As a general property, symplectic integrators conserve the energy quite well and therefore an artificial damping (excitation) caused by the accumulation of the local truncation error cannot occur.  Symplectic integrators have been applied to the Kepler problem, the motion of minor bodies in the solar system and the long-term evolution of outer planets.}}

@article{Wortel:2007:ExmplCirc,
	Author = {Wortel, Stephanie and Malin, Shimon and Semon, Mark D.},
	Date-Added = {2009-11-24 14:07:45 -0700},
	Date-Modified = {2009-11-24 14:07:45 -0700},
	Journal = ajp,
	Month = dec,
	Number = {12},
	Pages = {1123--1133},
	Title = {Two examples of circular motion for introductory courses in relativity},
	Volume = {75},
	Year = {2007},
	Abstract = {The circular twin paradox and Thomas precession are presented in a way that makes them accessible to students in introductory relativity courses.  Both are discussed by examining what happens during travel around a polygon and then in the limit as the polygon becomes a circle.  Because relativistic predictions based on these examples are verified in experiments with macroscopic objects (such as atomic clocks flown in airplanes and the gyroscopes on Gravity Probe B), they are especially convincing to introductory students.}}

@manual{Wolfram:2008:Mathematica70,
	Address = {Champaign, IL},
	Author = {{Wolfram Research, Inc.}},
	Date-Added = {2009-11-24 14:07:28 -0700},
	Date-Modified = {2009-11-24 14:07:28 -0700},
	Title = {Mathematica, Version 7.0},
	Year = {2008}}

@article{Wisdom:1991:SympMapsN,
	Author = {Wisdom, Jack and Holman, Matthew J.},
	Date-Added = {2009-11-24 14:07:08 -0700},
	Date-Modified = {2009-11-24 14:07:08 -0700},
	Journal = astrnj,
	Month = oct,
	Number = {4},
	Pages = {1528--1538},
	Title = {Symplectic Maps for the $n$-Body Problem},
	Volume = {102},
	Year = {1991},
	Abstract = {The mapping method of Wisdom [AJ, 87, 577 (1982)] is generalized to encompass all gravitational $n$-body problems with a dominant central mass.  The method is used to compute the evolution of the outer planets for a billion years.  This calculation provides independent numerical confirmation of the result of Sussman \& Wisdom [Sci, 241, 433 (1988)] that the motion of the planet Pluto is chaotic.}}

@article{Wisdom:1992:SympMapsN,
	Author = {Wisdom, Jack and Holman, Matthew J.},
	Date-Added = {2009-11-24 14:07:08 -0700},
	Date-Modified = {2009-11-24 14:07:08 -0700},
	Journal = astrnj,
	Month = nov,
	Number = {5},
	Pages = {2022--2029},
	Title = {Symplectic Maps for the $n$-Body Problem: Stability Analysis},
	Volume = {104},
	Year = {1992},
	Abstract = {The stability of the symplectic mapping method for the $n$-body problem introduced recently by Wisdom \& Holman [AJ, 102, 1528 (1991)] is analyzed in a novel application of the methods of nonlinear dynamics.}}

@inproceedings{Wisdom:1996:SymplecticCorr,
	Author = {Wisdom, Jack and Holman, Matthew J. and Touma, Jihad},
	Crossref = {FIC:1996:IntAlg},
	Date-Added = {2009-11-24 14:07:08 -0700},
	Date-Modified = {2009-11-24 14:07:08 -0700},
	Pages = {217--244},
	Title = {Symplectic Correctors},
	Abstract = {Symplectic integration algorithms typically yield trajectories that exhibit spurious oscillation in energy and state variables.  In the delta function formulation of symplectic integration these oscillations have a clear origin, and canonical transformations can be made to remove them.  The accuracy of symplectic integrators is substantially improved when combined with these symplectic correctors.  The methods developed here are generally applicable to the integration of perturbed dynamical systems, but illustrated here by applications to the planetary $n$-body problem.}}

@article{Wisdom:1998:SymplecticCorrN,
	Author = {Wisdom, Jack},
	Date-Added = {2009-11-24 14:07:08 -0700},
	Date-Modified = {2009-11-24 14:07:08 -0700},
	Journal = astrnj,
	Keywords = {celestial mechanics, gravitation, analytical method, numerical method, solar system},
	Month = apr,
	Number = {4},
	Pages = {2294--2298},
	Title = {Symplectic Correctors for Canonical Heliocentric $n$-Body Maps},
	Volume = {131},
	Year = {1998},
	Abstract = {Symplectic correctors are developed for $n$-body maps (symplectic integrators) in canonical heliocentric coordinates.  Several correctors are presented explicitly.}}

@article{Werner:2008:ExtractDegen,
	Author = {Werner, Gregory R. and Cary, John R.},
	Date-Added = {2009-11-24 14:06:02 -0700},
	Date-Modified = {2009-11-24 14:06:02 -0700},
	Journal = jcompp,
	Keywords = {FDM, filter-diagonalization eigenmode, degenerate mode, normal mode analysis, harmonic inversion, FDTD, simulation, time-domain, electromagnetic},
	Month = may,
	Number = {10},
	Pages = {5200--5214},
	Title = {Extracting degenerate modes and frequencies from time-domain simulations with filter-diagonalization},
	Volume = {227},
	Year = {2008},
	Abstract = {A variant of the filter-diagonalization method, using targeted excitation to filter out unwanted modes, can extract exactly or nearly degenerate eigenmodes and frequencies from time-domain simulations.  Excitation provides a particularly simple way to produce filtered states with already-existing time-domain simulations, while requiring minimal storage space.  Moreover, using broader excitations that cover the entire range of desired frequencies requires just one-fifth as much computation as using narrow excitations.  With this method, almost any time-domain code can be easily turned into an efficient eigenmode solver with little or no change to the code.  To distinguish $M$ degenerate modes requires running at least $M$ different simulations, so the computational effort is proportional to the size of the degeneracy, no matter how closely-spaced the modes; however, from those $M$ simulations many other non-degenerate modes can also be extracted with high accuracy, without much extra effort.  This method allows relatively simple FDTD algorithms to compete with frequency-domain solvers, offering advantages of simplicity, flexibility and ease of implementation; also, it scales to very large problems and massively parallel computation, and it can be used to extract high-frequency modes without first having to identify lower-frequency modes.  The accuracy of this method is demonstrated by finding eigenmodes and frequencies of an electromagnetic resonant cavity.}}

@book{Weyl:1946:ClassicalGroups,
	Address = {Princeton, NJ},
	Author = {Weyl, Hermann},
	Date-Added = {2009-11-24 14:06:02 -0700},
	Date-Modified = {2009-11-24 14:06:02 -0700},
	Publisher = {Princeton University Press},
	Title = {The Classical Groups: Their Invariants and Representations},
	Year = {1946}}

@article{Wendlandt:1997:MechIntegr,
	Author = {Wendlandt, Jeffrey M. and Marsden, Jerrold E.},
	Date-Added = {2009-11-24 14:05:41 -0700},
	Date-Modified = {2009-11-24 14:05:41 -0700},
	Journal = physd,
	Keywords = {discrete mechanics, rigid body integration, symplectic integration, symplectic-momentum integration},
	Month = aug,
	Number = {3--4},
	Pages = {223--246},
	Title = {Mechanical Integrators Derived from a Discrete Variational Principle},
	Volume = {106},
	Year = {1997},
	Abstract = {Many numerical integrators for mechanical system simulation are created by using discrete algorithms to approximate the continuous equations of motion.  In this paper, we present a procedure to construct time-stepping algorithms that approximate the flow of continuous ODEs for mechanical systems by discretizing Hamilton's principle rather than the equations of motion.  The discrete equations share similarities to the continuous equations by preserving invariants, including the symplectic form and the momentum map.  We first present a formulation of discrete mechanics along with a discrete variational principle.  We then show that the resulting equations of motion preserve the symplectic form and that this formulation of mechanics leads to conservation laws from a discrete version of Noether's theorem.  We then use the discrete mechanics formulation to develop a procedure for constructing symplectic-momentum mechanical integrators for Lagrangian systems with holonomic constraints.  We apply the construction procedure to the rigid body and the double spherical pendulum to demonstrate numerical properties of the integrators.}}

@book{Weissert:1997:GenesisSim,
	Address = {New York, NY},
	Author = {Weissert, Thomas P.},
	Date-Added = {2009-11-24 14:05:32 -0700},
	Date-Modified = {2009-11-24 14:05:32 -0700},
	Publisher = {Springer-Verlag},
	Title = {The Genesis of Simulation in Dynamics: Pursuing the Fermi-Pasta-Ulam Problem},
	Year = {1997}}

@inproceedings{Weissbaecker:1999:NLSpinMaps,
	Author = {Wei{\ss}b{\"a}cker, Carl and Hoffst{\"a}tter, Georg H.},
	Booktitle = {Proceedings of the Workshop on Polarized Protons at High Energies, Hamburg, Germany, 17--20 May 1999},
	Date-Added = {2009-11-24 14:05:18 -0700},
	Date-Modified = {2009-11-24 14:05:18 -0700},
	Note = {Available at \url{http://www.desy.de/lp97-docs/spin/machine/weissbacher.ps}},
	Title = {Nonlinear spin transfer maps},
	Year = {1999},
	Abstract = {An analytic solution of the spin orbit equation of motion up to a given order in the initial phase space coordinates is derived for an arbitrary electromagnetic field.  An iterative procedure successively leads from a first order expansion to the required order in the initial coordinates.  Finally a simple example is presented.}}

@book{Wangler:2008:RFAccel,
	Address = {Weinheim, Germany},
	Author = {Wangler, Thomas P.},
	Date-Added = {2009-11-24 14:02:16 -0700},
	Date-Modified = {2009-11-24 14:02:16 -0700},
	Edition = {Second},
	Publisher = {Wiley-VCH},
	Title = {RF Linear Accelerators},
	Year = {2008}}

@phdthesis{Vogt:2000:PhDthesis,
	Author = {Vogt, Mathias},
	Date-Added = {2009-11-24 14:01:28 -0700},
	Date-Modified = {2009-11-24 14:01:28 -0700},
	School = {Universit{\"a}t Hamburg},
	Title = {Bounds on the Maximum Attainable Equilibrium Polarization of Protons at High Energy in HERA},
	Year = {2000},
	Abstract = {For some years HERA has been supplying longitudinally spin polarised electron and positron ($e^\pm$) beams to the HERMES experiment and in the future longitudinal polarisation will be supplied to the H1 and ZEUS experiments.  As a result there has been a development of interest in complementing the polarised $e^\pm$ beams with polarised protons.  In contrast to the case of $e^\pm$ where spin flip due to synchrotron radiation in the main bending dipoles leads to self polarisation owing to an up-down asymmetry in the spin flip rates (Sokolov-Ternov effect), there is no convincing self polarisation mechanism for protons at high energy.  Therefore protons must be polarised almost at rest in a source and then accelerated to the working energy.

At HERA, if no special measures are adopted, this means that the spins must cross several thousand ``spin-orbit resonances''.  Resonance crossing can lead to loss of polarisation and at high energy such effects are potentially strong since spin precession is very pronounced in the very large magnetic fields needed to contain the proton beam in HERA-\emph{p}.  Moreover simple models which have been successfully used to describe spin motion at low and medium energies are no longer adequate.  Instead, careful numerical spin-orbit tracking simulations are needed and a new, mathematically rigorous look at the theoretical concepts is required.

This thesis describes the underlying theoretical concepts, the computational tools (SPRINT) and the results of such a study.  In particular strong emphasis is put on the concept of the invariant spin field and its non-perturbative construction.  The invariant spin field is then used to define the amplitude dependent spin tune and to obtain numerical non-perturbative estimates of the latter.  By means of these two key concepts the nature of higher order resonances in the presence of snakes is clarified and their impact on the beam polarisation is analysed.  We then go on to discuss the special aspects of the HERA-\emph{p} ring and measures for minimising the perturbations to the spin motion ($\rightarrow$ depolarisation) and thereby obtain first upper bounds on the permissible beam emittances needed to maintain polarisation up to high energy in HERA-\emph{p}.}}

@techreport{VanLoan:1975:StudyMxExp,
	Address = {Manchester, UK},
	Author = {Van Loan, Charles F.},
	Date-Added = {2009-11-24 12:29:36 -0700},
	Date-Modified = {2009-11-24 12:29:36 -0700},
	Institution = {University of Manchester},
	Month = aug,
	Note = {Reissued as MIMS EPrint 2006.397, Manchester Institute for Mathematical Sciences, November 2006},
	Number = {10},
	Title = {A study of the matrix exponential},
	Type = {Numerical Analysis Report},
	Year = {1975}}

@article{VanLoan:1977:SensitivityMxExp,
	Author = {Van Loan, Charles F.},
	Date-Added = {2009-11-24 12:29:36 -0700},
	Date-Modified = {2009-11-24 12:29:36 -0700},
	Journal = siamjna,
	Keywords = {matrix exponential, condition, log norm, eigensystem},
	Month = dec,
	Number = {6},
	Pages = {971--981},
	Title = {The Sensitivity of the Matrix Exponential},
	Volume = {14},
	Year = {1977},
	Abstract = {In this paper we examine how the matrix exponential $e^{At}$ is affected by perturbations in $A$.  Elementary techniques using $\log$ norms and the Jordan and Schur factorizations indicate that $e^{At}$ is least sensitive when $A$ is normal.  Through the formulation of an exponential condition number, more insight is gained into the complicated connection between the condition of the eigensystem of $A$ and the sensitivity of $e^{At}$.}}

@book{Tufte:1983:VDQI,
	Address = {Cheshire, CT},
	Author = {Tufte, Edward R.},
	Date-Added = {2009-11-24 12:28:57 -0700},
	Date-Modified = {2009-11-24 12:28:57 -0700},
	Publisher = {Graphics Press},
	Title = {The Visual Display of Quantitative Information},
	Year = {1983},
	Bdsk-Url-1 = {http://www.edwardtufte.com/tufte/books_vdqi}}

@book{Tufte:1990:EnvisInfo,
	Address = {Cheshire, CT},
	Author = {Tufte, Edward R.},
	Date-Added = {2009-11-24 12:28:57 -0700},
	Date-Modified = {2009-11-24 12:28:57 -0700},
	Publisher = {Graphics Press},
	Title = {Envisioning Information},
	Year = {1990},
	Bdsk-Url-1 = {http://www.edwardtufte.com/tufte/books_ei}}

@book{Tufte:1997:VisExplan,
	Address = {Cheshire, CT},
	Author = {Tufte, Edward R.},
	Date-Added = {2009-11-24 12:28:57 -0700},
	Date-Modified = {2009-11-24 12:28:57 -0700},
	Publisher = {Graphics Press},
	Title = {Visual Explanations},
	Year = {1997},
	Bdsk-Url-1 = {http://www.edwardtufte.com/tufte/books_visex}}

@book{Tufte:2006:BeautEvid,
	Address = {Cheshire, CT},
	Author = {Tufte, Edward R.},
	Date-Added = {2009-11-24 12:28:57 -0700},
	Date-Modified = {2009-11-24 12:28:57 -0700},
	Publisher = {Graphics Press},
	Title = {Beautiful Evidence},
	Year = {2006},
	Bdsk-Url-1 = {http://www.edwardtufte.com/tufte/books_be}}

@inproceedings{Trbojevic:2003:FFAGDistributedRF,
	Author = {Trbojevic, Dejan and Berg, J. Scott and Blaskiewicz, Michael M. and Courant, Ernest D. and Palmer, Robert B. and Garren, Alper A.},
	Crossref = {PAC:2003},
	Date-Added = {2009-11-24 12:28:32 -0700},
	Date-Modified = {2009-11-24 12:28:32 -0700},
	Pages = {1816--1818},
	Title = {{FFAG} lattice for muon acceleration with distributed {RF}}}

@article{Trbojevic:2005:DesignNSFFAG,
	Author = {Trbojevic, Dejan and Courant, Ernest D. and Blaskiewicz, Michael},
	Date-Added = {2009-11-24 12:28:32 -0700},
	Date-Modified = {2009-11-24 12:28:32 -0700},
	Doi = {10.1103/PhysRevSTAB.8.050101},
	Journal = prstab,
	Keywords = {ffag},
	Month = may,
	Number = {5},
	Pages = {050101},
	Title = {Design of a nonscaling fixed field alternating gradient accelerator},
	Volume = {8},
	Year = {2005},
	Abstract = {We present a design of nonscaling fixed field alternating gradient accelerators (FFAG) minimizing the dispersion action function $H$.  The design is considered both analytically and via computer modeling.  We present the basic principles of a nonscaling FFAG lattice and discuss optimization strategies so that one can accelerate over a broad range of momentum with reasonable apertures.  Acceleration schemes for muons are discussed.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevSTAB.8.050101}}

@article{Trbojevic:2007:CPTherapy,
	Author = {Trbojevic, Dejan and Parker, Brett and Keil, Eberhard and Sessler, Andrew M.},
	Date-Added = {2009-11-24 12:28:32 -0700},
	Date-Modified = {2009-11-24 12:28:32 -0700},
	Doi = {10.1103/PhysRevSTAB.10.053503},
	Journal = prstab,
	Keywords = {ffag, hadron therapy},
	Month = may,
	Number = {5},
	Pages = {053503},
	Title = {Carbon/proton therapy: A novel gantry design},
	Volume = {10},
	Year = {2007},
	Abstract = {A major expense and design challenge in carbon/proton cancer therapy machines are the isocentric gantries.  The transport elements of the carbon/proton gantry are presently made of standard conducting dipoles.  Because of their large weight, of the order of $\sim100$\,tons, the total weight of the gantry with support structure is $\sim600$\,tons.  The novel gantry design that is described here is made of fixed field superconducting magnets, thus dramatically reducing magnet size and weight compared to conventional magnets.  In addition, the magnetic field is constant throughout the whole energy region required for tumor treatment.  Particles make very small orbit offsets, passing through the beam line.  The beam line is built of combined-function dipoles such as a nonscaling fixed field alternating gradient (NS-FFAG) structure.  The very large momentum acceptance NS-FFAG comes from very strong focusing and very small dispersion.  The NS-FFAG small magnets almost completely filled the beam line.  They first make a quarter (or close to a quarter) of an arc bending upward and an additional half of a circle beam line finishing so that the beam is pointed towards the patient.  At the end of the gantry, additional magnets with a fast response are required to allow radial scanning and to provide the required position and spot size.  The fixed field combined-function magnets for the carbon gantry could be made of superconducting magnets by using low temperature superconducting cable or by using high temperature superconductors.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevSTAB.10.053503}}

@article{Touma:1994:LiePoisson,
	Author = {Touma, Jihad and Wisdom, Jack},
	Date-Added = {2009-11-24 12:28:01 -0700},
	Date-Modified = {2009-11-24 12:28:01 -0700},
	Journal = astrnj,
	Month = mar,
	Number = {3},
	Pages = {1189--1202},
	Title = {Lie-{P}oisson Integrators for Rigid-Body Dynamics in the Solar System},
	Volume = {107},
	Year = {1994},
	Abstract = {The $n$-body mapping method of Wisdom \& Holman [AJ, 102, 1528 (1991)] is generalized to encompass rotational dynamics.  The Lie-Poisson structure of rigid body dynamics is discussed.  Integrators which preserve that structure are derived for the motion of a free rigid body and for the motion of rigid bodies interacting gravitationally with mass points.}}

@book{Tomonaga:1997:StorySpin,
	Author = {Tomonaga, Sin-itiro},
	Date-Added = {2009-11-24 12:27:37 -0700},
	Date-Modified = {2009-11-24 12:27:37 -0700},
	Note = {Translated by Takeshi Oka from \emph{Spin Wa Meguru}, first published in 1974},
	Publisher = {The University of Chicago Press},
	Title = {The Story of Spin},
	Year = {1997}}

@article{Thomas:1927:KinElectronAxis,
	Author = {Thomas, Llewellyn H.},
	Date-Added = {2009-11-24 12:26:44 -0700},
	Date-Modified = {2009-11-24 12:26:44 -0700},
	Journal = {Philos. Mag. S 7},
	Month = jan,
	Number = {13},
	Title = {The Kinematics of an Electron with an Axis},
	Volume = {3},
	Year = {1927}}

@article{Thomas:1938:PathsIonsCyclo1,
	Author = {Thomas, Llewellyn H.},
	Date-Added = {2009-11-24 12:26:44 -0700},
	Date-Modified = {2009-11-24 12:26:44 -0700},
	Doi = {10.1103/PhysRev.54.580},
	Journal = prev,
	Month = oct,
	Number = {8},
	Pages = {580--588},
	Title = {The Paths of Ions in the Cyclotron {I}. {O}rbits in the Magnetic Field},
	Volume = {54},
	Year = {1938},
	Abstract = {Bethe and Rose maintain in a recent letter and paper that a maximum energy for the beam from a cyclotron is fixed by the incompatibility of the conditions for resonance and focusing when the relativity increase of mass with velocity is taken into account. It is shown below that, while this result holds for a radially symmetrical magnetic field, it is not necessarily true in general; and that for a field varying with polar angle there is an additional focusing effect. If the relative variation of the field with polar angle is of the order of the ratio of the velocity of the ion to the velocity of light, this focusing effect will compensate the defocusing effect of Bethe and Rose. It is shown further that if this variation has period $\pi/2$, a family of stable periodic orbits exists which are nearly concentric circles. The second order effects due to the simultaneous action of the variations with polar angle of the magnetic field and the accelerating electric field will be considered in a second paper.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRev.54.580}}

@article{Thomas:1938:PathsIonsCyclo2,
	Author = {Thomas, Llewellyn H.},
	Date-Added = {2009-11-24 12:26:44 -0700},
	Date-Modified = {2009-11-24 12:26:44 -0700},
	Doi = {10.1103/PhysRev.54.588},
	Journal = prev,
	Month = oct,
	Number = {8},
	Pages = {588--598},
	Title = {The Paths of Ions in the Cyclotron {II}. {P}aths in the Combined Electric and Magnetic Fields},
	Volume = {54},
	Year = {1938},
	Abstract = {It has been pointed out in a recent paper that a variation of the magnetic field of a cyclotron with polar angle can produce a focusing effect on the beam, while preserving resonance and stability. In that paper the effects of the magnetic field alone were considered. It is shown below that the effects of variation with polar angle of the accelerating electric field and of the magnetic field can be considered as almost independent; the second order cross terms between them are without practical effect. Thus the results contained in the above paper (1) may simply be superposed on those obtained by other workers.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRev.54.588}}

@article{Thomas:1945:RelativisticInvar,
	Author = {Thomas, Llewellyn H.},
	Date-Added = {2009-11-24 12:26:44 -0700},
	Date-Modified = {2009-11-24 12:26:44 -0700},
	Doi = {10.1103/RevModPhys.17.182},
	Journal = revmp,
	Keywords = {statistical physics, thermodynamics},
	Number = {2--3},
	Pages = {182--186},
	Title = {Relativistic Invariance},
	Volume = {17},
	Year = {1945},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/RevModPhys.17.182}}

@article{Thomas:1952:RelativDynDistance,
	Author = {Thomas, Llewellyn H.},
	Date-Added = {2009-11-24 12:26:44 -0700},
	Date-Modified = {2009-11-24 12:26:44 -0700},
	Doi = {10.1103/PhysRev.85.868},
	Journal = prev,
	Month = mar,
	Number = {5},
	Pages = {868--872},
	Title = {The Relativistic Dynamics of a System of Particles Interacting at a Distance},
	Volume = {85},
	Year = {1952},
	Abstract = {The dynamics of a system of particles acting on one another at a distance can be relativistically invariant if the assumption of invariant world-lines is given up. This is shown by constructing a particular dynamics in which invariance over the homogeneous Lorentz group is trivial, but space as well as time displacement requires the solution of equations of motion or of a Schroedinger equation. This particular dynamics reduces in the nonrelativistic limit to the most general dynamics of a system of interacting particles admitting the Newtonian group.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRev.85.868}}

@article{Talman:1995:MobiusAccel,
	Author = {Talman, Richard},
	Date-Added = {2009-11-24 12:26:12 -0700},
	Date-Modified = {2009-11-24 12:26:12 -0700},
	Doi = {10.1103/PhysRevLett.74.1590},
	Journal = prevl,
	Month = feb,
	Number = {9},
	Pages = {1590--1593},
	Title = {A Proposed {M}{\"o}bius Accelerator},
	Volume = {74},
	Year = {1995},
	Abstract = {Any existing circular accelerator can be converted inexpensively for ``M{\"o}bius operation'' by introducing one ``twist'' element that interchanges horizontal and vertical betatron oscillations on each particle passage.  Two, not one, traversals of the ring are required to return to a corresponding state.  The ring exhibits properties different from and, in important ways, superior to the original.  Beam brightness can be increased while preserving large amplitude stability, and the (necessarily round) beams are robust against beam-beam interaction in colliding beam operation.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevLett.74.1590}}

@article{Symon:1956:FFAG,
	Author = {Symon, Keith R. and Kerst, Donald W. and Jones, Lawrence W. and Laslett, L. Jackson and Terwilliger, Kent M.},
	Date-Added = {2009-11-24 12:25:43 -0700},
	Date-Modified = {2009-11-24 12:25:43 -0700},
	Journal = prev,
	Keywords = {particle accelerator, cyclotron, synchrotron, ffag},
	Month = sep,
	Number = {6},
	Pages = {1837--1859},
	Title = {Fixed-Field Alternating-Gradient Particle Accelerators},
	Volume = {103},
	Year = {1956},
	Abstract = {It is possible, by using alternating-gradient focusing, to design circular accelerators with magnetic guide fields which are constant in time, and which can accommodate stable orbits at all energies from injection to output energy.  Such accelerators are in some respects simpler to construct and operate, and moreover, they show promise of greater output currents than conventional synchrotrons and synchrocyclotrons.  Two important types of magnetic field patterns are described, the radial-sector and spiral-sector patterns, the former being easier to understand and simpler to construct, the latter resulting in a much smaller accelerator for a given energy.  A theory of orbits in fixed-field alternating-gradient accelerators has been worked out in linear approximation, which yields approximate general relationships between machine parameters, as well as more accurate formulas which can be used for design purposes.  There are promising applications of these principles to the design of fixed-field synchrotrons, betatrons, and high-energy cyclotrons.}}

@techreport{Symon:1997:DerivHam,
	Address = {Argonne, IL},
	Author = {Symon, Keith R.},
	Date-Added = {2009-11-24 12:25:43 -0700},
	Date-Modified = {2009-11-24 12:25:43 -0700},
	Institution = {Argonne National Laboratory},
	Keywords = {Hamiltonian system},
	Month = sep,
	Number = {ANL/APS/TB-28},
	Title = {Derivation of {H}amiltonians for Accelerators},
	Type = {Tecnical Bulletin},
	Year = {1997}}

@inproceedings{Symon:2003:MURAdays,
	Author = {Symon, Keith R.},
	Crossref = {PAC:2003},
	Date-Added = {2009-11-24 12:25:43 -0700},
	Date-Modified = {2009-11-24 12:25:43 -0700},
	Pages = {452--456},
	Title = {{MURA} Days},
	Abstract = {The Midwestern Universities Research Association (MURA), incorporated in the mid nineteen-fifties, was a unique institution in that, although it never succeeded in its primary goal of building a multi-GeV particle accelerator, it remained in existence for more than ten years, during which the MURA group made many contributions to the science of particle accelerators.  Included among these were the invention of fixed field alternating gradient (FFAG) accelerators and spiral sector cyclotrons, an extensive analysis of rf acceleration with particular attention to the consequences of Liouville's theorem, beam stacking, analytic and computational studies of nonlinear orbit theory, studies of collective instabilities, and the first demonstration of practical ways to achieve colliding beams.  Although no large FFAG accelerators were ever built, model FFAG accelerators turned out to be excellent devices for the experimental study of accelerator problems because they separate the guide field from the acceleration process.  Models were used to study nonlinear resonances, acceleration processes, space charge limits, and beam stacking.  Among the last MURA projects was an electron storage ring that became the first machine dedicated exclusively to the production of synchrotron radiation for experiments, a facility which evolved into the highly successful Synchrotron Radiation Center at the University of Wisconsin-Madison.}}

@article{Simon:1989:HamTurnsPol,
	Author = {Simon, R. and Mukunda, N. and Sudarshan, E. C. G.},
	Date-Added = {2009-11-24 12:23:37 -0700},
	Date-Modified = {2009-11-24 12:23:37 -0700},
	Doi = {10.1007/BF02845998},
	Journal = pramana,
	Keywords = {spin dynamics},
	Month = jun,
	Number = {6},
	Pages = {769--792},
	Title = {Hamilton's theory of turns and a new geometrical representation for polarization optics},
	Volume = {32},
	Year = {1989},
	Abstract = {Hamilton's theory of turns for the group $SU(2)$ is exploited to develop a new geometrical representation for polarization optics. While pure polarization states are represented by points on the Poincar{\'e} sphere, linear intensity preserving optical systems are represented by great circle arcs on another sphere. Composition of systems, and their action on polarization states, are both reduced to geometrical operations. Several synthesis problems, especially in relation to the Pancharatnam-Berry-Aharonov-Anandan geometrical phase, are clarified with the new representation. The general relation between the geometrical phase, and the solid angle on the Poincar{\'e} sphere, is established.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/BF02845998}}

@article{Simon:1989:HamTurnsSp2R,
	Author = {Simon, R. and Mukunda, N. and Sudarshan, E. C. G.},
	Date-Added = {2009-11-24 12:23:37 -0700},
	Date-Modified = {2009-11-24 12:23:37 -0700},
	Journal = prevl,
	Keywords = {symplectic group, quaternions},
	Month = mar,
	Number = {12},
	Pages = {1331--1334},
	Title = {Hamilton's Theory of Turns Generalized to {$\mathrm{Sp}(2,R)$}},
	Volume = {62},
	Year = {2006},
	Abstract = {We present a generalization of Hamilton's geometric theory of turns, originally invented for SU(2), to the noncompact group Sp(2,R) relevant in a variety of physical applications.}}

@article{Simon:1992:HamTurnsGeom,
	Author = {Simon, R. and Mukunda, N.},
	Date-Added = {2009-11-24 12:23:37 -0700},
	Date-Modified = {2009-11-24 12:23:37 -0700},
	Doi = {10.1088/0305-4470/25/22/034},
	Journal = jphysa,
	Keywords = {rotation group},
	Month = nov,
	Number = {22},
	Pages = {6135--6144},
	Title = {Hamilton's turn and geometric phase for two-level systems},
	Volume = {25},
	Year = {1992},
	Abstract = {Hamilton, in the course of his studies on quaternions, introduced an elegant geometric representation for the composition of $SU(2)$ elements, in terms of turns on the unit sphere $\mathbb{S}^2$. The authors use these turns to study two-level systems, with particular reference to geometric phase. The special roles played by piecewise geodesic circuits in the state space and evolution under constant Hamiltonian are recognized.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1088/0305-4470/25/22/034}}

@article{Simon:2006:HamTurnsLorentz,
	Author = {Simon, R. and Chaturvedi, S. and Srinivasan, V. and Mukunda, N.},
	Date-Added = {2009-11-24 12:23:37 -0700},
	Date-Modified = {2009-11-24 12:23:37 -0700},
	Journal = intjtp,
	Keywords = {rotation group, Lorentz group, quaternions},
	Month = nov,
	Number = {11},
	Pages = {2051--2070},
	Title = {Hamilton's Turns for the {L}orentz Group},
	Volume = {45},
	Year = {2006},
	Abstract = {Hamilton in the course of his studies on quaternions came up with an elegant geometric picture for the group $SU(2)$.  In this picture the group elements are represented by ``turns'', which are equivalence classes of directed great circle arcs on the unit sphere $S^2$, in such a manner that the rule for composition of group elements takes the form of the familiar parallelogram law for the Euclidean translation group.  It is only recently that this construction has been generalized to the simplest noncompact group $SU(1,1)=Sp(2,R)=SL(2,R)$, the double cover of $SO(2,1)$.  The present work develops a theory of turns for $SL(2,C)$, the double and universal cover of $SO(3,1)$ and $SO(3,C)$, rendering a geometric representation in the spirit of Hamilton available for all low dimensional semisimple Lie groups of interest in physics.  The geometric construction is illustrated through application to polar decomposition, and to the composition of Lorentz boosts and the resulting Wigner or Thomas rotation.},
	Bdsk-Url-1 = {http://www.ingentaconnect.com/content/klu/ijtp/2006/00000045/00000011/00009171}}

@book{Siegel:1971:LectCelestMech,
	Address = {Berlin},
	Author = {Siegel, Carl L. and Moser, J{\"u}rgen K.},
	Date-Added = {2009-11-24 12:23:04 -0700},
	Date-Modified = {2009-11-24 12:23:04 -0700},
	Note = {Revised and enlarged translation of \textit{Vorlesungen {\"u}ber Himmelsmechanik} by C.L. Siegel, 1956},
	Publisher = {Springer-Verlag},
	Series = {Classics in Mathematics},
	Title = {Lectures on Celestial Mechanics},
	Year = {1971}}

@book{Siegel:1964:Symplectic-Geometry,
	Address = {New York, NY},
	Author = {Siegel, Carl L.},
	Date-Added = {2009-11-24 12:22:55 -0700},
	Date-Modified = {2009-11-24 12:22:55 -0700},
	Note = {Reprinted, with errata, from \textit{Amer.\ J.\ Math.}, Vol.\,LXV, No,\,1, January, 1943},
	Publisher = {Academic Press},
	Title = {Symplectic Geometry},
	Year = {1964}}

@article{Shatunov:2008:SpinFlipper,
	Author = {Shatunov, Yuri M. and Mane, S. R.},
	Date-Added = {2009-11-24 12:21:16 -0700},
	Date-Modified = {2009-11-24 12:21:16 -0700},
	Journal = prstab,
	Month = sep,
	Number = {9},
	Pages = {094002},
	Title = {Analysis of data for stored polarized beams using a spin flipper},
	Volume = {11},
	Year = {2008},
	Abstract = {We employ the so-called ``spin response formalism,'' which is a linear response theory applied to the spin dynamics in circular accelerators, to analyze recent measurements of spin-flip resonance widths.  The data was taken using a radial field rf dipole spin flipper to flip the spins of stored polarized proton and deuteron beams at the COSY storage ring.  Numerical calculations are presented, which provide a satisfactory fit to the data.}}

@article{Shatunov:2009:CalcSpinRespFn,
	Author = {Shatunov, Yuri M. and Mane, Sateesh R.},
	Date-Added = {2009-11-24 12:21:16 -0700},
	Date-Modified = {2009-11-24 12:21:16 -0700},
	Journal = prstab,
	Month = feb,
	Number = {2},
	Pages = {024001},
	Title = {Calculations of spin response functions in rings with {S}iberian {S}nakes and spin rotators},
	Volume = {12},
	Year = {2009},
	Abstract = {The so-called spin response formalism, which is linear response theory applied to spin dynamics in storage rings, can calculate the resonance strengths for spin flippers in storage rings of arbitrary structure, including rings with Siberian Snakes and spin rotators.  We calculate so-called spin response functions for a model of the RHIC lattice, for various scenarios of spin rotator settings.}}

@article{Shatunov:2009:ErratumCalcSRF,
	Author = {Shatunov, Yuri M. and Mane, Sateesh R.},
	Date-Added = {2009-11-24 12:21:16 -0700},
	Date-Modified = {2009-11-24 12:21:16 -0700},
	Journal = prstab,
	Month = mar,
	Number = {3},
	Pages = {039902},
	Title = {Erratum: Calculations of spin response functions in rings with {S}iberian {S}nakes and spin rotators},
	Volume = {12},
	Year = {2009}}

@article{Scuro:2005:FwdSympInt,
	Author = {Scuro, Sante R. and Chin, Siu A.},
	Date-Added = {2009-11-24 12:20:40 -0700},
	Date-Modified = {2009-11-24 12:20:40 -0700},
	Journal = preve,
	Month = may,
	Number = {5},
	Pages = {056703},
	Title = {Forward symplectic integrators and the long-time phase error in periodic motions},
	Volume = {71},
	Year = {2005},
	Abstract = {We show that when time-reversible symplectic algorithms are used to solve periodic motions, the energy error after one period is generally two orders higher than that of the algorithm.  By use of correctable algorithms, we show that the phase error can also be eliminated two orders higher than that of the integrator.  The use of fourth order forward time step integrators can result in sixth order accuracy for the phase error and eighth order accuracy in the periodic energy.  We study the one-dimensional harmonic oscillator and the two-dimensional Kepler problem in great detail, and compare the effectiveness of some recent fourth order algorithms.}}

@article{Schwinger:1973:ClassRadII,
	Author = {Schwinger, Julian S.},
	Date-Added = {2009-11-24 12:19:29 -0700},
	Date-Modified = {2009-11-24 12:19:29 -0700},
	Journal = prevd,
	Month = mar,
	Number = {6},
	Pages = {1696--1701},
	Title = {Classical Radiation of Accelerated Electrons. {II}. {A} Quantum Viewpoint},
	Volume = {7},
	Year = {1973},
	Abstract = {The known classical radiation spectrum of a high-energy charged particle in a homogeneous magnetic field is rederived.  The method applies, and illuminates, an exact (to order $\alpha$) expression for the inverse propagation function of a spinless particle in a homogeneous field.  An erratum list for paper I is appended.}}

@book{Schwinger:1998:CED,
	Address = {Reading, MA},
	Author = {Schwinger, Julian and DeRaad, Jr., Lester L. and Milton, Kimball A. and Tsai, Wu-yang},
	Date-Added = {2009-11-24 12:19:29 -0700},
	Date-Modified = {2009-11-24 12:19:29 -0700},
	Publisher = {Perseus Books},
	Title = {Classical Electrodynamics},
	Year = {1998}}

@techreport{Schwinger:1945:RadElectrons,
	Address = {Berkeley, CA},
	Author = {Schwinger, Julian S.},
	Date-Added = {2009-11-24 12:19:13 -0700},
	Date-Modified = {2009-11-24 12:19:13 -0700},
	Institution = {Lawrence Berkeley National Laboratory},
	Month = jan,
	Note = {Transcribed in 1996 by Miguel A. Furman from a 1945 preprint, this paper is available at \url{http://mafurman.lbl.gov/LBNL-39088.pdf}.},
	Number = {LBNL-39088},
	Title = {On Radiation by Electrons in a Betatron},
	Year = {1945},
	Abstract = {We complement the concept of the invariant spin field in storage rings by defining the invariant polarisation-tensor field for spin-1 particles and we suggest how to calculate it by stroboscopic averaging or directly from the invariant spin field.  The invariant polarisation tensor field and the invariant spin field are used to construct equilibrium spin density-matrix fields, and thereby offer a clean framework for describing equilibrium spin-1 ensembles in storage rings.  We also introduce a formalism for describing the effect of noise and damping on the polarisation tensor.}}

@article{Schwinger:1949:OnClassRad,
	Author = {Schwinger, Julian S.},
	Date-Added = {2009-11-24 12:19:13 -0700},
	Date-Modified = {2009-11-24 12:19:13 -0700},
	Journal = prev,
	Month = jun,
	Number = {12},
	Pages = {1912--1925},
	Title = {On the Classical Radiation of Accelerated Electrons},
	Volume = {75},
	Year = {1949},
	Abstract = {This paper is concerned with the properties of the radiation from a high energy accelerated electron, as recently observed in the General Electric synchrotron.  An elementary derivation of the total rate of radiation is first presented, based on Larmor's formula for a slowly moving electron, and arguments of relativistic invariance.  We then construct an expression for the instantaneous power radiated by an electron moving along an arbitrary, prescribed path.  By casting this result into various forms, one obtains the angular distribution, the spectral distribution, or the combined angular and spectral distributions of the radiation.  The method is based on an examination of the rate at which the electron irreversibly transfers energy to the electromagnetic field, as determined by half the difference of retarded and advanced electric field intensities.  Formulas are obtained for an arbitrary charge-current distribution and then specialized to a point charge.  The total radiated power and its angular distribution are obtained for an arbitrary trajectory.  It is found that the direction of motion is a strongly preferred direction of emission at high energies.  The spectral distribution of the radiation depends upon the detailed motion over a time interval large compared to the period of the radiation.  However, the narrow cone of radiation generated by an energetic electron indicates that only a small part of the trajectory is effective in producing radiation observed in a given direction, which also implies that very high frequencies are emitted.  Accordingly, we evaluate the spectral and angular distributions of the high frequency radiation by an energetic electron, in their dependence upon the parameters characterizing the instantaneous orbit.  The average spectral distribution, as observed in the synchrotron measurements, is obtained by averaging the electron energy over an acceleration cycle.  The entire spectrum emitted by an electron moving with constant speed in a circular path is also discussed.  Finally, it is observed that quantum effects will modify the classical results here obtained only at extraordinarily large energies.}}

@techreport{Sands:1979:PhysElectronSR,
	Author = {Sands, Matthew},
	Date-Added = {2009-11-24 12:18:15 -0700},
	Date-Modified = {2009-11-24 12:18:15 -0700},
	Institution = {Stanford Linear Accelerator Center},
	Month = may,
	Note = {Includes an addendum to the version first published in November of 1970},
	Number = {SLAC-R-121},
	Title = {The Physics of Electron Storage Rings: An Introduction},
	Year = {1979}}

@article{Sakanaka:2005:ClassModesRF,
	Author = {Sakanaka, Shogo},
	Date-Added = {2009-11-24 12:17:56 -0700},
	Date-Modified = {2009-11-24 12:17:56 -0700},
	Journal = prstab,
	Month = jul,
	Number = {7},
	Pages = {072002},
	Title = {Classification of eigenmodes in rf cavities using the group theory},
	Volume = {8},
	Year = {2005},
	Abstract = {For many damped-accelerating cavities for high-intensity beams, classifications of eigenmodes according to azimuthal indices are generally insufficient due to a lack of their axial symmetry.  To classify the eigenmodes in such cavities having general symmetry, the application of group theory is studied.  By taking basis functions from a complete set of eigenmodes, one can form a representation of the symmetry group of the cavity.  The eigenmodes can then be classified according to irreducible representations of the symmetry group.  This method is particularly useful for classifying the eigenmodes in complicated cavities, and for understanding the effects of perturbations on the eigenmodes.}}

@article{Sagan:1999:LACoupledLat,
	Author = {Sagan, David and Rubin, David L.},
	Date-Added = {2009-11-24 12:17:45 -0700},
	Date-Modified = {2009-11-24 12:17:45 -0700},
	Doi = {10.1103/PhysRevSTAB.2.074001},
	Journal = prstab,
	Month = jul,
	Number = {7},
	Pages = {074001},
	Title = {Linear analysis of coupled lattices},
	Volume = {2},
	Year = {1999},
	Abstract = {A formalism for describing the coupled two-dimensional motion of high energy particle beams in a storage ring is developed and extended to circumstances where the coupling is very strong, such as for the M{\"o}bius twist accelerator.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevSTAB.2.074001}}

@article{Sagan:2009:Ext1dCSR,
	Author = {Sagan, David and Hoffstaetter, Georg H. and Mayes, Christopher and Sae-Ueng, Udom},
	Date-Added = {2009-11-24 12:17:45 -0700},
	Date-Modified = {2009-11-24 12:17:45 -0700},
	Doi = {10.1103/PhysRevSTAB.12.040703},
	Journal = prstab,
	Keywords = {coherent synchrotron radiation},
	Month = apr,
	Number = {4},
	Pages = {040703},
	Title = {Extended one-dimensional method for coherent synchrotron radiation including shielding},
	Volume = {12},
	Year = {2009},
	Abstract = {Coherent synchrotron radiation can severely limit the performance of accelerators designed for high brightness and short bunch length. Examples include light sources based on energy recovery LINAC or free-electron lasers, and bunch compressors for linear colliders. In order to better simulate coherent synchrotron radiation, a one-dimensional formalism due to Saldin, Schneidmiller, and Yurkov has been implemented in the general beam dynamics code Bmad. Wide vacuum chambers are simulated by means of vertical image charges. Results from Bmad are here compared to analytical approximations, to numerical solutions of the Maxwell equations, and to the simulation code \textsc{elegant} and the code of Agoh and Yokoya.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevSTAB.12.040703}}

@phdthesis{Sacherer:1968:PhDthesis,
	Address = {Berkeley, CA},
	Author = {Sacherer, Frank James},
	Date-Added = {2009-11-24 12:16:52 -0700},
	Date-Modified = {2009-11-24 12:16:52 -0700},
	Note = {This paper is posted at the eScholarship Repository, University of California, \url{http://repositories.cdlib.org/lbnl/UCRL-18454/}},
	School = {University of California},
	Title = {Transverse Spaced-Charge Effects in Circular Accelerators},
	Year = {1968},
	Abstract = {The particles in an accelerator interact with one another by electromagnetic forces and are held together by external focusing forces.  Such a many-body system has a large number of transverse modes of oscillation (plasma oscillations) that can be excited at characteristic frequencies by errors in the external guide field.

In Part I we examine one mode of oscillation in detail, namely the quadrupole mode that is excited in uniformly charged beams by gradient errors.  We derive self-consistent equations of motion for the beam envelope and solve these equations for the case in which the space-charge force is much less than the external focusing force, i.e., for strong-focusing synchrotrons.  We find that the resonance intensity is shifted from the value predicted by the usual transverse incoherent space-charge limit; moreover, because the space-charge force depends on the shape and size of the beam, the beam growth in always limited.  For gradient errors of the magnitude normally present in strong-focusing synchrotrons, the increase in beam size is small provided the beam parameters are properly chosen; otherwise the growth may be large.  Thus gradient errors need not impose a limit on the number of particles that can be accelerated. 

In Part II we examine the other modes of collective oscillation that are excited by machine imperfections.  For simplicity we consider only one-dimensional beams that are confined by harmonic potentials, and only small-amplitude oscillations.  The linearized Vlasov and Poisson equations are used to find the twofold infinity of normal modes and eigenfrequencies for the stationary distribution that has uniform charge density in real space.  In practice, only the low-order modes (the dipole, quadrupole, sextupole, and one or two additional modes) will be serious, and the resonant conditions for these modes are located on a tune diagram.  These results, which are valid for all beam intensities, are compared with the known eigenfrequencies for the stationary distribution that has uniform particle density in phase space, and are extrapolated to the Gaussian distribution observed in the Brookhaven AGS.}}

@techreport{Sacherer:1970:MatchDist,
	Address = {Geneva},
	Author = {Sacherer, Frank James},
	Date-Added = {2009-11-24 12:16:52 -0700},
	Date-Modified = {2009-11-24 12:16:52 -0700},
	Institution = {European Organization for Nuclear Research},
	Month = jun,
	Note = {Available online at \url{http://cdsweb.cern.ch/record/322517}},
	Number = {CERN/SI/Int.\,DL/70-5},
	Title = {Matched distributions with non-uniform space charge and no emittance growth},
	Year = {1970},
	Bdsk-Url-1 = {http://cdsweb.cern.ch/record/322517}}

@inproceedings{Sacherer:1971:EffectSCTransp,
	Author = {Sacherer, Frank James and Sherwood, T. J.},
	Crossref = {PAC:1971},
	Date-Added = {2009-11-24 12:16:52 -0700},
	Date-Modified = {2009-11-24 12:16:52 -0700},
	Pages = {1066--1067},
	Title = {The Effect of Space Charge in Beam Transport Lines}}

@inproceedings{Sacherer:1971:RMSEnvEqs,
	Author = {Sacherer, Frank James},
	Crossref = {PAC:1971},
	Date-Added = {2009-11-24 12:16:52 -0700},
	Date-Modified = {2009-11-24 12:16:52 -0700},
	Pages = {1105--1107},
	Title = {{RMS} Envelope Equations with Space Charge},
	Abstract = {Envelope equations for a continuous beam with uniform charge density and elliptical cross-section were first derived by Kapchinsky and Vladimirsky (K-V).  In fact, the K-V equations are not restricted to uniformly charged beams, but are equally valid for any charge distribution with elliptical symmetry, provided the beam boundary and emittance are defined by rms (root-mean-square) values.  This results because (i) the second moments of any particle distribution depend only on the linear part of the force (determined by least squares method), while (ii) this linear part of the force in turn depends only on the second moments of the distribution.  This is also true in practice for three-dimensional bunched beams with ellipsoidal symmetry, and allows the formulation of envelope equations that include the effect of space charge on bunch length and energy spread.  The utility of this rms approach was first demonstrated by Lapostolle for stationary distributions.  Subsequently, Gluckstern proved that the rms version of the K-V equations remain valid for all continuous beams with axial symmetry.  In this report these results are extended to continuous beams with elliptical symmetry as well as to bunched beams with ellipsoidal form, and also to one-dimensional motion.}}

@inproceedings{Sacherer:1973:LongStabCrit,
	Author = {Sacherer, Frank James},
	Crossref = {PAC:1973},
	Date-Added = {2009-11-24 12:16:52 -0700},
	Date-Modified = {2009-11-24 12:16:52 -0700},
	Pages = {825--829},
	Title = {A Longitudinal Stability Criterion for Bunched Beams},
	Abstract = {The unstable motion of a bunched beam consists of rigid-bunch (dipole) and higher bunch-shape oscillations of the individual bunches (individual-bunch modes), plus perhaps coupled motion of the different bunches (coupled-bunch modes).  Stability is achieved either by decoupling the bunches or by a spread in synchrotron frequencies within a bunch.  A stability criterion analogous to the Keil-Schnell criterion for coasting beams is given which includes the effect of a beam interacting with perfectly conducting walls, resistive walls, and resonant structures.  Some examples for the CERN accelerators are included.}}

@inproceedings{Sacherer:1977:BunchLen,
	Author = {Sacherer, Frank James},
	Crossref = {PAC:1977},
	Date-Added = {2009-11-24 12:16:52 -0700},
	Date-Modified = {2009-11-24 12:16:52 -0700},
	Pages = {1393--1395},
	Title = {Bunch Lengthening and Microwave Instability},
	Abstract = {A single-bunch instability that leads to blow-up of bunch area and microwave signals (100\,MHz to 3\,GHz) has been observed in the PS and the ISR.  A similar instability may cause bunch lengthening in electron storage rings.  Attempts to explain this as a high-frequency coasting-beam instability require $e$-folding rates faster than a synchrotron period, and wavelengths shorter than a bunch length.  In this case, the usual Keil-Schnell coasting-beam criterion is used, but with local values of bunch current and momentum spread, as suggested by Boussard.  This yields $|Z/n|\approx13\Omega$ for the ISR, and values about five to ten times larger for the PS.  The restricitons mentioned above, however, are not fulfilled near threshold, or for frequencies as low as 100\,MHz.}}

@techreport{Roser:2006:CongManPP,
	Author = {Roser, Thomas and MacKay, William W. and Alekseev, Igor G. and others},
	Date-Added = {2009-11-24 12:15:17 -0700},
	Date-Modified = {2009-11-24 12:15:17 -0700},
	Institution = {Brookhaven National Laboratory},
	Note = {Available at \url{http://www.agsrhichome.bnl.gov/RHIC/Spin/design/CMan/CMan.pdf}},
	Title = {Configuration Manual: Polarized Proton Collider at {RHIC}},
	Year = {2006},
	Bdsk-Url-1 = {http://www.agsrhichome.bnl.gov/RHIC/Spin/design/CMan/CMan.pdf}}

@inproceedings{Roser:1999:AccelPolProt,
	Author = {Roser, Thomas},
	Crossref = {PAC:2003},
	Date-Added = {2009-11-24 12:15:07 -0700},
	Date-Modified = {2009-11-24 12:15:07 -0700},
	Title = {Acceleration of Polarized Protons to High Energy},
	Abstract = {High energy polarized beam collisions will open up the unique physics opportunities of studying spin effects in hard processes.  However, the acceleration of polarized beams in circular accelerators is complicated by the numerous depolarizing spin resonances.  Using a partial Siberian Snake and a rf dipole that ensure stable adiabatic spin motion during acceleration has made it possible to accelerate polarized protons to 25\,GeV at the Brookhaven AGS.  Full Siberian Snakes and polarimeters are being developed for RHIC to make the acceleration of polarized protons to 250\,GeV possible.  A similar scheme is being studied for the 800\,GeV HERA proton accelerator.}}

@article{Robin:1999:BeneRestoredPeriod,
	Author = {Robin, David S. and Safranek, James A. and Decking, Winfried},
	Date-Added = {2009-11-24 12:14:07 -0700},
	Date-Modified = {2009-11-24 12:14:07 -0700},
	Journal = prstab,
	Month = apr,
	Number = {4},
	Pages = {044001},
	Title = {Realizing the benefits of restored periodicity in the advanced light source},
	Volume = {2},
	Year = {1999},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevSTAB.2.044001}}

@article{Rhodes:2004:RelVelSpace,
	Author = {Rhodes, John A. and Semon, Mark D.},
	Date-Added = {2009-11-24 12:13:44 -0700},
	Date-Modified = {2009-11-24 12:13:44 -0700},
	Journal = ajp,
	Month = jul,
	Number = {7},
	Pages = {943--960},
	Title = {Relativistic velocity space, {W}igner rotation, and {T}homas precession},
	Volume = {72},
	Year = {2004},
	Abstract = {We develop a relativistic velocity space called \emph{rapidity space} from the single assumption of Lorentz invariance, and use it to visualize and calculate effects resulting from the successive application of non-collinear Lorentz boosts.  In particular, we show how rapidity space provides a geometric approach to Wigner rotation and Thomas precession in the same way that space -- time provides a geometrical approach to kinematic effects in special relativity.}}

@article{Richardson:1927:DeferredLimit,
	Author = {Richardson, Lewis F. and Gaunt, J. Arthur},
	Date-Added = {2009-11-24 12:13:44 -0700},
	Date-Modified = {2009-11-24 12:13:44 -0700},
	Journal = phtrrsa,
	Month = jan,
	Number = {636--646},
	Pages = {299--361},
	Title = {The Deferred Approach to the Limit. {P}art {I}.\ {S}ingle Lattice. {P}art {II}.\ {I}nterpenetrating Lattices},
	Volume = {226},
	Year = {1927},
	Bdsk-Url-1 = {http://dx.doi.org/10.1098/rsta.1927.0008}}

@article{Rempe:2009:BifurExpMap,
	Author = {Rempe, Lasse and Schleicher, Dierk},
	Date-Added = {2009-11-24 12:13:29 -0700},
	Date-Modified = {2009-11-24 12:13:29 -0700},
	Doi = {10.1007/s00222-008-0147-5},
	Journal = invmath,
	Keywords = {complex dynamics},
	Month = jan,
	Number = {1},
	Pages = {103--135},
	Title = {Bifurcations in the space of exponential maps},
	Volume = {175},
	Year = {2009},
	Abstract = {This article investigates the parameter space of the exponential family $z\mapsto\exp(z)+\kappa$. We prove that the boundary (in $\mathbb{C}$) of every hyperbolic component is a Jordan arc, as conjectured by Eremenko and Lyubich as well as Baker and Rippon. In fact, we prove the stronger statement that the exponential bifurcation locus is connected in $\mathbb{C}$, an analog of Douady and Hubbard's celebrated theorem that the Mandelbrot set is connected. We show furthermore that $\infty$ is not accessible through any nonhyperbolic (``queer'') stable component. The main part of the argument consists of demonstrating a general ``Squeezing Lemma'', which controls the structure of parameter space near infinity. We also prove a second conjecture of Eremenko and Lyubich concerning bifurcation trees of hyperbolic components.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s00222-008-0147-5}}

@book{Reiser:1994:ThDesignCPA,
	Address = {New York, NY},
	Author = {Reiser, Martin},
	Date-Added = {2009-11-24 12:13:17 -0700},
	Date-Modified = {2009-11-24 12:13:17 -0700},
	Publisher = {John Wiley \& Sons},
	Series = {Wiley Series in Beam Physics and Accelerator Technology},
	Title = {Theory and Design of Charged Particle Accelerators},
	Year = {1994}}

@article{Reich:1996:SympIntConstrained,
	Author = {Reich, Sebastian},
	Date-Added = {2009-11-24 12:13:02 -0700},
	Date-Modified = {2009-11-24 12:13:02 -0700},
	Doi = {10.1137/0733025},
	Journal = siamjna,
	Keywords = {symplectic integration},
	Month = apr,
	Number = {2},
	Pages = {475--491},
	Title = {Symplectic Integration of Constrained {H}amiltonian Systems by Composition Methods},
	Volume = {33},
	Year = {1996},
	Abstract = {Recent work reported in the literature suggests that for the long-term integration of Hamiltonian dynamical systems one should use methods that preserve the symplectic structure of the flow.  In this paper the symplecticity of numerical integrators is investigated for constrained Hamiltonian systems with holonomic constraints.  The following two results will be derived. (i) It is shown that any first- or second-order symplectic integrator for unconstrained problems can be generalized to constrained systems such that the resulting scheme is symplectic and preserves the constraints.  Based on this, higher-order methods can be derived by the same composition methods used for unconstrained problems.  (ii) Leimkuhler and Reich [\textit{Math.\ Comp.}, \textbf{63} (1994), pp.\,589--605] derived symplectic integrators based on Dirac's reformulation of the constrained problem as an unconstrained Hamiltonian system.  However, although the unconstrained reformulation can be handled by direct application of any symplectic implicit Runge--Kutta method, the resulting schemes do not preserve the constraints.  In this paper it is shown that these schemes can be modified such that they also preserve the constraints.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1137/0733025}}

@article{Reich:1999:BackwardError,
	Author = {Reich, Sebastian},
	Date-Added = {2009-11-24 12:13:02 -0700},
	Date-Modified = {2009-11-24 12:13:02 -0700},
	Doi = {10.1137/S0036142997329797},
	Journal = siamjna,
	Keywords = {numerical integration, Hamiltonian system},
	Number = {5},
	Pages = {1549--1570},
	Title = {Backward Error Analysis for Numerical Integrators},
	Volume = {36},
	Year = {1999},
	Abstract = {Backward error analysis has become an important tool for understanding the long time behavior of numerical integration methods.  This is true in particular for the integration of Hamiltonian systems where backward error analysis can be used to show that a symplectic method will conserve energy over exponentially long periods of time.  Such results are typically based on two aspects of backward error analysis: (i) It can be shown that the modified vector fields have some qualitative properties which they share with the given problem and (ii) an estimate is given for the difference between the best interpolating vector field and the numerical method.  These aspects have been investigated recently, for example, by Benettin and Giorgilli in [\textit{J.\ Statist.\ Phys.}, \textbf{74} (1994), pp.\,1117--1143], by Hairer in [\textit{Ann.\ Numer.\ Math.}, \textbf{1} (1994), pp.\,107--132], and by Hairer and Lubich in [\textit{Numer.\ Math.}, \textbf{76} (1997), pp.\,441--462].  In this paper we aim at providing a unifying framework and a simplification of the existing results and corresponding proofs.  Our approach to backward error analysis is based on a simple recursive definition of the modified vector fields that does not require explicit Taylor series expansion of the numerical method and the corresponding flow maps as in the above-cited works.  As an application we discuss the long time integration of chaotic Hamiltonian systems and the approximation of time averages along numerically computed trajectories.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1137/S0036142997329797}}

@article{Quispel:2006:GeomNumIntegr,
	Author = {Quispel, G. Reinhout W. and McLachlan, Robert I.},
	Date-Added = {2009-11-24 12:12:12 -0700},
	Date-Modified = {2010-03-25 09:37:44 -0600},
	Doi = {10.1088/0305-4470/39/19/E01},
	Journal = jphysa,
	Keywords = {geometric integration},
	Month = may,
	Number = {19},
	Pages = {preface},
	Title = {Geometric Numerical Integration of Differential Equations},
	Volume = {39},
	Year = {2006},
	Bdsk-Url-1 = {http://dx.doi.org/10.1088/0305-4470/39/19/E01}}

@book{Poincare:1892:NewMethods,
	Author = {Poincar{\'e}, Henri},
	Date-Added = {2009-11-24 12:11:36 -0700},
	Date-Modified = {2009-11-24 12:11:36 -0700},
	Editor = {Goroff, Daniel L.},
	Note = {This is an extensive revision, correction, and updating (in three parts) of the original 1967 NASA translation of \emph{Les M{\'e}thodes nouvelles de la M{\'e}canique c{\'e}leste}, originally published in 1892--1899},
	Publisher = {American Institute of Physics},
	Series = {History of Modern Physics and Astronomy},
	Title = {New Methods of Celestial Mechanics},
	Volume = {13},
	Year = {1993}}

@article{Peggs:2009:GrazingFn,
	Author = {Peggs, Stephen G. and Previtali, Valentina},
	Date-Added = {2009-11-24 12:11:13 -0700},
	Date-Modified = {2009-11-24 12:11:13 -0700},
	Doi = {10.1103/PhysRevSTAB.12.114001},
	Journal = prstab,
	Month = nov,
	Number = {11},
	Pages = {114001},
	Title = {Grazing function $g$ and collimation angular acceptance},
	Volume = {12},
	Year = {2009},
	Abstract = {The grazing function $g$ is introduced---a synchrobetatron optical quantity that is analogous (and closely connected) to the Twiss and dispersion functions $\beta$, $\alpha$, $\eta$, and $\eta'$. It parametrizes the rate of change of total angle with respect to synchrotron amplitude for grazing particles, which just touch the surface of an aperture when their synchrotron and betatron oscillations are simultaneously (in time) at their extreme displacements. The grazing function can be important at collimators with limited acceptance angles. For example, it is important in both modes of crystal collimation operation---in channeling and in volume reflection. The grazing function is independent of the collimator type---crystal or amorphous---but can depend strongly on its azimuthal location. The rigorous synchrobetatron condition $g=0$ is solved, by invoking the close connection between the grazing function and the slope of the normalized dispersion. Propagation of the grazing function is described, through drifts, dipoles, and quadrupoles. Analytic expressions are developed for $g$ in perfectly matched periodic FODO cells, and in the presence of $\beta$ or $\eta$ error waves. These analytic approximations are shown to be, in general, in good agreement with realistic numerical examples. The grazing function is shown to scale linearly with FODO cell bend angle, but to be independent of FODO cell length. The ideal value is $g=0$ at the collimator, but finite nonzero values are acceptable. Practically achievable grazing functions are described and evaluated, for both amorphous and crystal primary collimators, at RHIC, the SPS (UA9), the Tevatron (T-980), and the LHC.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevSTAB.12.114001}}

@techreport{Palmer:1988:CrabCross,
	Address = {Stanford, CA},
	Author = {Palmer, Robert B.},
	Date-Added = {2009-11-24 12:10:50 -0700},
	Date-Modified = {2009-11-24 12:10:50 -0700},
	Institution = {Stanford Linear Accelerator Center},
	Month = dec,
	Number = {SLAC-PUB-4707},
	Title = {Energy Scaling, Crab Crossing, and the Pair Problem},
	Year = {1988},
	Bdsk-Url-1 = {http://www.slac.stanford.edu/pubs/slacpubs/4000/slac-pub-4707.html}}

@book{OzorioDeAlmeida:1988:HamSys,
	Address = {Cambridge, UK},
	Author = {Ozorio de Almeida, Alfredo M.},
	Date-Added = {2009-11-24 12:10:25 -0700},
	Date-Modified = {2009-11-24 12:10:25 -0700},
	Publisher = {Cambridge University Press},
	Series = {Cambridge Monographs on Mathematical Physics},
	Title = {Hamiltonian Systems: Chaos and Quantization},
	Year = {1988}}

@book{Ott:2002:ChaosDynSys,
	Address = {Cambridge, UK},
	Author = {Ott, Edward},
	Date-Added = {2009-11-24 12:10:13 -0700},
	Date-Modified = {2009-11-24 12:10:13 -0700},
	Edition = {Second},
	Publisher = {Cambridge University Press},
	Title = {Chaos in Dynamical Systems},
	Year = {2002}}

@book{Olver:1993:AppLieGroups,
	Address = {New York, NY},
	Author = {Olver, Peter J.},
	Date-Added = {2009-11-24 12:09:46 -0700},
	Date-Modified = {2009-11-24 12:09:46 -0700},
	Edition = {Second},
	Publisher = {Springer-Verlag},
	Series = {Graduate Texts in Mathematics},
	Title = {Applications of Lie Groups to Differential Equations},
	Volume = {107},
	Year = {1993}}

@book{Olver:1995:EquivInvarSymm,
	Address = {Cambridge, England},
	Author = {Olver, Peter J.},
	Date-Added = {2009-11-24 12:09:46 -0700},
	Date-Modified = {2009-11-24 12:09:46 -0700},
	Publisher = {Cambridge University Press},
	Title = {Equivalence, Invariants, and Symmetry},
	Year = {1995}}

@book{Olver:1999:ClassInvarTh,
	Address = {Cambridge, UK},
	Author = {Olver, Peter J.},
	Date-Added = {2009-11-24 12:09:46 -0700},
	Date-Modified = {2009-11-24 12:09:46 -0700},
	Publisher = {Cambridge University Press},
	Series = {London Mathematical Society Student Texts},
	Title = {Classical Invariant Theory},
	Volume = {44},
	Year = {1999}}

@article{Berrut:2004:BarycentricLagrange,
	Author = {Berrut, Jean-Paul and Trefethen, Lloyd N.},
	Date-Added = {2009-11-24 12:07:28 -0700},
	Date-Modified = {2009-11-24 12:07:28 -0700},
	Doi = {10.1137/S0036144502417715},
	Journal = siamr,
	Keywords = {barycentric formula, interpolation, Lagrange interpolation},
	Number = {3},
	Pages = {501--517},
	Title = {Barycentric {L}agrange Interpolation},
	Volume = {46},
	Year = {2004},
	Abstract = {Barycentric interpolation is a variant of Lagrange polynomial interpolation that is fast and stable.  It deserves to be known as the standard method of polynomial interpolation.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1137/S0036144502417715}}

@article{Higham:2004:StabilityBary,
	Author = {Higham, Nicholas J.},
	Date-Added = {2009-11-24 12:05:53 -0700},
	Date-Modified = {2009-11-24 12:05:53 -0700},
	Journal = imajna,
	Keywords = {polynomial interpolation, Lagrange interpolation, barycentric formula, rounding error analysis, backward error, forward error, Lebesgue constant},
	Month = oct,
	Number = {4},
	Pages = {547--556},
	Title = {The numerical stability of barycentric {L}agrange interpolation},
	Volume = {24},
	Year = {2004},
	Abstract = {The Lagrange representation of the interpolating polynomial can be rewritten in two more computationally attractive forms: a modified Lagrange form and a barycentric form.  We give an error analysis of the evaluation of the interpolating polynomial using these two forms.  The modified Lagrange formula is shown to be backward stable.  The barycentric formula has a less favourable error analysis, but is forward stable for any set of interpolating points with a small Lebesgue constant.  Therefore the barycentric formula can be significantly less accurate than the modified Lagrange formula only for a poor choice of interpolating points.  This analysis provides further weight to the argument of Berrut and Trefethen that barycentric Lagrange interpolation should be the polynomial interpolation method of choice.}}

@book{Needham:1998:VisualCA,
	Address = {Oxford, UK},
	Author = {Needham, Tristan},
	Date-Added = {2009-11-24 12:04:49 -0700},
	Date-Modified = {2009-11-24 12:04:49 -0700},
	Note = {Reprinted with corrections, 1998},
	Publisher = {Oxford University Press},
	Title = {Visual Complex Analysis},
	Year = {1997}}

@article{Morozov:2003:Spin1Flip,
	Author = {Morozov, V. S. and Etienne, Z. B. and Kandes, M. C. and others},
	Date-Added = {2009-11-24 12:03:27 -0700},
	Date-Modified = {2009-11-24 12:03:27 -0700},
	Journal = prevl,
	Month = nov,
	Number = {21},
	Pages = {214801},
	Title = {First Spin Flipping of a Stored Spin-1 Polarized Beam},
	Volume = {91},
	Year = {2003},
	Abstract = {We recently studied spin flipping of a 270\,MeV vertically polarized deuteron beam stored in the Indiana University Cyclotron Facility Cooler Ring.  We adiabatically swept an rf solenoid's frequency through an rf-induced spin resonance and observed its effect on the deuterons' vector and tensor polarizations.  After optimizing the resonance crossing rate and maximizing the solenoid's voltage, we measured a vector spin-flip efficiency of $94.2\% \pm 0.3\%$.  We also found striking behavior of the spin-1 tensor polarization.}}

@article{Morozov:2005:Spin1Manip,
	Author = {Morozov, V. S. and Krisch, A. D. and Leonova, M. A. and others},
	Date-Added = {2009-11-24 12:03:27 -0700},
	Date-Modified = {2009-11-24 12:03:27 -0700},
	Journal = prstab,
	Month = jun,
	Number = {6},
	Pages = {061001},
	Title = {Spin manipulating stored 1.85\,{GeV/$c$} vector and tensor polarized spin-1 bosons},
	Volume = {8},
	Year = {2005},
	Abstract = {We recently studied the spin manipulation of $1.85\,\text{GeV}/c$ vertically polarized deuterons stored in the COSY cooler synchrotron.  We adiabatically swept an rf dipole's frequency through an rf-induced spin resonance and observed its effect on the deuterons' vector and tensor polarizations.  After optimizing the resonance crossing rate and maximizing the rf dipole's voltage, we measured spin-flip efficiencies of $97 \pm 1\%$ and $98.5 \pm 0.3\%$ in two separate runs.  We also confirmed at higher energy the striking behavior of the spin-1 tensor polarization recently found at IUCF.}}

@book{Morse:1953:MethTheorPhys,
	Address = {New York},
	Author = {Morse, Phillip M. and Feshbach, Herman},
	Date-Added = {2009-11-24 12:03:27 -0700},
	Date-Modified = {2009-11-24 12:03:27 -0700},
	Note = {Two volumes},
	Publisher = {McGraw-Hill Book Company, Inc.},
	Series = {International Series in Pure and Applied Physics},
	Title = {Methods of Theoretical Physics},
	Year = {1953}}

@article{Moser:1994:QuadSympMap,
	Author = {Moser, J{\"u}rgen K.},
	Date-Added = {2009-11-24 12:03:27 -0700},
	Date-Modified = {2009-11-24 12:03:27 -0700},
	Journal = mathz,
	Month = may,
	Number = {1},
	Pages = {417--430},
	Title = {On quadratic symplectic mappings},
	Volume = {216},
	Year = {1994},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/BF02572331}}

@misc{Mukunda:2009:HamTurnsRevisited,
	Author = {Mukunda, N. and Chaturvedi, S. and Simon, R.},
	Date-Added = {2009-11-24 12:03:27 -0700},
	Date-Modified = {2009-11-24 12:03:27 -0700},
	Howpublished = {Eprint \url{http://arxiv.org/abs/0904.4787}},
	Keywords = {rotation group, quaternions},
	Month = apr,
	Title = {Hamilton's theory of turns revisited},
	Year = {2009},
	Abstract = {We present a new approach to Hamilton's theory of turns for the groups $SO(3)$ and $SU(2)$ which renders their properties, in particular their composition law, nearly trivial and immediately evident upon inspection. We show that the entire construction can be based on binary rotations rather than mirror reflections.}}

@article{Muller:1992:ThomasPrec,
	Author = {Muller, Richard A.},
	Date-Added = {2009-11-24 12:03:27 -0700},
	Date-Modified = {2009-11-24 12:03:27 -0700},
	Journal = ajp,
	Month = apr,
	Number = {4},
	Pages = {313--317},
	Title = {Thomas precession: Where is the torque?},
	Volume = {60},
	Year = {1992},
	Abstract = {Special relativity appears to violate the conservation of angular momentum $\mathbf{L}$ since it predicts that an accelerated gyroscope will precess, i.e., $\mathbf{L}$ will change in the absence of any applied torque.  The paradox is resolved in a simple example by demonstrating that there is a torque present.  The mass distribution in the gyroscope undergoes a relativistic distortion, and the center of mass is displaced away from the position of the accelerating force.  The resulting torque $\pmb{\tau}=d\mathbf{L}/dt$.  The model also shows the physical origins of spin-orbit coupling and of the ``oscillating term.''  A related calculation shows why a moving magnetic dipole has an \emph{electric} dipole moment.}}

@article{MoortgatPick:2008:Challenge,
	Author = {Moortgat-Pick, Gudrid and Bailey, I. R. and Barber, Desmond P. and Baynham, E. and Birch, A. and Bradshaw, T. and Brummitt, A. and Carr, S. and Clarke, J. A. and Cooke, P. and Dainton, J. B. and Hartin, T. and Jenner, L. J. and Lintern, A. and Malysheva, L. I. and Malyshev, O. B. and Rochford, J. and Riemann, S. and Sch{\"a}licke, A. and Schmid, P. and Scott, D. J. and Ushakov, A. and Ivanyushenkov, Y.},
	Date-Added = {2009-11-24 12:02:25 -0700},
	Date-Modified = {2009-11-24 12:02:25 -0700},
	Journal = jphyscs,
	Pages = {112004},
	Title = {Challenge of polarized beams at future colliders},
	Volume = {110},
	Year = {2008},
	Abstract = {A short overview is given about the potential of polarized beams at future colliders is given.  In particular the baseline design for polarized beams at the ILC is presented and the physics case for polarized $e^{-}$ and $e^{+}$ is discussed. In order to fulfil the precision requirements, spin tracking from the source to the interaction point is needed.  Updates concerning the theoretical calculations as well as their implementation in simulation codes are reported.}}

@article{Moler:1978:19ways,
	Author = {Moler, Cleve B. and Van Loan, Charles F.},
	Date-Added = {2009-11-24 12:02:04 -0700},
	Date-Modified = {2009-11-24 12:02:04 -0700},
	Journal = siamr,
	Keywords = {matrix, exponential, matrix exponential, roundoff error, truncation error, condition},
	Number = {4},
	Pages = {801--836},
	Title = {Nineteen Dubious Ways to Compute the Exponential of a Matrix},
	Volume = {20},
	Year = {1978},
	Abstract = {In principle, the exponential of a matrix could be computed in many ways.  Methods involving approximation theory, differential equations, the matrix eigenvalues, and the matrix characteristic polynomial have been proposed.  In practice, consideration of computational stability and efficiency indicates that some of the methods are preferable to others, but that none are completely satisfactory.}}

@article{Moler:2003:19ways+25,
	Author = {Moler, Cleve B. and Van Loan, Charles F.},
	Date-Added = {2009-11-24 12:02:04 -0700},
	Date-Modified = {2009-11-24 12:02:04 -0700},
	Journal = siamr,
	Keywords = {matrix, exponential, matrix exponential, roundoff error, truncation error, condition},
	Number = {1},
	Pages = {3--49},
	Title = {Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later},
	Volume = {45},
	Year = {2003},
	Abstract = {In principle, the exponential of a matrix could be computed in many ways.  Methods involving approximation theory, differential equations, the matrix eigenvalues, and the matrix characteristic polynomial have been proposed.  In practice, consideration of computational stability and efficiency indicates that some of the methods are preferable to others, but that none are completely satisfactory.  Most of this paper was originally published in 1978.  An update, with a separate bibliography, describes a few recent developments.}}

@book{Misner:1973:Gravitation,
	Address = {San Francisco, CA},
	Author = {Misner, Charles W. and Thorne, Kip S. and Wheeler, John Archibald},
	Date-Added = {2009-11-24 12:01:36 -0700},
	Date-Modified = {2009-11-24 12:01:36 -0700},
	Publisher = {W. H. Freeman and Co.},
	Title = {Gravitation},
	Year = {1973}}

@book{Michelotti:1995:ClassDyn,
	Address = {New York, NY},
	Author = {Michelotti, Leo},
	Date-Added = {2009-11-24 12:01:23 -0700},
	Date-Modified = {2009-11-24 12:01:23 -0700},
	Publisher = {John Wiley \& Sons},
	Series = {Wiley Series in Beam Physics and Accelerator Technology},
	Title = {Intermediate Classical Dynamics with Applications to Beam Physics},
	Year = {1995}}

@article{Meiss:1992:SymplecticMaps,
	Author = {Meiss, James D.},
	Date-Added = {2009-11-24 12:00:56 -0700},
	Date-Modified = {2009-11-24 12:00:56 -0700},
	Journal = revmp,
	Month = jul,
	Number = {3},
	Pages = {795--848},
	Title = {Symplectic maps, variational principles, and transport},
	Volume = {64},
	Year = {1992},
	Abstract = {Symplectic maps are the discrete-time analog of Hamiltonian motion.  They arise in many applications including accelerator, chemical, condensed-matter, plasma, and fluid physics.  Twist maps correspond to Hamiltonians for which the velocity is a monotonic function of the canonical momentum.  Twist maps have a Lagrangian variational formulation.  One-parameter families of twist maps typically exhibit the full range of possible dynamics-from simple or integrable motion to complex or chaotic motion.  One class of orbits, the minimizing orbits, can be found throughout this transition; the properties of the minimizing orbits are discussed in detail.  Among these orbits are the periodic and quasiperiodic orbits, which form a scaffold in the phase space and constrain the motion of the remaining orbits.  The theory of transport deals with the motion of ensembles of trajectories.  The variational principle provides an efficient technique for computing the flux escaping from regions bounded by partial barriers formed from minimizing orbits.  Unsolved problems in the theory of transport include the explanation for algebraic tails in correlation functions, and its extension to maps of more than two dimensions.}}

@article{McLachlan:1998:Unified-Approach,
	Author = {McLachlan, Robert I. and Quispel, G. Reinhout W. and Robidoux, Nicolas},
	Date-Added = {2009-11-24 11:54:44 -0700},
	Date-Modified = {2009-11-24 11:54:44 -0700},
	Journal = prevl,
	Month = sep,
	Number = {12},
	Pages = {2399--2403},
	Title = {Unified Approach to {H}amiltonian Systems, {P}oisson Systems, Gradient Systems, and Systems with {L}yapunov Functions or First Integrals},
	Volume = {81},
	Year = {1998},
	Abstract = {We show that systems with a first integral (i.e., a constant of motion) or a Lyapunov function can be written as ``linear-gradient systems,'' $\dot{x}  =  L(x)\nabla V(x)$, for an appropriate matrix function $L$, with a generalization to several integrals or Lyapunov functions.  The discrete-time analog, $\Delta x / \Delta t = L\bar{\nabla}V$, where $\bar{\nabla}$ is a ``discrete gradient,'' preserves $V$ as an integral or Lyapunov function, respectively.}}

@incollection{McLachlan:2001:SixLectures,
	Address = {Cambridge, UK},
	Author = {McLachlan, Robert I. and Quispel, G. Reinhout W.},
	Booktitle = {Foundations of Computational Mathematics},
	Date-Added = {2009-11-24 11:54:44 -0700},
	Date-Modified = {2009-11-24 11:54:44 -0700},
	Editor = {DeVore, Ronald A. and Iserles, Arieh and S{\"u}li, Endre},
	Pages = {155--210},
	Publisher = {Cambridge University Press},
	Series = {London Mathematical Society Lecture Note Series},
	Title = {Six Lectures on the Geometric Integration of ODEs},
	Volume = {284},
	Year = {2001}}

@article{McLachlan:2002:SplitMeth,
	Author = {McLachlan, Robert I. and Quispel, G. Reinhout W.},
	Date-Added = {2009-11-24 11:54:44 -0700},
	Date-Modified = {2010-03-25 09:33:06 -0600},
	Doi = {10.1017/S0962492902000053},
	Journal = actanum,
	Keywords = {geometric integration},
	Month = jan,
	Pages = {341--434},
	Title = {Splitting methods},
	Volume = {11},
	Year = {2002},
	Abstract = {We survey splitting methods for the numerical integration of ordinary differential equations (ODEs).  Splitting methods arise when a vector field can be split into a sum of two or more parts that are each simpler to integrate than the original (in a sense to be made precise).  One of the main applications of splitting methods is in geometric integration, that is, the integration of vector fields that possess a certain geometric property (\emph{e.g.}, being Hamiltonian, or divergence-free, or possessing a symmetry or first integral) that one wants to preserve.  We first survey the classification of geometric properties of dynamical systems, before considering the theory and applications of splitting in each case.  Once a splitting is constructed, the pieces are composed to form the integrator; we discuss the theory of such `composition methods' and summarize the best currently known methods.  Finally, we survey applications from celestial mechanics, quantum mechanics, accelerator physics, molecular dynamics, and fluid dynamics, and examples from dynamical systems, biology and reaction-diffusion systems.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1017/S0962492902000053}}

@article{McLachlan:2006:GeomIntegr,
	Author = {McLachlan, Robert I. and Quispel, G. Reinhout W.},
	Date-Added = {2009-11-24 11:54:44 -0700},
	Date-Modified = {2010-03-25 09:35:53 -0600},
	Doi = {10.1088/0305-4470/39/19/S01},
	Journal = jphysa,
	Keywords = {geometric integration},
	Month = may,
	Number = {19},
	Pages = {5251--5285},
	Title = {Geometric Integrators for {ODE}s},
	Volume = {39},
	Year = {2006},
	Abstract = {Geometric integration is the numerical integration of a differential equation, while preserving one or more of its `geometric' properties exactly, i.e. to within round-off error.  Many of these geometric properties are of crucial importance in physical applications: preservation of energy, momentum, angular momentum, phase-space volume, symmetries, time-reversal symmetry, symplectic structure and dissipation are examples.  In this paper we present a survey of geometric numerical integration methods for ordinary differential equations.  Our aim has been to make the review of use for both the novice and the more experienced practitioner interested in the new developments and directions of the past decade.  To this end, the reader who is interested in reading up on detailed technicalities will be provided with numerous signposts to the relevant literature.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1088/0305-4470/39/19/S01}}

@article{Mayes:2009:Exact1DModelCSR,
	Author = {Mayes, Christopher and Hoffstaetter, Georg H.},
	Date-Added = {2009-11-24 11:54:21 -0700},
	Date-Modified = {2009-11-24 11:54:21 -0700},
	Doi = {10.1103/PhysRevSTAB.12.024401},
	Journal = prstab,
	Keywords = {coherent synchrotron radiation},
	Month = feb,
	Number = {2},
	Pages = {024401},
	Title = {Exact {1D} model for coherent synchrotron radiation with shielding and bunch compression},
	Volume = {12},
	Year = {2009},
	Abstract = {Coherent synchrotron radiation has been studied effectively using a one-dimensional model for the charge distribution in the realm of small angle approximations and high energies.  Here we use Jefimenko's form of Maxwell's equations, without such approximations, to calculate the exact wakefields due to this effect in multiple bends and drifts.  It has been shown before that the influence of a drift can propagate well into a subsequent bend.  We show, for reasonable parameters, that the influence of a previous bend can also propagate well into a subsequent bend, and that this is especially important at the beginning of a bend.  Shielding by conducting parallel plates is simulated using the image charge method.  We extend the formalism to situations with compressing and decompressing distributions, and conclude that simpler approximations to bunch compression usually overestimate the effect.  Additionally, an exact formula for the coherent power radiated by a Gaussian bunch is derived by considering the coherent synchrotron radiation spectrum, and is used to check the accuracy of wakefield calculations.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevSTAB.12.024401}}

@article{Maruskin:2009:SympSubvol,
	Author = {Maruskin, Jared M. and Scheeres, Daniel J. and Bloch, Anthony M.},
	Date-Added = {2009-11-24 11:53:50 -0700},
	Date-Modified = {2009-11-24 11:53:50 -0700},
	Journal = siamjads,
	Keywords = {Liouville theorem, integral invariant, symplectic manifold, symplectic eigenskeleton},
	Note = {A preprint version is available at \url{http://arxiv.org/abs/0709.1282}},
	Number = {1},
	Pages = {180--201},
	Title = {Dynamics of Symplectic Subvolumes},
	Volume = {8},
	Year = {2009},
	Abstract = {In this paper we analyze the evolution of $2k$-dimensional submanifolds in the $2n$-dimensional Hamiltonian phase space, with $k<n$.  We show that parasymplectic subvolumes (to be defined in the paper), which can be thought of as even-dimensional subvolumes that are initially parallel to $k$ of the symplectic planes, have a minimal obtainable $2k$-volume.  We define volume expansion factors along the flow, and also the projection factors one obtains by projecting the volumes onto various planes.  This structure can be computed by looking at various subdeterminants or Gram determinants of the state transition matrix.  We also relate these various subdeterminants to classical integral invariants, giving a practical analytical method for their computation.  We then indicate how this can be used to quantify probability expansions in asteroid or space debris tracking problems, with large uncertainty distributions along one of the symplectic planes.  We also show how local subvolume expansion leads to the local collapse of phase space along solution trajectories.  Despite this general tendency we will also compute a preferred, orthogonal, symplectic basis associated with any linear(ized) symplectomorphism that retains its orthogonality after being mapped to the final state.}}

@book{Marsden:1994:IntroMechSymm,
	Author = {Marsden, Jerrold E. and Ratiu, Tudor},
	Date-Added = {2009-11-24 11:53:26 -0700},
	Date-Modified = {2009-11-24 11:53:26 -0700},
	Publisher = {Springer-Verlag},
	Series = {Texts in Applied Mathematics},
	Title = {Introduction to Mechanics and Symmetry},
	Volume = {17},
	Year = {1994}}

@article{Marsden:2001:DiscreteMech,
	Author = {Marsden, Jerrold E. and West, Matthew},
	Date-Added = {2009-11-24 11:53:26 -0700},
	Date-Modified = {2009-11-24 11:53:26 -0700},
	Journal = actanum,
	Pages = {357--514},
	Title = {Discrete Mechanics and Variational Integrators},
	Volume = {10},
	Year = {2001},
	Abstract = {This paper gives a review of integration algorithms for finite dimensional mechanical systems that are based on discrete variational principles.  The variational technique gives a unified treatment of many symplectic schemes, including those of higher order, as well as a natural treatment of the discrete Noether theorem.  The approach also allows us to include forces, dissipation and constraints in a natural way.  Amongst the many specific schemes treated as examples, the Verlet, SHAKE, RATTLE, Newmark, and the symplectic partitioned Runge-Kutta schemes are presented.}}

@article{Mane:1986:DerivEqPol,
	Author = {Mane, Sateesh R.},
	Date-Added = {2009-11-24 11:52:08 -0700},
	Date-Modified = {2009-11-24 11:52:08 -0700},
	Journal = prevl,
	Month = jul,
	Number = {1},
	Pages = {78--81},
	Title = {Derivation of the equilibrium degree of polarization in high-energy electron storage rings},
	Volume = {57},
	Year = {1986},
	Abstract = {A semiclassical approach is used to derive, and extend to first order in $g-2$, the equilibrium degree of polarization in high-energy electron storage rings (the Derbenev-Kondratenko formula).  Statistical concepts are shown to be essential for an understanding of this phenomenon.  In so doing, some aspects of the polarization mechanism not previously recognized are uncovered.}}

@article{Mane:1986:DerivEqPolErr,
	Author = {Mane, Sateesh R.},
	Date-Added = {2009-11-24 11:52:08 -0700},
	Date-Modified = {2009-11-24 11:52:08 -0700},
	Journal = prevl,
	Month = sep,
	Note = {Errata},
	Number = {9},
	Pages = {1192},
	Title = {Derivation of the equilibrium degree of polarization in high-energy electron storage rings},
	Volume = {57},
	Year = {1986}}

@article{Mane:1987:ElectronSPI,
	Author = {Mane, Sateesh R.},
	Date-Added = {2009-11-24 11:52:08 -0700},
	Date-Modified = {2009-11-24 11:52:08 -0700},
	Journal = preva,
	Month = jul,
	Number = {1},
	Pages = {105--119},
	Title = {Electron-spin polarization in high-energy storage rings. {I}. {D}erivation of the equilibrium polarization},
	Volume = {36},
	Year = {1987},
	Abstract = {A detailed exposition on the origin and buildup of polarization in high-energy electron storage rings is presented.  Fundamental, but not clearly understood, theoretical results are rederived and clarified (Ya.S. Derbenev and A.M. Kondratenko, Zh.\ Eksp.\ Teor.\ Fiz.\ \textbf{64}, 1918 (1973) [Sov.\ Phys.---JETP \textbf{37}, 968 (1973)]).  It is explained how to diagonalize the Hamiltonian of a storage ring, in particular the spin-dependent terms, to the first order in Planck's constant.  Relevant perturbations, their time scales, and the various ensemble averages, are elucidated: the use of statistical concepts is shown to be essential to the calculation.  Semiclassical techniques are used to derive, and extend to first order in $g-2$, the equilibrium degree of polarization (the Derbenev-Kondratenko formula).  In so doing, some aspects of the polarization mechanism not previously recognized are uncovered.  Because Derbenev and Kondratenko use a different mathematical approach, a proof is given of the equivalence between their formalism and the one used here.}}

@article{Mane:1987:ElectronSPII,
	Author = {Mane, Sateesh R.},
	Date-Added = {2009-11-24 11:52:08 -0700},
	Date-Modified = {2009-11-24 11:52:08 -0700},
	Journal = preva,
	Month = jul,
	Number = {1},
	Pages = {120--130},
	Title = {Electron-spin polarization in high-energy storage rings. {II}. {E}valuation of the equilibrium polarization},
	Volume = {36},
	Year = {1987},
	Abstract = {A new algorithm is presented to evaluate the equilibrium degree of polarization in a high-energy electron storage ring (the Derbenev-Kondratenko formula).  The algorithm includes all modes of orbital motion, to arbitrary orders in principle, thus facilitating the calculation of so-called ``spin resonances,'' especially higher-order resonances.  The algorithm is applicable to storage rings of arbitrary geometry and energy, and, in particular, is able to deal with overlapping resonances.  Precautions are described to ensure stability of the algorithm.  In the approximation of linear orbital dynamics, a computer program has been written to implement this algorithm, and sample results are presented.}}

@article{Mane:1987:GeneralizedDK,
	Author = {Mane, Sateesh R.},
	Date-Added = {2009-11-24 11:52:08 -0700},
	Date-Modified = {2009-11-24 11:52:08 -0700},
	Journal = preva,
	Month = aug,
	Number = {3},
	Pages = {1469--1470},
	Title = {Generalization of the {D}erbenev-{K}ondratenko formula to arbitrary values of the particle gyromagnetic ratio},
	Volume = {36},
	Year = {1987},
	Abstract = {The formula for the asymptotic degree of radiative polarization in a high-energy storage ring (the Derbenev-Kondratenko formula) was recently rederived and extended to first order in $g-2$.  Here the formula is generalized to all values of $g$.}}

@article{Mane:1992:CurvLaplace,
	Author = {Mane, Sateesh R.},
	Date-Added = {2009-11-24 11:52:08 -0700},
	Date-Modified = {2009-11-24 11:52:08 -0700},
	Journal = nucima,
	Number = {1--2},
	Pages = {365--375},
	Title = {Solutions of {L}aplace's equation in two dimensions with a curved longitudinal axis},
	Volume = {321},
	Year = {1992},
	Abstract = {We derive a set of functions which satisfies Laplace's equation in two dimensions $x$ and $y$, when the longitudinal or $z$ axis has a constant but nonzero curvature.  The functions generalize the Fourier harmonics of the standard two-dimensional multipole expansion.  Both the electrostatic scalar potential and the magnetic vector potential, and the electric and magnetic fields, are treated.  Recursion relations are also supplied, in a form suitable for use in a computer program, to evaluate the multipoles to arbitrary order.  A comparison with other work in the field is also presented.}}

@article{Mane:1993:IntegrSpinOrbit,
	Author = {Mane, Sateesh R.},
	Date-Added = {2009-11-24 11:52:08 -0700},
	Date-Modified = {2009-11-24 11:52:08 -0700},
	Journal = physla,
	Month = jun,
	Number = {6},
	Pages = {411--414},
	Title = {Symplectic integrators for spin-orbit motion using {R}uth-{Y}oshida techniques},
	Volume = {177},
	Year = {1993},
	Abstract = {The theory of symplectic integrators for particle motion in accelerators is extended to include the particle spin.  The Yoshida-Ruth method is used to derive second- and higher-order integrators.  The connection with the Forest-Bengtsson-Reusch multimap integrators is established.}}

@article{Mane:2002:AnalyticalISF,
	Author = {Mane, Sateesh R.},
	Date-Added = {2009-11-24 11:52:08 -0700},
	Date-Modified = {2009-11-24 11:52:08 -0700},
	Journal = nucima,
	Month = jun,
	Number = {3},
	Pages = {277--297},
	Title = {Analytical solutions for the invariant spin field for model storage rings},
	Volume = {485},
	Year = {2002},
	Abstract = {We present nonperturbative analytical expressions for the invariant spin field for several storage ring models.  In particular, we solve the important models of a ring with one Snake and a single resonance driving term, and a ring with two Snakes and a single resonance driving term.  We also treat several other models, all of which contain Siberian Snakes.  Our solutions contain some novel features, e.g. in some cases the polarization does not point along the direction of the closed-orbit spin quantization axis.  We also include vertical resonance driving terms, and consider the contributions of sextupoles and higher order multipoles to the resonance driving terms, and argue that these can play a significant role in some circumstances.  We offer some brief remarks on the so-called Snake resonances.  We relate our results to observations of higher-order depolarizing spin resonances for polarized proton beams in a real ring, and offer some suggestions as to how our ideas might be verified.}}

@article{Mane:2002:ExactSolnST,
	Author = {Mane, Sateesh R.},
	Date-Added = {2009-11-24 11:52:08 -0700},
	Date-Modified = {2009-11-24 11:52:08 -0700},
	Journal = nucima,
	Month = mar,
	Number = {2--3},
	Pages = {328--338},
	Title = {Exact solutions for the spin tune for model storage rings},
	Volume = {480},
	Year = {2002},
	Abstract = {We present exact analytical expressions for the spin tune for arbitrary values of the orbital action for several storage ring models.  The models we treat contain Siberian Snakes, the use of which is essential to preserve the polarization of beams in high-energy proton storage rings.  Our solutions contain some novel features.  We also prove a previously conjectured claim about the behavior of spin tuneshifts in rings with multiple Snakes.  The conjecture is based on numerical simulations, but our proof is analytical, and also nonperturbative.}}

@article{Mane:2003:ExceptOrb,
	Author = {Mane, Sateesh R.},
	Date-Added = {2009-11-24 11:52:08 -0700},
	Date-Modified = {2009-11-24 11:52:08 -0700},
	Journal = nucima,
	Keywords = {polarized beam, storage ring, dynamical system},
	Number = {1--3},
	Pages = {52--89},
	Title = {Exceptional orbits: a new class of spin trajectories in circular accelerators},
	Volume = {498},
	Year = {2003},
	Abstract = {We claim there is a new class of spin trajectories in circular accelerators, which are not accounted for in current theories of spin dynamics.  We call them exceptional orbits.  On such orbits the \emph{spin} motion drives a secular growth of the \emph{orbital} amplitude(s).  Our results do not by themselves prove the spatial separation of spin states of a relativistic charged particle beam, but our findings are consistent with those of other workers.  Our findings \emph{do} invalidate the unconditional use of the semiclassical approximation to treat the orbital motion, to diagonalize the spin--orbit Hamiltonian.  We analyze a simple model in detail to demonstrate our ideas.  We review the canonical transformation theory of spin dynamics in storage rings, and extend it to account for exceptional orbits.  We also examine how exceptional orbits affect map-based algorithms.  We show that the algorithms can sometimes break down, in ways not hitherto suspected.  We show that on an exceptional orbit the secular rate of spin phase advance depends explicitly on the orbital arc-length, in contradiction to claims that the spin tune depends only on the orbital amplitudes.}}

@article{Mane:2003:Miles,
	Author = {Mane, Sateesh R.},
	Date-Added = {2009-11-24 11:52:08 -0700},
	Date-Modified = {2009-11-24 11:52:08 -0700},
	Journal = nucima,
	Keywords = {polarized beam, storage ring, dynamical system},
	Number = {1--3},
	Pages = {1--15},
	Title = {{\textsc{Miles}}: a new nonperturbative formalism to calculate the invariant spin field in circular accelerators},
	Volume = {498},
	Year = {2003},
	Abstract = {We describe a new nonperturbative algorithm called \textsc{Miles} to calculate the invariant spin field in circular accelerators.  It is a map-based algorithm, based exclusively on the field-theoretic transformation of a vector field under the flow in the orbital phase-space.  We employ the method to derive the exact analytical solution for a model of a planar ring with one Siberian Snake and a single resonance driving term.  This model is in some sense the classic problem in the field.  The solution contains new types of mathematical functions, which we call ``sine-factorial'' and ``sine-Bessel'' functions.  We also display the exact analytical solutions for several other storage ring models, including rings with two or more Snakes.  We compare our method against other formalisms, including numerical tracking programs.}}

@article{Mane:2004:CritiicalAnalysis,
	Author = {Mane, Sateesh R.},
	Date-Added = {2009-11-24 11:52:08 -0700},
	Date-Modified = {2009-11-24 11:52:08 -0700},
	Journal = nucima,
	Month = aug,
	Number = {3},
	Pages = {677--706},
	Title = {A critical analysis of the conventional theory of spin resonances in storage rings},
	Volume = {528},
	Year = {2004},
	Abstract = {We present a critical assessment of the conventional theory of spin resonances in storage rings.  We show that an application of the rigorous formula for the locations of spin-resonant orbits, using the nonperturbative off-axis solution for the spin tune, frequently fails to correctly identify the locations of depolarization.  We use recently discovered analytical solutions for the invariant spin field and spin tune in several storage ring models, to obtain a general overview of the spin dynamics and also of the polarization.  We calculate the long-term polarization and the depolarizing spin resonances for each model.  In particular, we present a detailed examination of the so-called ``Snake resonances''.  We also compare our analytical solutions against the results of numerical simulations.  We consider various measures of the degree of long-term polarization and point out fallacious tacit assumptions in the conventional literature.  We also present some new mathematical results linking the so-called sine-Bessel functions to the complete elliptic integral of the first kind.}}

@article{Mane:2005:AnalyISFErrata,
	Author = {Mane, Sateesh R.},
	Date-Added = {2009-11-24 11:52:08 -0700},
	Date-Modified = {2009-11-24 11:52:08 -0700},
	Journal = nucima,
	Month = may,
	Number = {2--3},
	Pages = {654},
	Title = {Erratum to ``{A}nalytical solutions for the invariant spin field for model storage rings'' \textit{Nucl.\ Instr.\ and Meth.\ A} \textbf{485} (2002) 277},
	Volume = {543},
	Year = {2005}}

@article{Mane:2005:HESpin,
	Author = {Mane, S. R. and Shatunov, Yu. M. and Yokoya, K.},
	Date-Added = {2009-11-24 11:52:08 -0700},
	Date-Modified = {2009-11-24 11:52:08 -0700},
	Journal = reppp,
	Month = sep,
	Number = {9},
	Pages = {1997--2265},
	Title = {Spin-polarized charged particle beams in high-energy accelerators},
	Volume = {68},
	Year = {2005},
	Abstract = {We present a comprehensive survey of the dynamics of spin-polarized beams in high-energy particle accelerators.  A major theme of this review is to clarify the distinction between the properties of an \emph{individual} particle---a \emph{spin}---and that of a \emph{beam}---the \emph{polarization}.  We include work from a number of institutions, including high- and medium-energy facilities, synchrotron light sources and muon storage rings (including a proposal to measure the muon electric dipole moment) and, briefly, linear accelerators and recirculating linacs.  High-precision tests of the Standard Model using spin-polarized beams are reviewed; also innovative studies using spin dynamics as a tool for accelerator physics \emph{per se}.  We include important historical works as well as modern developments in the field.  The fundamental theory is derived in detail, starting from the basic principles of quantum mechanics, electrodynamics and statistical mechanics, as well as `accelerator physics'.  The principal theoretical formulae in the field (Froissart-Stora, Sokolov-Ternov and Derbenev-Kondratenko) are presented, with in-depth attention to the quantum-statistical mechanics, as opposed to purely `accelerator physics'.}}

@article{Mane:2005:Snakes,
	Author = {Mane, S. R. and Shatunov, Yu. M. and Yokoya, K.},
	Date-Added = {2009-11-24 11:52:08 -0700},
	Date-Modified = {2009-11-24 11:52:08 -0700},
	Journal = jphysg,
	Month = sep,
	Number = {9},
	Pages = {R151--R209},
	Title = {Siberian {S}nakes in high-energy accelerators},
	Volume = {31},
	Year = {2005},
	Abstract = {We review modern techniques to accelerate spin-polarized beams to high energy and to preserve their polarization in storage rings.  Crucial to the success of such work is the use of so-called Siberian Snakes.  We explain these devices and the reason for their necessity.  Closely related to Snakes is the concept of `spin rotators'.  The designs and merits of several types of Snakes and spin rotators are examined.  Theoretical work with Snakes and spin rotators, and experimental results from several storage rings, are reviewed, including the so-called Snake resonances.}}

@article{Mane:2007:DeutSpinFlip,
	Author = {Mane, Sateesh R.},
	Date-Added = {2009-11-24 11:52:08 -0700},
	Date-Modified = {2009-11-24 11:52:08 -0700},
	Journal = prstab,
	Month = nov,
	Number = {11},
	Pages = {111001},
	Title = {Deuteron spin-flip resonance widths and the spin response function},
	Volume = {10},
	Year = {2007},
	Abstract = {The spin response function is used to analyze the spin-flip resonance widths of stored polarized deuteron beams.  It is found, using simple model assumptions, that the contribution of the vertical betatron oscillations (for an rf radial dipole field spin-flipper) reduces the resonance width by an amount in good agreement with recent measurements.  It is also noted that, for spin-flip measurements with an rf-solenoid spin flipper, the spin response formalism \emph{also} yields an answer consistent with experimental data.}}

@article{Mane:2008:AnSolnSRF,
	Author = {Mane, Sateesh R.},
	Date-Added = {2009-11-24 11:52:08 -0700},
	Date-Modified = {2009-11-24 11:52:08 -0700},
	Doi = {10.1016/j.nima.2008.11.131},
	Journal = nucima,
	Keywords = {spin dynamics},
	Month = mar,
	Number = {2},
	Pages = {383--390},
	Title = {Analytical solutions for spin response functions in model storage rings with {S}iberian {S}nakes},
	Volume = {600},
	Year = {2008},
	Abstract = {I present analytical solutions for the spin response functions for radial field rf dipole spin flippers in models of storage rings with one Siberian Snake or two diametrically opposed orthogonal Siberian Snakes. The solutions can serve as benchmarks tests for computer programs. The spin response functions can be used to calculate the resonance strengths for radial field rf dipole spin flippers in storage rings.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.nima.2008.11.131}}

@article{Mane:2008:StoredPolarized,
	Author = {Mane, Sateesh R.},
	Date-Added = {2009-11-24 11:52:08 -0700},
	Date-Modified = {2009-11-24 11:52:08 -0700},
	Journal = nucima,
	Month = mar,
	Number = {2--3},
	Pages = {188--212},
	Title = {Stored polarized beams: \textsc{Miles}, \textsc{Limes}, \textsc{Smile}, sine-{B}essels and \textsc{Sodom2} too},
	Volume = {587},
	Year = {2008},
	Abstract = {The fundamental theory underlying several computational algorithms for the spin dynamics of stored polarized beams is analyzed.  Particular attention is paid to the consequences of the use of finite-dimensional matrices and/or Fourier series.  The single resonance model with a pair of diametrically opposed nonorthogonal pointlike Siberian Snakes is analyzed in detail to clarify several points pertaining to the above algorithms, and more generally to the spin dynamics of stored polarized beams in rings with Snakes.  New analytical results are also presented, e.g. for the spin tune shift in the nonorthogonal Snakes model, and the sine-Bessel functions for the orthogonal Snakes model.  Many results are derived using multiple algorithms, which serves as a check on their mutual consistency.}}

@article{Mane:2009:CommentFullSpinFlip,
	Author = {Mane, Sateesh R.},
	Date-Added = {2009-11-24 11:52:08 -0700},
	Date-Modified = {2009-11-24 11:52:08 -0700},
	Doi = {10.1103/PhysRevSTAB.12.099001},
	Journal = prstab,
	Keywords = {spin dynamics},
	Month = sep,
	Number = {9},
	Pages = {099001},
	Title = {Comment on ``{F}ull spin flipping in the presence of full {S}iberian {S}nake''},
	Volume = {12},
	Year = {2009},
	Abstract = {Bai and Roser [\textit{Phys.\ Rev.\ ST Accel.\ Beams} \textbf{11}, 091001 (2008), \textit{Phys.\ Rev.\ ST Accel.\ Beams} \textbf{12}, 019901(E) (2009)] have published an idea for a design of a spin flipper, consisting of two radial field rf dipoles with correlated phases, to operate with full strength Siberian Snakes, at a spin tune of $1/2$. Some details of their design analysis are oversimplified.
},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevSTAB.12.099001}}

@techreport{Mane:2009:PTCSpin,
	Address = {Tsukuba, Japan},
	Author = {Mane, Sateesh R.},
	Date-Added = {2009-11-24 11:52:08 -0700},
	Date-Modified = {2009-11-24 11:52:08 -0700},
	Institution = {KEK},
	Keywords = {spin dynamics},
	Month = sep,
	Number = {2009-8},
	Title = {{PTC} {SPIN}: benchmark tests for analytically solvable models},
	Type = {KEK Report},
	Year = {2009},
	Abstract = {{\'E}tienne Forest has extended PTC (the Polymorphic Tracking Code) to treat spin-orbit coupling. I have run 
several benchmark tests to compare the PTC output with the solutions from various analytically solvable 
models, including thin Siberian Snakes. I present the details here. PTC has passed all of the tests.}}

@article{Mahan:2005:ClassWavesNLLatt,
	Author = {Mahan, Gerald D.},
	Date-Added = {2009-11-24 11:51:35 -0700},
	Date-Modified = {2009-11-24 11:51:35 -0700},
	Doi = {10.1103/PhysRevB.72.144302},
	Journal = prevb,
	Month = oct,
	Number = {14},
	Pages = {144302},
	Title = {Classical waves on nonlinear lattices},
	Volume = {72},
	Year = {2005},
	Abstract = {We discuss the solution to classical vibrations on several nonlinear lattices in one dimension. One lattice has nearest-neighbor potential energy with both quadratic and quartic terms in the relative displacements $q$. Another lattice has the potential energy terms going as $\cosh(q)$. Exact analytical solutions are derived for periodic waves that have a period of two, three, and four lattice constants. Several of these cases employ Jacobian elliptic functions, while one solution uses ordinary cosines. The quadratic term in the potential energy can have either sign, and a double well occurs when it is negative and the quartic is positive. Solutions are also found for this double-well potential.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevB.72.144302}}

@article{Mahan:2009:ClassWaves2Qn,
	Author = {Mahan, Gerald D.},
	Date-Added = {2009-11-24 11:51:35 -0700},
	Date-Modified = {2009-11-24 11:51:35 -0700},
	Journal = jmathp,
	Month = jan,
	Number = {1},
	Pages = {012701},
	Title = {Classical waves on nonlinear lattices. {II}. {$Q^n$}},
	Volume = {50},
	Year = {2009},
	Abstract = {Exact analytical solutions are found for classical vibrations of nonlinear oscillators with higher powers of spring constants, such as $Q^6$ and $Q^8$.  The solutions are based on a new type of elliptic function that has been created to solve these problems.}}

@book{MacKay:1987:HamDynSys,
	Address = {Bristol, England},
	Date-Added = {2009-11-24 11:51:04 -0700},
	Date-Modified = {2009-11-24 11:51:04 -0700},
	Editor = {MacKay, Robert S. and Meiss, James D.},
	Publisher = {Adam Hilger},
	Title = {Hamiltonian Dynamical Systems: A Preprint Selection},
	Year = {1987}}

@article{MacKay:1995:RecProgressHamDyn,
	Author = {MacKay, Robert S.},
	Date-Added = {2009-11-24 11:51:04 -0700},
	Date-Modified = {2009-11-24 11:51:04 -0700},
	Journal = physd,
	Month = sep,
	Number = {1--2},
	Pages = {122--133},
	Title = {Recent progress and outstanding problems in Hamiltonian dynamics},
	Volume = {86},
	Year = {1995},
	Abstract = {Progress in Hamiltonian dynamics over the last five years is reviewed, some outstanding problems are identified, and recent work with Aubry on ``discrete breathers'' is summarised.}}

@inproceedings{MacKay:2006:DecohMeas,
	Author = {MacKay, William W.},
	Crossref = {EPAC:2006},
	Date-Added = {2009-11-24 11:51:04 -0700},
	Date-Modified = {2009-11-24 11:51:04 -0700},
	Title = {On the Feasibility of a Spin Decoherence Measurement},
	Abstract = {In this paper, I study the feasibility of making a turn-by-turn spin measurement to extract the spin tune from a polarized beam injected perpendicular to the stable spin direction.  For the ideal case of a zero-emittance beam with no spin-tune spread, there would be no spin decoherence, and a measurement of the spin tune could easily be made by collecting turn-indexed polarization data over several million turns.  However, in a real beam there is a momentum spread which provides a spin-tune spread.  With a coasting beam the tune spread can cause decoherence of the spins resulting in a fast depolarization of the beam in as few as a thousand turns.  With synchrotron oscillations the decoherence time can be greatly increased, so that a measurement becomes feasible with summation of the turn-by-turn data from a reasonable number of bunches ($\lesssim 100$).  Three cases of $1$, $2$, and $2\frac{1}{2} Siberian snakes are considered.  By using spin tune measurements for both the single and double snake cases, we could vastly improve the calibration of the optimum settings for the RHIC snakes.}}

@inproceedings{MacKay:2006:SpinTransport,
	Author = {MacKay, William W. and Luccio, Alfredo U. and Tsoupas, Nicholaos and Takano, Junpei},
	Crossref = {EPAC:2006},
	Date-Added = {2009-11-24 11:51:04 -0700},
	Date-Modified = {2009-11-24 11:51:04 -0700},
	Title = {Spin Transport from {AGS} to {RHIC} with Two Partial {S}iberian Snakes in {AGS}},
	Abstract = {The stable spin direction in the RHIC rings is vertical.  With one or two partial helical Siberian snakes in the AGS, the stable spin direction at extraction is not vertical.  Interleaved vertical and horizontal bends in the transport line between AGS and the RHIC rings also tend to tip the spin away from the vertical.  In order to maximize polarization in RHIC, we examined several options to improve the matching of the stable spin direction during beam transfer from the AGS to each of the RHIC rings.  While the matching is not perfect, the most economical method appears to be a lowering of the injection energy by one unit of $G\gamma$ from 46.5 to 45.5.}}

@techreport{MacKay:2007:AccelDH,
	Address = {Upton, NY},
	Author = {MacKay, William W.},
	Date-Added = {2009-11-24 11:51:04 -0700},
	Date-Modified = {2009-11-24 11:51:04 -0700},
	Institution = {Brookhaven National Laboratory},
	Month = nov,
	Number = {C-A/AP/296},
	Title = {Prospects for Acceleration of Deuterons and Helions},
	Year = {2007},
	Abstract = {In order to study the spin structure of the neutron at high energy, a beam rich in polarized neutrons needs to be developed.  The neutron has no charge and cannot be accelerated, so either deuterons or helions must be considered.  When it comes to spin manipulation and stability of the polarization in a circular accelerator, it is the anomalous part of the magnetic moment which is important.  If the anomaly is too small, then manipulation becomes difficult as in the case of deuterons---spin rotators and Siberian snakes become ineffective.  ${}^3\text{He}$ nuclei appear to be the easiest choice for a polarized neutron beam.  In this paper I discuss the prospects for both helions and deuterons as polarized beams in RHIC or in an electron-ion collider.}}

@inproceedings{Machida:2001:BeamOpticsFFAG,
	Author = {Machida, Shinji and Forest, {\'E}tienne},
	Crossref = {CYC:2001},
	Date-Added = {2009-11-24 11:50:17 -0700},
	Date-Modified = {2009-11-24 11:50:17 -0700},
	Pages = {204--207},
	Title = {Beam Optics and Dynamics of FFAG Accelerators: Application of {TPSA} and Polymorphism},
	Year = {2001},
	Abstract = {As a versatile accelerator, especially for application with high repetition and high current beams, the FFAG (Fixed Field Alternating Gradient) synchrotron attracts growing attention.  We will discuss the design procedure and beam dynamics study from a modern view based on recent progress in high-energy accelerators.  Comparison between brute force tracking with direct use of 3D field mapping data and a newly introduced way modeling the entire field region with a collection of thin elements is presented.}}

@article{Machida:2006:LEmitGrowFFAG,
	Author = {Machida, Shinji},
	Date-Added = {2009-11-24 11:50:17 -0700},
	Date-Modified = {2009-11-24 11:50:17 -0700},
	Journal = prstab,
	Keywords = {ffag, emittance growth},
	Month = oct,
	Number = {10},
	Pages = {104002},
	Title = {Longitudinal emittance blowup in fixed field alternating gradient muon accelerators},
	Volume = {9},
	Year = {2006},
	Abstract = {The fixed field alternating gradient (FFAG) accelerator is proposed as a muon accelerator because of its large aperture and no need of magnet ramping.  In particular, the nonscaling type of FFAG has been studied because of its simple magnets and its unique acceleration method using the path out of the rf bucket.  A recent 6D tracking study reveals, however, that the time of flight difference due to transverse amplitude causes the longitudinal emittance blowup which limits the transverse acceptance.  This is a serious problem for an accelerator that is expected to accelerate a muon beam with huge transverse emittance.  Two methods of curing the problem are examined by particle tracking.  One is higher rf voltage and the other is higher harmonic rf in addition to the fundamental one.  A 50\% increase of rf voltage suppresses the emittance blowup.  Second and third harmonic rf also improve the final momentum spread.  Both methods work fine in a single FFAG system.  However, a few percent of particle loss is inevitable when two FFAG are cascaded.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevSTAB.9.104002}}

@article{Machida:2007:OrbitOptics,
	Author = {Machida, Shinji and Kelliher, David J.},
	Date-Added = {2009-11-24 11:50:17 -0700},
	Date-Modified = {2009-11-24 11:50:17 -0700},
	Doi = {10.1103/PhysRevSTAB.10.114001},
	Journal = prstab,
	Keywords = {ffag},
	Month = nov,
	Number = {11},
	Pages = {114001},
	Title = {Orbit and optics distortion in fixed field alternating gradient muon accelerators},
	Volume = {10},
	Year = {2007},
	Abstract = {In a linear nonscaling fixed field alternating gradient (FFAG) accelerator, betatron tunes vary over a wide range and a beam has to cross integer and half-integer tunes several times.  Although it is plausible to say that integer and half-integer resonances are not harmful if the crossing speed is fast, no quantitative argument exists.  With tracking simulation, we studied orbit and optics distortion due to alignment and magnet errors.  It was found that the concept of integer and half-integer resonance crossing is irrelevant to explain beam behavior in a nonscaling FFAG when acceleration is fast and betatron tunes change quickly.  In a muon FFAG accelerator, it takes 17 turns for acceleration and the betatron tunes change more than 10, for example.  Instead, the orbit and optics distortion is excited by random dipole and quadrupole kicks.  The latter causes beam size growth because the beam starts tumbling in phase space, but not necessarily with emittance growth.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevSTAB.10.114001}}

@inproceedings{Machida:2008:CollectiveEMMA,
	Author = {Machida, Shinji and Kelliher, David J. and Berg, J. Scott and Koscielniak, Shane},
	Crossref = {EPAC:2008},
	Date-Added = {2009-11-24 11:50:17 -0700},
	Date-Modified = {2009-11-24 11:50:17 -0700},
	Keywords = {ffag},
	Pages = {1652--1654},
	Title = {Collective Effects in the {EMMA} Non-scaling {FFAG}},
	Abstract = {EMMA is an electron accelerator to study beam dynamics in a linear nonscaling FFAG. We wish to verify that the behavior predicted by the theory and simulation is correct. In particular, we will study a novel accelerating mode outside an rf bucket (so-called serpentine acceleration), and the effects of crossing ``resonances''. In EMMA, some collective effects become a concern even though the beam stays in the ring for only 10 to 20 turns. We report studies of direct space charge, beam loading, and other collective effects with tracking simulations. There is strong possibility of a negative-mass instability for some operation modes.}}

@article{Machida:2008:ResCrossFFAG,
	Author = {Machida, Shinji},
	Date-Added = {2009-11-24 11:50:17 -0700},
	Date-Modified = {2009-11-24 11:50:17 -0700},
	Doi = {10.1103/PhysRevSTAB.11.094003},
	Journal = prstab,
	Month = sep,
	Number = {9},
	Pages = {094003},
	Title = {Resonance crossing and dynamic aperture in nonscaling fixed field alternating gradient accelerators},
	Volume = {11},
	Year = {2008},
	Abstract = {Operation with natural chromaticity in a linear nonscaling fixed field alternating gradient (FFAG) accelerator causes crossing of the low order resonances such as integer and half-integer.  Although those resonances are not systematic ones, small errors, such as a typical misalignment of $10\,\mu\mathrm{m}$ rms, significantly increase particle amplitude when the accelerator is operated with a slow acceleration rate.  For example, there is practically no dynamic aperture if it takes 1000 turns to finish the whole acceleration cycle.  Chromaticity correction with sextupole and octupole reduces the maximum available dynamic aperture in a lattice without errors.  On the other hand, the accelerator becomes less sensitive to errors.  To use a nonscaling FFAG for applications where, unlike a muon accelerator, the large acceptance is not a high priority demand (such as a proton driver or a particle therapy accelerator), chromaticity correction seems to be an essential ingredient.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevSTAB.11.094003}}

@article{Machida:2009:ScFFAGOrbit,
	Author = {Machida, Shinji},
	Date-Added = {2009-11-24 11:50:17 -0700},
	Date-Modified = {2009-11-24 11:50:17 -0700},
	Doi = {10.1103/PhysRevLett.103.164801},
	Journal = prevl,
	Keywords = {ffag},
	Month = oct,
	Number = {16},
	Pages = {164801},
	Title = {Scaling Fixed-Field Alternating Gradient Accelerators with a Small Orbit Excursion},
	Volume = {103},
	Year = {2009},
	Abstract = {A novel scaling type of fixed-field alternating gradient (FFAG) accelerator is proposed that solves the major problems of conventional scaling and nonscaling types. This scaling FFAG accelerator can achieve a much smaller orbit excursion by taking a larger field index $k$. A triplet focusing structure makes it possible to set the operating point in the second stability region of Hill's equation with a reasonable sensitivity to various errors. The orbit excursion is about 5 times smaller than in a conventional scaling FFAG accelerator and the beam size growth due to typical errors is at most 10\%.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevLett.103.164801}}

@book{Lichtenberg:1969:PSDynamics,
	Address = {New York},
	Author = {Lichtenberg, Allan J.},
	Date-Added = {2009-11-24 11:48:44 -0700},
	Date-Modified = {2009-11-24 11:48:44 -0700},
	Publisher = {John Wiley \& Sons},
	Series = {Wiley Series in Plasma Physics},
	Title = {Phase-Space Dynamics of Particles},
	Year = {1969},
	Abstract = {This monograph is a review of phase-space concepts for beams, accelerators, and confined particles together with descriptions of their relationship to basic theory.

Beginning with an introduction to the concepts of phase-space dynamics and a presentation of its fundamental theories, the text proceeds through a treatment of adiabatic invariance, a discussion of transformations of the phase space associated with a collection of particles, and a description of beam transport systems.  The final chapters consider selected topics from the areas of accelerator applications and the confinement, trapping, and heating of charged particles.  The underlying unity of the various subjects is emphasized throughout.}}

@book{Lichtenberg:1992:RegChaotic,
	Author = {Lichtenberg, Allan J. and Lieberman, Michael A.},
	Date-Added = {2009-11-24 11:48:44 -0700},
	Date-Modified = {2009-11-24 11:48:44 -0700},
	Edition = {Second},
	Publisher = {Springer-Verlag},
	Series = {Applied Mathematical Sciences},
	Title = {Regular and Chaotic Dynamics},
	Volume = {38},
	Year = {1992},
	Abstract = {This book treats nonlinear dynamics in both Hamiltonian and dissipative systems.  The emphasis is on the mechanics for generating chaotic motion, methods of calculating the transitions from regular to chaotic motion, and the dynamical and statistical properties of the dynamics when it is chaotic.  The book is intended as a self consistent treatment of the subject at the graduate level and as a reference for scientists already working in the field.  It emphasizes both methods of calculation and results.  It is accessible to physicists and engineers without training in modern mathematics.  The new edition brings the subject matter in a rapidly expanding field up to date, and has greatly expanded the treatment of dissipative dynamics to include most important subjects.  It can be used as a graduate text for a two semester course covering both Hamiltonian and dissipative dynamics.}}

@article{LeeWhiting:1970:ThirdOrdAberr,
	Author = {Lee-Whiting, Graham E.},
	Date-Added = {2009-11-24 11:46:22 -0700},
	Date-Modified = {2009-11-24 11:46:22 -0700},
	Journal = nucim,
	Month = jun,
	Number = {2},
	Pages = {232--244},
	Title = {Third-order aberrations of a magnetic quadrupole lens},
	Volume = {83},
	Year = {1970},
	Abstract = {General expressions for the aberration coefficients are derived in a form in which derivatives of the magnetic gradient do not appear.  Specializations to a segment of the optic axis on which the gradient is uniform and to the rectangular model are given.  A segment on which the gradient varies is treated by expansion in a power series; the expansion coefficients depend on form-factors similar to those occurring in the first-order theory.  Momentum-dependent aberrations and the transit-time are handled in the same way.  In all cases laws are given for combining the effects of two adjacent segments.  The calculations do not support the idea that hyperboloidal pole-ends result in reduced aberrations.}}

@article{LeeWhiting:1990:MotionFringe,
	Author = {Lee-Whiting, Graham E.},
	Date-Added = {2009-11-24 11:46:22 -0700},
	Date-Modified = {2009-11-24 11:46:22 -0700},
	Doi = {10.1016/0168-9002(90)91825-V},
	Journal = nucima,
	Month = sep,
	Number = {1--2},
	Pages = {31--71},
	Title = {First- and second-order motion through the fringing field of a bending magnet},
	Volume = {294},
	Year = {1990},
	Abstract = {With the assumption that the fringing field of a straight-edged bending magnet is two-dimensional, exact expression are derived for all the first- and second-order matrix elements corresponding to motion in the median symmetry plane.  The analogous matrix elements for skew trajectories are related to the solution of an explicitly given differential equation.  Each matrix element is expanded to three terms in powers of the reciprocal of the particle stiffness.  All expressions are checked by comparison with numerical integrations of the trajectory equations for a typical field distribution.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/0168-9002(90)91825-V}}

@article{Lee:2005:QuasiperiodicComm,
	Author = {Lee, S. Y. and Mane, S. R.},
	Date-Added = {2009-11-24 11:45:58 -0700},
	Date-Modified = {2009-11-24 11:45:58 -0700},
	Journal = prstab,
	Month = aug,
	Number = {8},
	Pages = {089001},
	Title = {Comment on ``{Q}uasiperiodic spin-orbit motion and spin tunes in storage rings''},
	Volume = {8},
	Year = {2005},
	Abstract = {Contrary to the claim of the recent publication by Barber, Ellison, and Heinemann [Phys. Rev. ST Accel. Beams \textbf{7}, 124002 (2004).], we explain in this Comment that (1) the snake resonances are spin depolarizing resonances just like other spin depolarizing resonances and (2) the perturbed spin tune is useful to understand depolarization phenomena.}}

@book{Lee:1997:SpinDynamics,
	Address = {Singapore},
	Author = {Lee, S. Y.},
	Date-Added = {2009-11-24 11:45:42 -0700},
	Date-Modified = {2009-11-24 11:45:42 -0700},
	Publisher = {World Scientific},
	Title = {Spin Dynamics and Snakes in Synchrotrons},
	Year = {1997}}

@techreport{Lapostolle:1989:PLinacTheorHist,
	Address = {Los Alamos, NM},
	Author = {Lapostolle, Pierre M.},
	Date-Added = {2009-11-24 11:45:07 -0700},
	Date-Modified = {2009-11-24 11:45:07 -0700},
	Institution = {Los Alamos National Laboratory},
	Month = jul,
	Number = {LA-11601-MS},
	Title = {Proton Linear Accelerators: A Theoretical and Historical Introduction},
	Year = {1989}}

@phdthesis{Koseleff:1994:PhDthesis,
	Author = {Koseleff, Pierre-Vincent},
	Date-Added = {2009-11-24 11:43:14 -0700},
	Date-Modified = {2009-11-24 11:43:14 -0700},
	Note = {Translated by Dani{\`e}le Boucher, with technical assistance from {\'E}tienne Forest. Available also as Technical Report LBID-2030 Rev.\ from Lawrence Berkely Laboratory},
	School = {{\'E}cole Polytechnique},
	Title = {Formal Calculus for Lie Methods in Hamiltonian Mechanics},
	Year = {1994}}

@article{Kane:1999:SympEPVarInteg,
	Author = {Kane, C. and Marsden, Jerrold E. and Ortiz, Michael},
	Date-Added = {2009-11-24 11:41:07 -0700},
	Date-Modified = {2009-11-24 11:41:07 -0700},
	Journal = jmathp,
	Month = jul,
	Number = {7},
	Pages = {3353--3371},
	Title = {Symplectic-energy-momentum preserving variational integrators},
	Volume = {40},
	Year = {1999},
	Abstract = {The purpose of this paper is to develop variational integrators for conservative mechanical systems that are symplectic and energy and momentum conserving.  To do this, a space--time view of variational integrators is employed and time step adaptation is used to impose the constraint of conservation of energy.  Criteria for the solvability of the time steps and some numerical examples are given.}}

@techreport{Kaltchev:2009:SmearLRBmBm,
	Address = {Geneva},
	Author = {Kaltchev, Dobrin I. and Herr, Werner},
	Date-Added = {2009-11-24 11:40:44 -0700},
	Date-Modified = {2009-11-24 11:40:44 -0700},
	Institution = {European Organization for Nuclear Research},
	Keywords = {beam-beam interaction},
	Month = jul,
	Number = {CERN-ATS-2009},
	Title = {Analytical calculation of the smear for long-range beam-beam interactions},
	Year = {2009},
	Abstract = {The Lie-algebraic method is used to develop generalized Courant-Snyder invariant in the presence of an arbitrary number of beam-beam collisions, head-on or long-range, in a storage ring collider. The invariant is obtained by concatenating nonlinear beam-beam maps in the horizontal plane and to first order in the beam-beam parameter. Tracking evidence is presented to illustrate that with LHC parameters the invariant is indeed preserved and can be used to predict the smear of horizontal emittance observed in tracking simulations. We discuss the limits of applicability of this model for realistic LHC collision schemes.}}

@book{Jose:1998:CD,
	Address = {Cambridge, UK},
	Author = {Jos{\'e}, Jorge V. and Saleton, Eugene J.},
	Date-Added = {2009-11-24 11:40:19 -0700},
	Date-Modified = {2009-11-24 11:40:19 -0700},
	Publisher = {Cambridge University Press},
	Title = {Classical Dynamics: A Contemporary Approach},
	Year = {1998}}

@article{Juarez:1982:TurnsLorentz,
	Author = {Ju{\'a}rez, Manuela and Santander, Mariano},
	Date-Added = {2009-11-24 11:40:19 -0700},
	Date-Modified = {2009-11-24 11:40:19 -0700},
	Journal = jphysa,
	Month = nov,
	Number = {11},
	Pages = {3411--3424},
	Title = {Turns for the {L}orentz Group},
	Volume = {15},
	Year = {1982},
	Abstract = {A geometrical description of the composition law for pure inertial transformations in relativity is developed, in close analogy with the description of rotations by means of turns.  This affords a very intuitive and visual image of all problems involving a composition of velocities, and clearly shows the appearance of hyperbolic geometry in relativistic kinematics.  The pertinent geometrical constructions as well as some applications are discussed.  For the case of light the preceding constructions are surprisingly simple, and from them emerges a connection between the geometrical idea of parallelism angle and the physical Doppler effect.  A slide rule which can be used to carry out all needed computations is also described.}}

@article{Jia:2006:GeomIntegrMTS,
	Author = {Jia, Zhidong and Leimkuhler, Ben},
	Date-Added = {2009-11-24 11:39:50 -0700},
	Date-Modified = {2009-11-24 11:39:50 -0700},
	Journal = jphysa,
	Month = may,
	Number = {19},
	Pages = {5379--5403},
	Title = {Geometric integrators for multiple time-scale simulation},
	Volume = {39},
	Year = {2006},
	Abstract = {In this paper, we review and extend recent research on averaging integrators for multiple time-scale simulation such as are needed for physical $N$-body problems including molecular dynamics, materials modelling and celestial mechanics.  A number of methods have been proposed for direct numerical integration of multiscale problems with special structure, such as the mollified impulse method (Garcia-Archilla, Sanz-Serna and Skeel 1999 \textit{SIAM J. Sci. Comput.} \textbf{20} 930--63) and the reversible averaging method (Leimkuhler and Reich 2001 \textit{J. Comput. Phys.} \textbf{171} 95--114).  Features of problems of interest, such as thermostatted coarse-grained molecular dynamics, require extension of the standard framework.  At the same time, in some applications the computation of averages plays a crucial role, but the available methods have deficiencies in this regard.  We demonstrate that a new approach based on the introduction of shadow variables, which mirror physical variables, has promised for broadening the usefulness of multiscale methods and enhancing accuracy of or simplifying computation of averages.  The shadow variables must be computed from an auxiliary equation.  While a geometric integrator in the extended space is possible, in practice we observe enhanced long-term energy behaviour only through use of a variant of the method which controls drift of the shadow variables using dissipation and sacrifices the formal geometric properties such as time-reversibility and volume preservation in the enlarged phase space, stabilizing the corresponding properties in the physical variables.  The method is applied to a gravitational three-body problem as well as a partially thermostatted model problem for a dilute gas of diatomic molecules.}}

@inproceedings{Abell:1994:TSDomConv,
	Author = {Abell, Dan T. and Dragt, Alex J.},
	Crossref = {SPMSR:1992},
	Date-Added = {2009-11-24 11:37:37 -0700},
	Date-Modified = {2010-03-30 17:19:19 -0600},
	Doi = {10.1063/1.45111},
	Keywords = {Taylor series, Taylor map, transfer map, domain of convergence},
	Pages = {230--259},
	Title = {Taylor Series Maps and their Domain of Convergence},
	Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.45111}}

@phdthesis{Abell:1995:PhDthesis,
	Address = {College Park, MD},
	Author = {Abell, Dan T.},
	Date-Added = {2009-11-24 11:37:37 -0700},
	Date-Modified = {2009-11-24 11:37:37 -0700},
	Keywords = {Taylor series, Taylor map, transfer map, domain of convergence, dynamical system, Hamiltonian, Cremona map},
	School = {University of Maryland},
	Title = {Analytic Properties and Cremona Approximation of Transfer Maps for Hamiltonian Systems},
	Year = {1995}}

@article{Ahrens:2009:InvarQuadSphere,
	Author = {Ahrens, Cory and Beylkin, Gregory},
	Date-Added = {2009-11-24 11:36:53 -0700},
	Date-Modified = {2009-11-24 11:36:53 -0700},
	Doi = {10.1098/rspa.2009.0104},
	Journal = procrsa,
	Keywords = {numerical quadrature},
	Month = oct,
	Number = {2110},
	Pages = {3103--3125},
	Title = {Rotationally invariant quadratures for the sphere},
	Volume = {465},
	Year = {2009},
	Abstract = {We construct near-optimal quadratures for the sphere that are invariant under the icosahedral rotation group. These quadratures integrate all $(N+1)^2$ linearly independent functions in a rotationally invariant subspace of maximal order and degree N. The nodes of these quadratures are nearly uniformly distributed, and the number of nodes is only marginally more than the optimal $(N+1)^2/3$ nodes. Using these quadratures, we discretize the reproducing kernel on a rotationally invariant subspace to construct an analogue of Lagrange interpolation on the sphere. This representation uses function values at the quadrature nodes. In addition, the representation yields an expansion that uses a single function centred and mostly concentrated at nodes of the quadrature, thus providing a much better localization than spherical harmonic expansions. We show that this representation may be localized even further. We also describe two algorithms of complexity $\mathcal{O}(N^3)$ for using these grids and representations. Finally, we note that our approach is also applicable to other discrete rotation groups.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1098/rspa.2009.0104}}

@book{Altman:2005:RotsQuats,
	Address = {Mineola, NY},
	Author = {Altman, Simon L.},
	Date-Added = {2009-11-24 11:36:42 -0700},
	Date-Modified = {2009-11-24 11:36:42 -0700},
	Keywords = {rotation group, quaternions},
	Note = {Slightly corrected republication of the edition published by Oxford University Press, Oxford and New York, in 1986},
	Publisher = {Dover Publications, Inc.},
	Title = {Rotations, Quaternions, and Double Groups},
	Year = {2005}}

@article{Agoh:2004:CalcCSRMesh,
	Author = {Agoh, Tomonori and Yokoya, Kaoru},
	Date-Added = {2009-11-24 11:36:26 -0700},
	Date-Modified = {2009-11-24 11:36:26 -0700},
	Doi = {10.1103/PhysRevSTAB.7.054403},
	Journal = prstab,
	Keywords = {coherent synchrotron radiation},
	Month = may,
	Number = {5},
	Pages = {054403},
	Title = {Calculation of coherent synchrotron radiation using mesh},
	Volume = {7},
	Year = {2004},
	Abstract = {We develop a new method to simulate coherent synchrotron radiation numerically. It is based on the mesh calculation of the electromagnetic field in the frequency domain. We make an approximation in the Maxwell equation which allows a mesh size much larger than the relevant wavelength so that the computing time is tolerable. Using the equation, we can perform a mesh calculation of coherent synchrotron radiation in transient states with shielding effects by the vacuum chamber. The simulation results obtained by this method are compared with analytic solutions. Though, for the comparison with theories, we adopt simplifications such as longitudinal Gaussian distribution, zero-width transverse distribution, horizontal uniform bend, and a vacuum chamber with rectangular cross section, the method is applicable to general cases.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevSTAB.7.054403}}

@article{Agoh:2009:SteadyCSR,
	Author = {Agoh, Tomonori},
	Date-Added = {2009-11-24 11:36:26 -0700},
	Date-Modified = {2009-11-24 11:36:26 -0700},
	Doi = {10.1103/PhysRevSTAB.12.094402},
	Journal = prstab,
	Keywords = {coherent synchrotron radiation},
	Month = sep,
	Number = {9},
	Pages = {094402},
	Title = {Steady fields of coherent synchrotron radiation in a rectangular pipe},
	Volume = {12},
	Year = {2009},
	Abstract = {We study longitudinal fields of coherent synchrotron radiation in a perfectly conducting rectangular pipe. Our theory is based on the paraxial approximation of electromagnetic waves in the frequency domain. The longitudinal impedance of coherent radiation is obtained. By considering the pole structure of the impedance in a rectangular pipe, we have derived the analytical expression of the longitudinal field in the time domain. According to the analysis, we show how the sidewalls of the vacuum chamber affect the longitudinal field of coherent radiation. In addition, we discuss the limit of applicability of the paraxial approximation.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevSTAB.12.094402}}

@book{James:1993:RepsCharsGroups,
	Address = {Cambridge, England},
	Author = {James, Gordon and Liebeck, Martin},
	Date-Added = {2009-11-24 11:35:42 -0700},
	Date-Modified = {2009-11-24 11:35:42 -0700},
	Publisher = {Cambridge University Press},
	Title = {Representations and Characters of Groups},
	Year = {1993}}

@article{Iserles:2000:LieGrpMeth,
	Author = {Iserles, Arieh and Munthe-Kaas, Hans Z. and N{\o}rsett, Syvert P. and Zanna, Antonella},
	Date-Added = {2009-11-24 11:34:47 -0700},
	Date-Modified = {2009-11-24 11:34:47 -0700},
	Journal = actanum,
	Pages = {215--365},
	Title = {Lie-group Methods},
	Volume = {9},
	Year = {2000},
	Abstract = {Many differential equations of practical interest evolve on Lie groups or on manifolds acted upon by Lie groups.  The retention of Lie-group structure under discretization is often vital in the recovery of qualitatively-correct geometry and dynamics and in the minimisation of numerical error.  Having introduced requisite elements of differential geometry, this paper surveys the novel theory of numerical integrators that respect Lie-group structure, high-lighting theory, algorithmic issues and a number of applications.}}

@article{Howard:1987:LinearStabSymp,
	Author = {Howard, James E. and MacKay, Robert S.},
	Date-Added = {2009-11-24 11:31:13 -0700},
	Date-Modified = {2009-11-28 12:50:50 -0700},
	Doi = {10.1063/1.527544},
	Journal = jmathp,
	Month = may,
	Number = {5},
	Pages = {1036--1051},
	Title = {Linear stability of symplectic maps},
	Volume = {28},
	Year = {1987},
	Abstract = {A general method is presented for analytically calculating linear stability limits for symplectic maps of arbitrary dimension in terms of the coefficients of the characteristic polynomial and the Krein signatures.  Explicit results are given for dimensions 4, 6, and 8.  The codimension and unfolding are calculated for all cases having a double eigenvalue on the unit circle.  The results are applicable to many physical problems, including the restricted three-body problem and orbital stability in particle accelerators.}}

@article{Howard:1998:LinStabNatSymp,
	Author = {Howard, James E. and Dullin, Holger R.},
	Date-Added = {2009-11-24 11:30:56 -0700},
	Date-Modified = {2009-11-24 11:30:56 -0700},
	Journal = physla,
	Month = sep,
	Number = {3--4},
	Pages = {273--283},
	Title = {Linear stability of natural symplectic maps},
	Volume = {246},
	Year = {1998},
	Abstract = {We calculate linear stability boundaries for natural symplectic maps, which are symplectic mappings derived from Lagrangian generating functions having positive definite kinetic energy.  Simplified stability conditions are obtained in terms of the Hessian of the potential and applied to a four-dimensional pair of coupled standard maps.}}

@phdthesis{Hoffstaetter:2000:Habil,
	Author = {Hoffst{\"a}tter, Georg Heinz},
	Date-Added = {2009-11-24 11:29:15 -0700},
	Date-Modified = {2009-11-24 11:29:15 -0700},
	Month = jan,
	School = {Technische Universit{\"a}t Darmstadt},
	Title = {Aspects of the Invariant Spin Field for High Energy Polarized Proton Beams},
	Type = {Habilitation},
	Year = {2000},
	Bdsk-Url-1 = {http://www.lns.cornell.edu/~hoff/proton_pol/hoffpapers/00habil.pdf}}

@inproceedings{Hoffstaetter:2003:AccelRings,
	Author = {Hoffstaetter, Georg H.},
	Booktitle = {COSY Summer School and Workshop 2002},
	Date-Added = {2009-11-24 11:29:15 -0700},
	Date-Modified = {2009-11-24 11:29:15 -0700},
	Keywords = {spin dynamics, quaternions},
	Pages = {85--125},
	Title = {Accelerator Rings with Polarized Beams and Spin Manipulation},
	Volume = {1},
	Year = {2003},
	Abstract = {The basic formulas of describing polarization dynamics in accelerators will be presented.  These include the equation of spin motion in a comoving coordinate frame for spin vectors, spin transport matrices, spin transport quaternions, and spinors.  It will also be shown how spin fields evolve in these four ways of descibing spin motion.  Furthermore, some basic concepts of polarized beams in ring accelerators will be discussed.  These include the periodic spin direction on the closed orbit, the closed orbit spin tune, the invariant spin field, the amplitude dependent spin tune, the Froissart-Stora formula, and transfer maps of linearized spin-orbit motion, with their relation to resonance strength and to spin-orbit coupling integrals.  The here presented material is intended to be a tutorial of the basic processes 
involved when polarized beams travel around circular accelerators and of the theory used to describe first order effects.  Much of this material has been presented in [G.H. Hoffstaetter. Aspects of the invariant spin field for high energy polarized proton beams. Habilitation, Darmstadt Univ., 2000], where it served as the basis to extend the analysis of spin motion to higher--order phenomena.}}

@inproceedings{Hoffstaetter:2003:MatchSnakes,
	Author = {Hoffstaetter, Georg H.},
	Booktitle = {Increasing the {AGS} Polarization},
	Date-Added = {2009-11-24 11:29:15 -0700},
	Date-Modified = {2009-11-24 11:29:15 -0700},
	Editor = {Krisch, A. D. and Lin, A. M. T. and Roser, Thomas},
	Month = jun,
	Pages = {93--102},
	Publisher = {Springer},
	Series = aipcp,
	Title = {Matching of {S}iberian Snakes},
	Volume = {667},
	Year = {2003},
	Abstract = {It is shown how one can choose suitable combinations of Siberian Snakes and betatron phase advances to optimize the ability of a ring to accelerate a polarized beam with little reduction of polarization.  In an analysis of HERA-p, these methods have lead to a 14-fold increase of the vertical beam emittance for which polarization could be preserved.  This is not only impressive as a result, but also the methods which lead to this result are very interesting.  They contain detailed spin-orbit tracking and the application of the Froissart-Stora Formula for higher order spin-orbit resonances, for which an algorithm of determining resonance strength has been found.}}

@article{Hoffstaetter:2004:HORes,
	Author = {Hoffstaetter, Georg H. and Vogt, Mathias},
	Date-Added = {2009-11-24 11:29:15 -0700},
	Date-Modified = {2009-11-24 11:29:15 -0700},
	Journal = preve,
	Month = may,
	Number = {5},
	Pages = {056501},
	Title = {Strength of higher-order spin-orbit resonances},
	Volume = {70},
	Year = {2004},
	Abstract = {When polarized particles are accelerated in a synchrotron, the spin precession can be periodically driven by Fourier components of the electromagnetic fields through which the particles travel.  This leads to resonant perturbations when the spin-precession frequency is close to a linear combination of the orbital frequencies.  When such resonance conditions are crossed, partial depolarization or spin flip can occur.  The amount of polarization that survives after resonance crossing is a function of the resonance strength and the crossing speed.  This function is commonly called the Froissart-Stora formula.  It is very useful for predicting the amount of polarization after an acceleration cycle of a synchrotron or for computing the required speed of the acceleration cycle to maintain a required amount of polarization.  However, the resonance strength could, in general, only be computed for first-order resonances and for synchrotron sidebands.  When Siberian Snakes adjust the spin tune to be $\frac{1}{2}$, as is required for high-energy accelerators, first-order resonances do not appear and higher-order resonances become dominant.  Here we will introduce the strength of a higher-order spin-orbit resonance, and also present an efficient method of computing it.  Several tracking examples will show that the so computed resonance strength can indeed be used in the Froissart-Stora formula.  HERA-p is used for these examples which demonstrate that our results are very relevant for existing accelerators.}}

@article{Hoffstaetter:2004:OptAxes,
	Author = {Hoffstaetter, Georg H.},
	Date-Added = {2009-11-24 11:29:15 -0700},
	Date-Modified = {2009-11-24 11:29:15 -0700},
	Journal = prstab,
	Month = dec,
	Pages = {121001},
	Title = {Optimal axes of {S}iberian snakes for polarized proton acceleration},
	Volume = {7},
	Year = {2004},
	Abstract = {Accelerating polarized proton beams and storing them for many turns can lead to a loss of polarization when accelerating through energies where a spin rotation frequency is in resonance with orbit oscillation frequencies.  First-order resonance effects can be avoided by installing Siberian snakes in the ring, devices which rotate the spin by $180^\circ$ around the snake axis while not changing the beam's orbit significantly.  For large rings, several Siberian snakes are required.  Here a criterion will be derived that allows one to find an optimal choice for the orientation of the snake axes.  Rings with superperiod four are analyzed in detail, and the HERA proton ring is used as an example for approximate fourfold symmetry.  The proposed arrangement of Siberian snakes matches their effects so that all spin-orbit coupling integrals vanish at all energies and therefore there is no first-order spin-orbit coupling at all for this choice, which I call snake matching.  It will be shown that in general at least eight Siberian snakes are needed and that there are exactly four possibilities to arrange their axes.  When the betatron phase advance between snakes is chosen suitably, four Siberian snakes can be sufficient.  Since the spin motion depends on a particle's trajectory, protons at different phase space positions generally have different spin directions.  The time averaged polarization at each phase space point is parallel to the invariant spin field, and the spread of this spin field limits the polarization that can be stored.  By the here presented choice of Siberian snakes this limit is completely eliminated up to first order in the transverse phase space coordinates.  The invariant spin field and the amplitude-dependent spin tune are also computed without linearization to show the advantages of this choice of snakes.  Ultimately, the goal of snake matching is to reduce the loss of polarization during the acceleration of the beam.  To show that a favorable choice of snakes has been found, polarized protons are tracked for part of HERA-p's acceleration cycle which shows that polarization is preserved best for the here proposed arrangement of Siberian snakes.}}

@article{Hoffstaetter:2006:AdInv,
	Author = {Hoffstaetter, Georg H. and Dumas, H. Scott and Ellison, James A.},
	Date-Added = {2009-11-24 11:29:15 -0700},
	Date-Modified = {2009-11-24 11:29:15 -0700},
	Journal = prstab,
	Month = jan,
	Number = {1},
	Pages = {014001},
	Title = {Adiabatic invariance of spin-orbit motion in accelerators},
	Volume = {9},
	Year = {2006},
	Abstract = {It has been predicted and found experimentally that the polarization direction of particles on the closed orbit of a circular accelerator can be manipulated, without a noticeable reduction of polarization, by means of a slow variation of magnetic fields.  This feature has been used to avoid imperfection resonances where the spin precession frequency is close to a multiple of the circulation frequency.  As a first step we show that this property is related to an adiabatic invariant of spin motion.  The proof is relatively simple since it involves only two frequencies, the spin-rotation frequency and the particle's rotation frequency on the closed orbit.  The invariant spin field (ISF) describes a periodic polarization state of a beam's phase-space distribution.  This ISF leads to a very useful parametrization of coupled spin and orbit dynamics.  We prove that this ISF gives rise to an adiabatic invariant of spin-orbit motion.  This proof is much more complicated since the orbital frequencies are involved.  Because of this adiabatic invariance, a beam's spin field follows slow changes of the accelerator's ISF that can occur during a slow acceleration cycle.  This feature is essential when high-order spin-orbit resonances are crossed, since it allows polarization that has been reduced at the resonance condition to be recovered, to a large degree, after the resonances have been crossed.}}

@book{Hoffstaetter:2006:HEPPbeams,
	Address = {New York, NY},
	Author = {Hoffstaetter, Georg Heinz},
	Date-Added = {2009-11-24 11:29:15 -0700},
	Date-Modified = {2009-11-24 11:29:15 -0700},
	Publisher = {Springer},
	Series = {Springer Tracts in Modern Physics},
	Title = {High-Energy Polarized Proton Beams: A Modern View},
	Volume = {218},
	Year = {2006}}

@book{Hockney:1988:CompSim,
	Address = {Bristol, UK},
	Author = {Hockney, Roger W. and Eastwood, James W.},
	Date-Added = {2009-11-24 11:28:28 -0700},
	Date-Modified = {2009-11-24 11:28:28 -0700},
	Publisher = {Institute of Physics Publishing},
	Title = {Computer Simulation Using Particles},
	Year = {1988}}

@article{Hirai:1965:CharsIrrepLorentz,
	Author = {Hirai, Takeshi},
	Date-Added = {2009-11-24 11:28:03 -0700},
	Date-Modified = {2009-11-24 11:28:03 -0700},
	Journal = procja,
	Number = {7},
	Pages = {526--531},
	Title = {The Characters of Irreducible Representations of the {L}orentz Group of $n$-th Order},
	Volume = {41},
	Year = {1965}}

@techreport{Heinemann:1996:OnSternGerlach,
	Address = {Hamburg, Germany},
	Author = {Heinemann, Klaus A.},
	Date-Added = {2009-11-24 11:12:34 -0700},
	Date-Modified = {2009-11-24 11:12:34 -0700},
	Institution = {Deutsches Elektronen-Synchrotron},
	Month = nov,
	Note = {Available at \url{http://arXiv.org/abs/physics/9611001}},
	Number = {DESY-96-229},
	Title = {On {S}tern-{G}erlach forces allowed by special relativity and the special case of the classical spinning particle of {D}erbenev-{K}ondratenko},
	Year = {1996},
	Abstract = {This work is devoted to an examination of Stern-Gerlach forces consistent with special relativity and is motivated by recent interest in the relativistic Stern-Gerlach force acting on polarized protons in high-energy particle accelerators.  The equations for the orbital and spin motion of a classical charged particle with arbitrary intrinsic magnetic dipole moment in an external electromagnetic field are considered and by imposing the constraints of special relativity and restricting to first order in spin (= first order $\hbar$) a well-defined class of spin-orbit systems is obtained.  All these systems can be treated on an equal footing including such prominent cases as those considered by Frenkel and by Good.  The Frenkel case is considered in great detail because I show that this system is identical with the one introduced by Derbenev and Kondratenko for studying spin motion in accelerators.  In particular I prove that the spin-orbit system of Derbenev and Kondratenko is (nonmanifestly) Poincar\'e covariant and identify the transformation properties of this system under the Poincar\'e group.  The Derbenev-Kondratenko Hamiltonian was originally proposed as a way to combine relativistic spin precession and the Lorentz force.  The aforementioned findings now demonstrate that the Derbenev-Kondratenko Hamiltonian also provides a legitimate framework for handling the relativistic Stern-Gerlach force.  Numerical examples based on the Frenkel and Good cases for the HERA proton ring and electromagnetic traps are provided.}}

@article{Heinemann:1996:StrobAvg,
	Author = {Heinemann, Klaus A. and Hoffst{\"a}tter, Georg H.},
	Date-Added = {2009-11-24 11:12:34 -0700},
	Date-Modified = {2009-11-24 11:12:34 -0700},
	Journal = preve,
	Month = oct,
	Number = {4},
	Pages = {4240--4255},
	Title = {Tracking algorithm for the stable spin polarization field in storage rings using stroboscopic averaging},
	Volume = {54},
	Year = {1996},
	Abstract = {Polarized protons have never been accelerated to more than about 25 GeV.  To achieve polarized proton beams in the Relativistic Heavy Ion Collider (RHIC, 250 GeV), the Hadron Electron Ring Accelerator (HERA, 820 GeV), and Fermilab's TeV accelerator (TEVATRON, 900 GeV), ideas and techniques applicable to accelerator physics are needed.  In this publication we will stress an important aspect of very high energy polarized proton beams, namely, the fact that the equilibrium polarization direction can vary substantially across the beam in the interaction region of a high energy experiment when no countermeasure is taken.  Such a divergence of the polarization direction would not only diminish the average polarization available to the particle physics experiment, but it would also make the polarization involved in each collision analyzed in a detector strongly dependent on the phase space position of the interacting particle.  In order to analyze and compensate for this effect, methods for computing the equilibrium polarization direction are needed.  In this paper we introduce the method of stroboscopic averaging, which computes this direction in a very efficient way.  Since only tracking data are needed, our method can be implemented easily in existing spin tracking programs.  Several examples demonstrate the importance of the spin divergence and the applicability of stroboscopic averaging.}}

@book{Gantmacher:1959:TheoryMatrices,
	Author = {Gantmacher, Feliks R.},
	Date-Added = {2009-11-24 11:07:29 -0700},
	Date-Modified = {2009-11-24 11:07:29 -0700},
	Note = {Translated by K.A. Hirsch from \emph{Teoriya Matrits}},
	Publisher = {Chelsea Publishing Co.},
	Title = {The Theory of Matrices},
	Year = {1959}}

@article{Furry:1955:LorentzTrans,
	Author = {Furry, Wendell H.},
	Date-Added = {2009-11-24 11:07:06 -0700},
	Date-Modified = {2009-11-24 11:07:06 -0700},
	Journal = ajp,
	Month = nov,
	Number = {8},
	Pages = {517--525},
	Title = {Lorentz Transformation and the {T}homas Precession},
	Volume = {23},
	Year = {1955},
	Abstract = {The various kinematic effects of special relativity are here treated by considering iterations of the infinitesimal Lorentz transformation.  There is only one relativistic effect that appears as a difference between an infinitesimal Lorentz transformation and the corresponding infinitesimal Galilei transformation; this effect is the relative character of simultaneity.  When this has been introduced by a physical argument (following Einstein), finite transformations and the other effects are obtained by iteration.  Special attention is given to an iteration procedure that reveals the existence of the Thomas precession.}}

@article{Franchi:2007:MagStrengthBPM,
	Author = {Franchi, Andrea and Tom{\'a}s, Rogelio and Schmidt, Frank},
	Date-Added = {2009-11-24 11:05:54 -0700},
	Date-Modified = {2009-11-24 11:05:54 -0700},
	Journal = prstab,
	Month = jul,
	Number = {7},
	Pages = {074001},
	Title = {Magnet strength measurement in circular accelerators from beam position monitor data},
	Volume = {10},
	Year = {2007},
	Abstract = {Recent measurements of resonance terms suggested the extension of the existing technique to measure magnet strengths from turn-by-turn beam position monitor data.  This article describes the algorithm to infer the magnet strength from the variation along the ring of the resonance terms and reports on the first measurement.  Both the algorithm and the software written for the analysis of the data can be particularly useful in the commissioning period of an accelerator in order to find magnets with wrong strengths or polarities as well as magnets with large magnetic errors.}}

@article{Franchetti:2008:MeasLocalNL,
	Author = {Franchetti, Giuliano and Parfenova, Angelina S. and Hofmann, Ingo},
	Date-Added = {2009-11-24 11:05:42 -0700},
	Date-Modified = {2009-11-24 11:05:42 -0700},
	Journal = prstab,
	Month = sep,
	Number = {9},
	Pages = {094001},
	Title = {Measuring localized nonlinear components in a circular accelerator with a nonlinear tune response matrix},
	Volume = {11},
	Year = {2008},
	Abstract = {In this paper we present a method for measuring the nonlinear errors in a circular accelerator by taking advantage of the feed-down effect of high order multipoles when the closed orbit is globally deformed.  We devise a nonlinear tune response matrix in which the response to a closed orbit deformation is obtained in terms of change of machine tune and correlated with the strength of the local multipoles.  A numerical example and a proof of principle experiment to validate the theoretical methods are presented and discussed.}}

@article{Floquet:1883:ODE1,
	Author = {Floquet, Gaston},
	Date-Added = {2009-11-24 11:04:21 -0700},
	Date-Modified = {2009-11-24 11:04:21 -0700},
	Journal = annsens2,
	Pages = {47--88},
	Title = {Sur les {\'e}quations diff{\'e}rentielles lin{\'e}aires {\`a} coefficients p{\'e}riodiques},
	Volume = {12},
	Year = {1883},
	Bdsk-Url-1 = {http://www.numdam.org/item?id=ASENS_1883_2_12__47_0}}

@article{Floquet:1884:ODE2,
	Author = {Floquet, Gaston},
	Date-Added = {2009-11-24 11:04:21 -0700},
	Date-Modified = {2009-11-24 11:04:21 -0700},
	Journal = annsens3,
	Pages = {181--238},
	Title = {Sur les {\'e}quations diff{\'e}rentielles lin{\'e}aires {\`a} coefficients doublement p{\'e}riodiques},
	Volume = {1},
	Year = {1884},
	Bdsk-Url-1 = {http://www.numdam.org/item?id=ASENS_1884_3_1__181_0}}

@article{Fisher:1972:ThomasPrec,
	Author = {Fisher, George P.},
	Date-Added = {2009-11-24 11:04:03 -0700},
	Date-Modified = {2009-11-24 11:04:03 -0700},
	Journal = ajp,
	Month = dec,
	Number = {12},
	Pages = {1772--1781},
	Title = {The {T}homas Precession},
	Volume = {40},
	Year = {1972},
	Abstract = {This paper is intended to give a simple physical understanding of the kinematic effect referred to as the Wigner rotation or, when applied to an orbiting object, the Thomas precession.  Since this is a kinematic effect it applies not only to particles with spin but to all physical bodies in which a direction can be defined.  To aid in avoiding the usual pitfalls in working with these problems, a review is made of several different approaches to the problem of an infinitesimally extended accelerating physical object.  The central problem is in taking successive Lorentz transformations between parallel coordinate systems and clearly distinguishing between physical rotations of the object and coordinate rotations.  When accounting for the energy associated with the Thomas precession a simple physical explanation is given rather than the misleading description popularly presented.}}

@book{Feynman:1963-65:LOP,
	Address = {Reading, MA},
	Author = {Feynman, Richard P. and Leighton, Robert B and Sands, Matthew},
	Date-Added = {2009-11-24 11:03:43 -0700},
	Date-Modified = {2009-11-24 11:03:43 -0700},
	Note = {Three volumes.},
	Publisher = {Addison-Wesley Publishing Co.},
	Title = {The Feynman Lectures on Physics},
	Year = {1963--65},
	Bdsk-Url-1 = {http://www.feynmanlectures.info/}}

@book{Feynman:1963:LOP1,
	Address = {Reading, MA},
	Author = {Feynman, Richard P. and Leighton, Robert B and Sands, Matthew},
	Date-Added = {2009-11-24 11:03:43 -0700},
	Date-Modified = {2009-11-24 11:03:43 -0700},
	Publisher = {Addison-Wesley Publishing Co.},
	Title = {The Feynman Lectures on Physics: Mainly Mechanics, Radiation, and Heat},
	Volume = {I},
	Year = {1963}}

@book{Feynman:1964:LOP2,
	Address = {Reading, MA},
	Author = {Feynman, Richard P. and Leighton, Robert B and Sands, Matthew},
	Date-Added = {2009-11-24 11:03:43 -0700},
	Date-Modified = {2009-11-24 11:03:43 -0700},
	Publisher = {Addison-Wesley Publishing Co.},
	Title = {The Feynman Lectures on Physics: Mainly Electromagnetism and Matter},
	Volume = {II},
	Year = {1964}}

@book{Feynman:1965:LOP3,
	Address = {Reading, MA},
	Author = {Feynman, Richard P. and Leighton, Robert B and Sands, Matthew},
	Date-Added = {2009-11-24 11:03:43 -0700},
	Date-Modified = {2009-11-24 11:03:43 -0700},
	Publisher = {Addison-Wesley Publishing Co.},
	Title = {The Feynman Lectures on Physics: Quantum Mechanics},
	Volume = {III},
	Year = {1965}}

@article{Ellison:2007:PolFields,
	Author = {Ellison, James A. and Heinemann, Klaus A.},
	Date-Added = {2009-11-24 11:02:47 -0700},
	Date-Modified = {2009-11-24 11:02:47 -0700},
	Journal = physd,
	Month = oct,
	Number = {2},
	Pages = {131--149},
	Title = {Polarization fields and phase space densities in storage rings: Stroboscopic averaging and the ergodic theorem},
	Volume = {234},
	Year = {2007},
	Abstract = {A class of orbital motions with volume preserving flows and with vector fields periodic in the ``time'' parameter $\theta$ is defined.  Spin motion coupled to the orbital dynamics is then defined, resulting in a class of spin-orbit motions which are important for storage rings.  Phase space densities and polarization fields are introduced.  It is important, in the context of storage rings, to understand the behavior of periodic polarization fields and phase space densities.  Due to the $2\pi$ time periodicity of the spin-orbit equations of motion the polarization field, taken at a sequence of increasing time values $\theta$, $\theta + 2\pi$, $\theta + 4\pi$, \dots, gives a sequence of polarization fields, called the stroboscopic sequence.  We show, by using the Birkhoff ergodic theorem, that under very general conditions the Ces\`aro averages of that sequence converge almost everywhere on phase space to a polarization field which is $2\pi$-periodic in time.  This fulfills the main aim of this paper in that it demonstrates that the tracking algorithm for stroboscopic averaging, encoded in the program SPRINT and used in the study of spin motion in storage rings, is mathematically well-founded.  The machinery developed is also shown to work for the stroboscopic average of phase space densities associated with the orbital dynamics.  This yields a large family of periodic phase space densities and, as an example, a quite detailed analysis of the so-called betatron motion in a storage ring is presented.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.physd.2007.07.007}}

@article{Dragt:1976:LieSerInvFns,
	Author = {Dragt, Alex J. and Finn, John M.},
	Date-Added = {2009-11-24 11:02:01 -0700},
	Date-Modified = {2009-11-24 11:02:01 -0700},
	Journal = jmathp,
	Month = dec,
	Number = {12},
	Pages = {2215--2227},
	Title = {Lie series and invariant functions for analytic symplectic maps},
	Volume = {17},
	Year = {1976},
	Abstract = {Symplectic maps (canonical transformations) are treated from the Lie algebraic point of view using Lie series and Lie algebraic techniques.  It is shown that under very general conditions an analytic symplectic map can be written as a product of Lie transformations.  Under certain conditions this product of Lie transformations can be combined to form a single Lie transformation by means of the Campbell--Baker--Hausdorff theorem.  This result leads to invariant functions and generalizes to several variables a classic result of Birkhoff for the case of two variables.  It also provides a new approach since the connection between symplectic maps, Lie algebras, invariant functions, and Birkhoff's work has not been previously recognized and exploited.  It is expected that the results obtained will be applicable to the normal form problem in Hamiltonian mechanics, the use of the Poincar{\'e} section map in stability analysis, and the behavior of magnetic field lines in a toroidal plasma device.}}

@article{Dragt:1979:NormalForm,
	Author = {Dragt, Alex J. and Finn, John M.},
	Date-Added = {2009-11-24 11:02:01 -0700},
	Date-Modified = {2009-11-24 11:02:01 -0700},
	Journal = jmathp,
	Month = dec,
	Number = {12},
	Pages = {2649--2660},
	Title = {Normal form for mirror machine {H}amiltonians},
	Volume = {20},
	Year = {1979},
	Abstract = {A systematic algorithm is developed for performing canonical transformations on Hamiltonians which govern particle motion in magnetic mirror machines.  These transformations are performed in such a way that the new Hamiltonian has a particularly simple normal form.  From this form it is possible to compute analytic expressions for gyro and bounce frequencies.  In addition, it is possible to obtain arbitrarily high order terms in the adiabatic magnetic moment expansion.  The algorithm makes use of Lie series, is an extension of Birkhoff's normal form method, and has been explicitly implemented by a digital computer programmed to perform the required algebraic manipulations.  Application is made to particle motion in a magnetic dipole field and to a simple mirror system.  Bounce frequencies and locations of periodic orbits are obtained and compared with numerical computations.  Both mirror systems are shown to be insoluble, i.e., trajectories are not confined to analytic hypersurfaces, there is no analytic third integral of motion, and the adiabatic magnetic moment expansion is divergent.  It is expected also that the normal form procedure will prove useful in the study of island structure and separatrices associated with periodic orbits, and should facilitate studies of breakdown of adiabaticity and the onset of ``stochastic'' behavior.}}

@inproceedings{Dragt:1980:BmBmXferMap,
	Author = {Dragt, Alex J. and Jakubowicz, Oleg G.},
	Crossref = {BBIS:1980},
	Date-Added = {2009-11-24 11:02:01 -0700},
	Date-Modified = {2009-11-24 11:02:01 -0700},
	Pages = {205--234},
	Title = {Analysis of the Beam-Beam Interaction Using Transfer Maps},
	Abstract = {The method of transfer maps is used to develop generalized Courant-Snyder invariants in the presence of the beam-beam interaction for both nonresonant and resonant tunes. Numerical evidence is presented to illustrate that the generalized invariants are indeed constant through terms of first order in the beam-beam interaction strength. The invariants are next used as a ``magnifying glass'' to search for irregularities and evidence of stochastic behavior. It is found that within the model employed, the beam-beam interaction at its contemplated strengths shows no evidence of producing particle loss in ISABELLE.}}

@article{Dragt:1982:ExactChrom,
	Author = {Dragt, Alex J.},
	Date-Added = {2009-11-24 11:02:01 -0700},
	Date-Modified = {2009-11-24 11:02:01 -0700},
	Journal = pacc,
	Note = {An extended version is available from the author},
	Pages = {205--218},
	Title = {Exact Numerical Calculation of Chromaticity in Small Rings},
	Volume = {12},
	Year = {1982}}

@inproceedings{Dragt:1982:NLOrbitDyn,
	Author = {Dragt, Alex J.},
	Crossref = {PHEPA:1982},
	Date-Added = {2009-11-24 11:02:01 -0700},
	Date-Modified = {2009-11-24 11:02:01 -0700},
	Title = {Lectures on Nonlinear Orbit Dynamics},
	Abstract = {Lie algebraic techniques are developed to analyze nonlinear orbit dynamics.  Application include charged-particle transport, light optics, and colliding beams.}}

@article{Dragt:1983:CompNLHam,
	Author = {Dragt, Alex J. and Forest, {\'E}tienne},
	Date-Added = {2009-11-24 11:02:01 -0700},
	Date-Modified = {2009-11-24 11:02:01 -0700},
	Journal = jmathp,
	Month = dec,
	Number = {12},
	Pages = {2734--2744},
	Title = {Computation of nonlinear behavior of {H}amiltonian systems using {L}ie algebraic methods},
	Volume = {24},
	Year = {1983},
	Abstract = {Lie algebraic methods are developed to describe the behavior of trajectories near a given trajectory for general Hamiltonian systems.  A procedure is presented for the computation of nonlinear effects of arbitrarily high degree, and explicit formulas are given through effects of degree $5$.  Expected applications include accelerator design, charged particle beam and light optics, other problems in the general area of nonlinear dynamics, and, perhaps, with suitable modification, the area of $S$-matrix expansions in quantum field theory.}}

@article{Dragt:1992:GenMomInvar,
	Author = {Dragt, Alex J. and Neri, Filippo and Rangarajan, Govindan},
	Date-Added = {2009-11-24 11:02:01 -0700},
	Date-Modified = {2009-11-24 11:02:01 -0700},
	Journal = preva,
	Month = nov,
	Number = {4},
	Pages = {2572--2585},
	Title = {General moment invariants for linear {H}amiltonian systems},
	Volume = {45},
	Year = {1992},
	Abstract = {This paper studies the behavior of the moments of a particle distribution as it is transported through a Hamiltonian system.  Functions of moments that remain invariant for an arbitrary linear Hamiltonian system are constructed.  These functions remain approximately invariant for Hamiltonian systems that are not strongly nonlinear.  Consequently, they can be used to characterize the degree of nonlinearity of the system.}}

@inproceedings{Dragt:1996:CompSympl,
	Author = {Dragt, Alex J. and Abell, Dan T.},
	Crossref = {FIC:1996:IntAlg},
	Date-Added = {2009-11-24 11:02:01 -0700},
	Date-Modified = {2009-11-24 11:02:01 -0700},
	Title = {Symplectic Maps and Computation of Orbits in Particle Accelerators}}

@article{Dragt:1996:SclSqrSpl,
	Author = {Dragt, Alex J.},
	Date-Added = {2009-11-24 11:02:01 -0700},
	Date-Modified = {2009-11-24 11:02:01 -0700},
	Journal = prevl,
	Month = sep,
	Number = {10},
	Pages = {1946--1948},
	Title = {Computation of Maps for Particle and Light Optics by Scaling, Splitting, and Squaring},
	Volume = {75},
	Year = {1996},
	Abstract = {New methods are presented for the integration of autonomous flows, with an emphasis on the Hamiltonian case.  The Hamiltonian results are expected to have important applications for charged-particle optics (including accelerator design) and for graded-index light optics.}}

@manual{Dragt:1999:MaryLieMan,
	Address = {University of Maryland, College Park, MD},
	Author = {Dragt, Alex J. and Ryne, Robert D. and Douglas, David R. and Neri, Filippo and others},
	Date-Added = {2009-11-24 11:02:01 -0700},
	Date-Modified = {2009-11-24 11:02:01 -0700},
	Organization = {Center for Theoretical Physics},
	Title = {{\textsc{MaryLie}} 3.0 User's Manual},
	Year = {1999}}

@article{Dragt:2005:SympGrpCM,
	Author = {Dragt, Alex J.},
	Date-Added = {2009-11-24 11:02:01 -0700},
	Date-Modified = {2009-11-24 11:02:01 -0700},
	Journal = annnyas,
	Keywords = {symplectic group, classical mechanics},
	Month = jun,
	Pages = {291--307},
	Title = {The Symplectic Group and Classical Mechanics},
	Volume = {1045},
	Year = {2005},
	Abstract = {The symplectic group is the underlying symmetry group for Hamiltonian dynamics.  Yet relatively little is commonly known about its properties including its Lie structure and representations.  This paper describes and summarizes some of these properties; and, as a first application of symplectic group theory, provides a symplectic classification of all first-order differential equations in an even number of variables.}}

@unpublished{Dragt:2009:LieMethNLDyn,
	Author = {Dragt, Alex J.},
	Date-Added = {2009-11-24 11:02:01 -0700},
	Date-Modified = {2009-11-24 11:02:01 -0700},
	Month = jan,
	Note = {Latest version available at \url{http://www.physics.umd.edu/dsat/}},
	Title = {Lie Methods for Nonlinear Dynamics with Applications to Accelerator Physics},
	Year = {2009}}

@phdthesis{Douglas:1982:PhDthesis,
	Address = {College Park, MD},
	Author = {Douglas, David R.},
	Date-Added = {2009-11-24 11:01:13 -0700},
	Date-Modified = {2009-11-24 11:01:13 -0700},
	School = {University of Maryland},
	Title = {Lie Algebraic Methods for Particle Accelerator Theory},
	Year = {1982}}

@article{Derbenev:1972:DiffSpin,
	Author = {Derbenev, Yaroslav and Kondratenko, Anatoly M.},
	Date-Added = {2009-11-24 11:00:18 -0700},
	Date-Modified = {2009-11-24 11:00:18 -0700},
	Journal = zekstf,
	Note = {In Russian.},
	Pages = {430--443},
	Title = {Diffusion of particle spins in storage elements},
	Volume = {62},
	Year = {1972}}

@article{Derbenev:1973:PolKin,
	Author = {Derbenev, Yaroslav and Kondratenko, Anatoly M.},
	Date-Added = {2009-11-24 11:00:18 -0700},
	Date-Modified = {2009-11-24 11:00:18 -0700},
	Journal = zekstf,
	Note = {In Russian.},
	Pages = {1918--1929},
	Title = {Polarization kinematics of particles in storage rings},
	Volume = {64},
	Year = {1973}}

@article{Derbenev:1993:RFResPolarimeterI,
	Author = {Derbenev, Yaroslav S.},
	Date-Added = {2009-11-24 11:00:18 -0700},
	Date-Modified = {2009-11-24 11:00:18 -0700},
	Journal = nucima,
	Month = nov,
	Note = {Available at \url{http: //hdl.handle.net/2027.42/30447}},
	Number = {1--2},
	Pages = {12--15},
	Title = {{RF}-resonance beam polarimeter {P}art {I}. {F}undamental concepts},
	Volume = {336},
	Year = {1993},
	Abstract = {The possibility of an RF-resonance polarimeter (RFP) for fast non-destructive measurement of beam polarization in an accelerator ring is considered.  In order to accumulate the transition radiation from the free oscillating coherent spin of the beam, a passive superconducting cavity is proposed.  The increase of effective voltage in the cavity with time (related to beam polarization) is calculated here.  The efficiency of the polarimeter does not decrease with beam energy and is proportional to the average beam current.  A possible scheme of measurement of the accumulated voltage is presented.  The noise limitations are taken into account and evaluated.  Siberian snakes can be used in order to provide a sufficiently small value for the spin tune spread.  Numerical examples are given.}}

@inproceedings{Derbenev:1995:RFResPolarimeterII,
	Author = {Derbenev, Yaroslav S.},
	Crossref = {HESP:1995},
	Date-Added = {2009-11-24 11:00:18 -0700},
	Date-Modified = {2009-11-24 11:00:18 -0700},
	Title = {{RF}-resonance beam polarimeter},
	Abstract = {The possibility of an RF-resonance polarimeter (RFP) for fast non-destructive measurement of beam polarization in an accelerator ring is considered.  In order to accumulate the spin-dependent beam transition radiation, a passive superconducting cavity is proposed.  The increase of effective voltage in the cavity (TM110 mode) with time, related to the free oscillating coherent spin of the beam, is calculated.  The efficiency of the RFP does not decrease with particle energy and is proportional to the average beam current.  Siberian snakes can be used in order to provide a sufficiently small value for the spin tune spread.  Possible schemes of measurement of the accumulated voltage are presented.  The noise limitations are taken into account and evaluated.  There are in the RFP dynamics different effects of the beam charge---cavity interaction, positive and negative.  The negative effects are the beam noises, while the positive ones are as follows: (i) the possibility to enhance the spin-dependent beam cavity interaction, via the spin-orbit coupling in the machine focusing lattice; (ii) the possibility to increase, if necessary, the effective quality of the superconducting resonator, via redistribution of decrements between the TM110 mode and the beam coherent oscillation.  A scheme of elimination of charge effects from the measurement is proposed, if needed, which is based on use of two cavities with a spin rotator (Siberian snake) between them.  Finally, the RFP scheme is transformed to a Beam Spin Maser system, which is a spin feedback based on the superconducting cavities.  This would allow one to create, to observe, and to use for polarization measurements the phenomenon of beam spontaneous coherent spin flip.  Numerical examples are given.
},
	Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.48865}}

@unpublished{Derbenev:2001:PolDeut,
	Author = {Derbenev, Yaroslav},
	Date-Added = {2009-11-24 11:00:18 -0700},
	Date-Modified = {2009-11-24 11:00:18 -0700},
	Note = {Talk presented at Snowmass},
	Title = {Polarized Deuterons in Colliders},
	Year = {2001},
	Abstract = {The possibilities of preserving and manipulating the deuteron polarization in colliders are discussed.  A small value of deuteron magnetic anomaly (-0.13 comparatively to 1.8 for protons) makes the Siberian snakes method impractical for deuterons, but it leaves the possibility to undertake all the measures on fast and adiabatic crossing of individual spin resonances in a ring developed and implemented earlier and in recent years at ZGS and AGS for polarized proton beams.  Fast crossing methods are estimated effective for deuteron energy range below 100\,GeV (EPIC collider).  At higher energies (up to 250\,GeV for RHIC and 1\,TeV for HERA or Tevatron), beam excitation by the static or RF dipoles above the statistical level (due to imperfections or beam emittance) is estimated to be efficient.  Static dipoles also can be used in order to transform the vertical polarization of injected and accelerated beam to the stable longitudinal polarization, in energy areas near the spin-resonance value.  The possibilities of spin RF-flipping are also discussed, including a possibility of RF-trapped longitudinal spin at half-integer spin tune.  Finally, an exotic scheme of a twisted spin synchrotron is described with the possibility of stable longitudinal spin in the whole energy range of storage facility.},
	Bdsk-Url-1 = {http://snowmassserver.snowmass2001.org/Working_Group_M5/www/TALKS/derbenev_deuterons.doc}}

@article{Courant:1958:ThAGS,
	Author = {Courant, Ernest D. and Snyder, Hartland S.},
	Date-Added = {2009-11-24 10:56:49 -0700},
	Date-Modified = {2009-11-24 10:56:49 -0700},
	Doi = {10.1016/0003-4916(58)90012-5},
	Journal = annphys,
	Month = jan,
	Number = {1},
	Pages = {1--48},
	Title = {Theory of the alternating-gradient synchrotron},
	Volume = {3},
	Year = {1958},
	Abstract = {The equations of motion of the particles in a synchrotron in which the field gradient index 
\[
  n = -(r/B)\partial B/\partial r
\]
varies along the equilibrium orbit are examined on the basis of the linear approximation. It is shown that if $n$ alternates rapidly between large positive and large negative values, the stability of both radial and vertical oscillations can be greatly increased compared to conventional accelerators in which $n$ is azimuthally constant and must lie between $0$ and $1$. Thus aperture requirements are reduced. For practical designs, the improvement is limited by the effects of constructional errors; these lead to resonance excitation of oscillations and consequent instability if $2\nu_x$ or $2\nu_z$ or $\nu_x + \nu_z$ is integral, where $\nu_x$ and $\nu_z$ are the frequencies of horizontal and vertical betatron oscillations, measured in units of the frequency of revolution.

The mechanism of phase stability is essentially the same as in a conventional synchrotron, but the radial amplitude of synchrotron oscillations is reduced substantially. Furthermore, at a ``transition energy'' $E_1 \approx \nu_x Mc^2$ the stable and unstable equilibrium phases exchange roles, necessitating a jump in the phase of the radiofrequency accelerating voltage. Calculations indicate that the manner in which this jump is performed is not very critical.},
	Annote = {This paper is a revised version of a report written by us in 1953 and privately circulated at that time. Many if not most of the results obtained here have also been obtained independently by numerous other authors, especially members of the accelerator design groups at CERN, Geneva; Saclay, France; Harwell, England; and Cambridge, Massachusetts. No attempt has been made here to allocate credit for every single result. Comprehensive accounts of the theory of betatron oscillations, using somewhat different approaches from ours, may be found in references 9, 13, and 14.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/0003-4916(58)90012-5}}

@article{Chin:2005:StructPositive,
	Author = {Chin, Siu A.},
	Date-Added = {2009-11-24 10:11:54 -0700},
	Date-Modified = {2009-11-24 10:11:54 -0700},
	Journal = preve,
	Month = jan,
	Number = {1},
	Pages = {016703},
	Title = {Structure of positive decompositions of exponential operators},
	Volume = {71},
	Year = {2005},
	Abstract = {The solution of many physical evolution equations can be expressed as an exponential of two or more operators acting on initial data.  Accurate solutions can be systematically derived by decomposing the exponential in a product form.  For time-reversible equations, such as the Hamilton or the Schr{\"o}dinger equation, it is immaterial whether or not the decomposition coefficients are positive.  In fact, most symplectic algorithms for solving classical dynamics contain some negative coefficients.  For time-irreversible systems, such as the Fokker-Planck equation or the quantum statistical propagator, only positive-coefficient decompositions, which respect the time-irreversibility of the diffusion kernel, can yield practical algorithms.  These positive time steps only, forward decompositions, are a highly effective class of factorization algorithms.  This work presents a framework for understanding the structure of these algorithms.  By a suitable representation of the factorization coefficients, we show that specific error terms and order conditions can be solved \emph{analytically}.  Using this framework, we can go beyond the Sheng-Suzuki theorem and derive a lower bound for the error coefficient $e_{VTV}$.  By generalizing the framework perturbatively, we can further prove that it is not possible to have a sixth-order forward algorithm by including only the commutator $[VTV]\equiv[V,[T,V]]$.  The pattern of these higher-order forward algorithms is that in going from the $(2n)$th to the $(2n+2)$th order, one must include a different commutator $[VT^{2n-1}V]$ in the decomposition process.}}

@article{Chin:2006:ThmSympInt,
	Author = {Chin, Siu A.},
	Date-Added = {2009-11-24 10:11:54 -0700},
	Date-Modified = {2009-11-24 10:11:54 -0700},
	Journal = physla,
	Month = jun,
	Note = {A preprint version is available at \url{http://arxiv.org/abs/math-ph/0511051}},
	Number = {5--6},
	Pages = {373--376},
	Title = {A fundamental theorem on the structure of symplectic integrators},
	Volume = {354},
	Year = {2006},
	Abstract = {I show that the basic structure of symplectic integrators is governed by a theorem which states \textit{precisely}, how symplectic integrators with positive coefficients cannot be corrected beyond second order.  All previous known results can now be derived quantitatively from this theorem.  The theorem provided sharp bounds on second-order error coefficients explicitly in terms of factorization coefficients.  By saturating these bounds, one can derive fourth-order algorithms analytically with arbitrary numbers of operators.}}

@article{Chin:2007:PhysSympInt,
	Author = {Chin, Siu A.},
	Date-Added = {2009-11-24 10:11:54 -0700},
	Date-Modified = {2009-11-24 10:11:54 -0700},
	Journal = preve,
	Keywords = {symplectic integrator, symplectic corrector, perihelion advance},
	Month = mar,
	Number = {3},
	Pages = {036701},
	Title = {Physics of symplectic integrators: Perihelion advances and symplectic corrector algorithms},
	Volume = {75},
	Year = {2007},
	Abstract = {Symplectic integrators evolve dynamical systems according to modified Hamiltonians whose error terms are also well-defined Hamiltonians.  The error of the algorithm is the sum of each error Hamiltonian's perturbation on the exact solution.  When symplectic integrators are applied to the Kepler problem, these error terms cause the orbit to precess.  In this work, by developing a general method of computing the perihelion advance via the Laplace-Runge-Lenz vector even for nonseparable Hamiltonians, I show that the precession error in symplectic integrators can be computed analytically.  It is found that at leading order, each paired error Hamiltonians cause the orbit to precess oppositely by exactly the same amount after each period.  Hence, symplectic corrector, or process integrators, which have equal coefficients for these paired error terms, will have their precession errors cancel at that order after each period.  With the use of correctable algorithms, both the energy and precession error are of effective order n+2 where n is the nominal order of the algorithm.  Thus the physics of symplectic integrators determines the optimal algorithm for integrating long-time periodic motions.}}

@article{Chin:2008:SympAlgMag,
	Author = {Chin, Siu A.},
	Date-Added = {2009-11-24 10:11:54 -0700},
	Date-Modified = {2009-11-24 10:11:54 -0700},
	Journal = preve,
	Month = jun,
	Number = {6},
	Pages = {066401},
	Title = {Symplectic and energy-conserving algorithms for solving magnetic field trajectories},
	Volume = {77},
	Year = {2008},
	Abstract = {The exponential splitting of the classical evolution operator yields symplectic integrators if the canonical Hamiltonian is separable.  Similar splitting of the noncanonical evolution operator for a charged particle in a magnetic field produces exact energy-conserving algorithms.  The latter algorithms evaluate the magnetic field directly with no need of a vector potential and are more stable with far less phase errors than symplectic integrators.  For a combined electric and magnetic field, these algorithms from splitting the noncanonical evolution operator are neither fully symplectic nor exactly energy conserving, yet they behave exactly like symplectic algorithms in having qualitatively correct trajectories and bounded periodic energy errors.  This work shows that exponential-splitting algorithms of any order for solving particle trajectories in a general electric and magnetic field can be systematically derived by use of the angular momentum operator of quantum mechanics.  The use of operator analysis in this work fully comprehends the intertwining interaction between electric and magnetic forces and makes possible the derivation of highly nontrivial integrators.}}

@article{Chin:2009:RelativMotionEMField,
	Author = {Chin, Siu A.},
	Date-Added = {2009-11-24 10:11:54 -0700},
	Date-Modified = {2009-11-24 10:11:54 -0700},
	Journal = jmathp,
	Month = jan,
	Note = {A preprint version is available at \url{http://arxiv.org/abs/0809.0859}},
	Number = {1},
	Pages = {012904},
	Title = {Relativistic Motion in a Constant Electromagnetic Field},
	Volume = {50},
	Year = {2009},
	Abstract = {For a relativistic charged particle moving in a constant electromagnetic field, its velocity 4-vector has been well studied.  However, despite the fact that both the electromagnetic field and the equations of motion are purely real, the resulting 4-velocity is seemingly due to a complex electromagnetic field.  This work shows that this is not due to some complex formalism used (such as Clifford algebra) but is intrinsically due to the fact that the $o(3,1)$ Lie algebra of the Lorentz group is equivalent to two commuting complex $su(2)$ algebras.  Expressing the complex $su(2)$ generators in terms of the boost and rotation operators then naturally introduces a complex electromagnetic field.  This work solves the equation of motion not as a matrix equation, but as an operator evolution equation in terms of the generators of the Lorentz group.  The factorization of the real evolution operator into two commuting complex evolution operators then directly gives the time evolution of the velocity 4-vector without any reference to an intermediate field.}}

@book{Chao:1993:PhysCBI,
	Address = {New York, NY},
	Author = {Chao, Alexander Wu},
	Date-Added = {2009-11-24 10:10:55 -0700},
	Date-Modified = {2009-11-24 10:10:55 -0700},
	Publisher = {John Wiley \& Sons},
	Series = {Wiley Series in Beam Physics and Accelerator Technology},
	Title = {Physics of Collective beam Instabilities in High Energy Accelerators},
	Year = {1993}}

@book{Chao:1999:APHandbook,
	Address = {Singapore},
	Date-Added = {2009-11-24 10:10:55 -0700},
	Date-Modified = {2009-11-24 10:10:55 -0700},
	Editor = {Chao, Alexander Wu and Tigner, Maury},
	Publisher = {World Scientific},
	Title = {Handbook of Accelerator Physics and Engineering},
	Year = {1999}}

@article{Chao:2005:MatrixSpinDyn,
	Author = {Chao, Alexander W.},
	Date-Added = {2009-11-24 10:10:55 -0700},
	Date-Modified = {2009-11-24 10:10:55 -0700},
	Journal = prstab,
	Month = oct,
	Number = {10},
	Pages = {1004001},
	Title = {Matrix formalism for spin dynamics near a single depolarization resonance},
	Volume = {8},
	Year = {2005},
	Abstract = {A matrix formalism is developed to describe the spin dynamics in a synchrotron near a single depolarization resonance as the particle energy (and therefore its spin precession frequency) is varied in a prescribed pattern as a function of time such as during acceleration.  This formalism is first applied to the case of crossing the resonance with a constant crossing speed and a finite total step size, and then applied also to other more involved cases when the single resonance is crossed repeatedly in a prescribed manner consisting of linear ramping segments or sudden jumps.  How repeated crossings produce an interference behavior is discussed using the results obtained.  For a polarized beam with finite energy spread, a spin echo experiment is suggested to explore this interference effect.}}

@article{Chao:2007:SpinEcho,
	Author = {Chao, Alexander W. and Courant, Ernest D.},
	Date-Added = {2009-11-24 10:10:55 -0700},
	Date-Modified = {2009-11-24 10:10:55 -0700},
	Journal = prstab,
	Month = jan,
	Number = {1},
	Pages = {014001},
	Title = {Spin echo in synchrotrons},
	Volume = {10},
	Year = {2007},
	Abstract = {As a polarized beam is accelerated through a depolarization resonance, its polarization is reduced by a well-defined calculable reduction factor.  When the beam subsequently crosses a second resonance, the final beam polarization is considered to be reduced by the product of the two reduction factors corresponding to the two crossings, each calculated independently of the other.  This is a good approximation when the spread of spin precession frequency $\Delta\nu_\text{spin}$ of the beam (particularly due to its energy spread) is sufficiently large that the spin precession phases of individual particles smear out completely during the time $\tau$ between the two crossings.  This approximate picture, however, ignores two spin dynamics effects: an interference-overlap effect and a spin echo effect.  This paper is to address these two effects.  The interference-overlap effect occurs when $\Delta\nu_\text{spin}$ is too small, or when $\tau$ is too short, to complete the smearing process.  In this case, the two resonance crossings overlap each other, and the final polarization exhibits constructive or destructive interference patterns depending on the exact value of $\tau$.  Typically, the beam's energy spread is large and this interference-overlap effect does not occur.  To study this effect, therefore, it is necessary to reduce the beam energy spread and to consider two resonance crossings very close to each other.  The other mechanism, also due to the interplay between two resonance crossings, is spin echo. It turns out that even when the precession phases appear to be completely smeared between the two crossings, there will still be a sudden and short-lived echo signal of beam polarization at a time $\tau$ after the second crossing; the magnitude of which can be as large as 57\%.  This echo signal exists even when the beam has a sizable energy spread and when $\tau$ is very large, and could be a sensitive (albeit challenging) way to experimentally test the intricate spin dynamics in a synchrotron.  After giving an analysis of the interference-overlap and the echo effects, two possible experiments to explore them are suggested.}}

@article{Chao:2009:GravInstability,
	Author = {Chao, Alexander Wu},
	Date-Added = {2009-11-24 10:10:55 -0700},
	Date-Modified = {2009-11-24 10:10:55 -0700},
	Doi = {10.1103/PhysRevSTAB.12.104201},
	Journal = prstab,
	Keywords = {space-charge},
	Month = oct,
	Number = {10},
	Pages = {104201},
	Title = {Gravitational instability of a nonrotating galaxy},
	Volume = {12},
	Year = {2009},
	Abstract = {Gravitational instability of the distribution of stars in a galaxy is a well-known phenomenon in astrophysics. This report is an attempt to analyze this phenomenon by applying standard tools developed in accelerator physics. It is found that a nonrotating galaxy would become unstable if its size exceeds a certain limit that depends on its mass density and its temperature.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevSTAB.12.104201}}

@article{Channell:1990:SympIntHam,
	Author = {Channell, Paul J. and Scovel, Clint},
	Date-Added = {2009-11-24 10:10:23 -0700},
	Date-Modified = {2009-11-24 10:10:23 -0700},
	Doi = {10.1088/0951-7715/3/2/001},
	Journal = nonli,
	Month = may,
	Number = {2},
	Pages = {231--259},
	Title = {Symplectic integration of {H}amiltonian systems},
	Volume = {3},
	Year = {1990},
	Abstract = {The authors survey past work and present new algorithms to numerically integrate the trajectories of Hamiltonian dynamical systems.  These algorithms exactly preserve the symplectic 2-form, i.e.\ they preserve all the Poincar{\'e} invariants.  The algorithms have been tested on a variety of examples and results are presented for the Fermi-Pasta-Ulam nonlinear string, the H{\'e}non-Heiles system, a four-vortex problem, and the geodesic flow on a manifold of constant negative curvature.  In all cases the algorithms possess long-time stability and preserve global geometrical structures in phase space.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1088/0951-7715/3/2/001}}

@article{Cary:1981:LiePerturbation,
	Author = {Cary, John R.},
	Date-Added = {2009-11-24 10:09:40 -0700},
	Date-Modified = {2009-11-24 10:09:40 -0700},
	Journal = physr,
	Month = dec,
	Number = {2},
	Pages = {129--159},
	Title = {Lie transform perturbation theory for {H}amiltonian systems},
	Volume = {79},
	Year = {1981},
	Abstract = {A review of the theory of Lie transform perturbation theory for Hamiltonian systems is presented.  The operator theory of Dewar for continuous families of canonical transformations is discussed.  It is then used to derive the perturbation method of Deprit.  Two examples of the use of this method are provided.  In addition, the more efficient perturbation method of Dragt and Finn is discussed.}}

@book{Burke:1985:AppliedDiffGeom,
	Address = {Cambridge, UK},
	Author = {Burke, William},
	Date-Added = {2009-11-24 10:07:27 -0700},
	Date-Modified = {2009-11-24 10:07:27 -0700},
	Publisher = {Cambridge University Press},
	Title = {Applied differential geometry},
	Year = {1985}}

@techreport{Bruck:1972:CircPartAccel,
	Author = {Bruck, Henri},
	Date-Added = {2009-11-24 10:07:17 -0700},
	Date-Modified = {2009-11-24 10:07:17 -0700},
	Institution = {Los Alamos National Laboratory},
	Note = {Translated by Ralph McElroy Co., Inc., from \emph{Acc{\'e}l{\'e}rateurs Circulaires de Particules}, first published by Presses Universitaires de France in 1966.},
	Number = {LA-TR-72-10-Rev},
	Title = {Circular Particle Accelerators},
	Year = {1972}}

@article{Brillouin:1945:TheoremLarmor,
	Author = {Brillouin, L{\'e}on},
	Date-Added = {2009-11-24 10:05:55 -0700},
	Date-Modified = {2009-11-24 10:05:55 -0700},
	Doi = {10.1103/PhysRev.67.260},
	Journal = prev,
	Month = apr,
	Number = {7--8},
	Pages = {260--266},
	Title = {A Theorem of {L}armor and Its Importance for Electrons in Magnetic Fields},
	Volume = {67},
	Year = {1945},
	Abstract = {The importance of a well-known theorem, originally due to Larmor, is emphasized.  It enables a definition of ``momentum'' and ``moment of momentum'' for electrons in a magnetic field, hence the possibility of writing the conservation of these quantities when the geometry of the structure is convenient.  As typical examples of the method, two special cases are discussed: a plane electron beam and a cylindrical electron beam with longitudinal magnetic field.  In both cases it is found that the space-charge density of the beam is entirely controlled by the magnetic field and that the maximum current is obtained for a suitable optimum magnetic field.}}

@book{Brillouin:1953:WaveProp,
	Address = {New York, NY},
	Author = {Brillouin, L{\'e}on},
	Date-Added = {2009-11-24 10:05:55 -0700},
	Date-Modified = {2009-11-24 10:05:55 -0700},
	Edition = {Second},
	Note = {Corrected and enlarged republication of the work first published by Mc-Graw Hill Book Co., Inc., in 1946},
	Publisher = {Dover Publications, Inc.},
	Title = {Wave Propogation in Periodic Structures: Electric Filters and Crystal Lattices},
	Year = {1953}}

@book{Bringhurst:2005:ElementsTS,
	Address = {Point Roberts, WA},
	Author = {Bringhurst, Robert},
	Date-Added = {2009-11-24 10:05:55 -0700},
	Date-Modified = {2009-11-24 10:05:55 -0700},
	Edition = {Third},
	Publisher = {Hartley \& Marks, Publishers},
	Title = {The Elements of Typographic Style: Version 3.1},
	Year = {2005}}

@article{Blanes:2005:AdaptGeomInteg,
	Author = {Blanes, Sergio and Budd, Chris J.},
	Date-Added = {2009-11-24 09:59:55 -0700},
	Date-Modified = {2009-11-24 09:59:55 -0700},
	Doi = {10.1137/S1064827502416630},
	Journal = siamjsc,
	Keywords = {symplectic integration, Hamiltonian system},
	Number = {4},
	Pages = {1089--1113},
	Title = {Adaptive Geometric Integrators for {H}amiltonian Problems with Approximate Scale Invariance},
	Volume = {26},
	Year = {2005},
	Abstract = {We consider adaptive geometric integrators for the numerical integration of Hamiltonian systems with greatly varying time scales.  A time regularization is considered using either the Sundman or the Poincar{\'e} transformation.  In the latter case, this gives a new Hamiltonian which is usually separable, but with one of the parts not always exactly solvable.  This system can be numerically integrated with a splitting scheme where each part can be computed using a symplectic implicit or explicit method, preserving the qualitative properties of the exact solution.  In this case, a backward error analysis for the numerical integration is presented.  For a one-dimensional near singular problem, this analysis reveals a strong dependence of the performance of the method with the choice of the monitor function $g$, which is also observed when using other symmetric nonsymplectic integrators.  We also show how this dependence greatly increases with the order of the numerical integrator used.  The optimal choice corresponds to the function $g$, which nearly preserves the scaling invariance of the system.  Numerical examples supporting this result are presented.  In some cases a canonical transformation can also be considered, making the system more regular or easy to compute, and this is also illustrated with some examples.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1137/S1064827502416630}}

@article{Blanes:2006:CommentStructPos,
	Author = {Blanes, Sergio and Casas, Fernando},
	Date-Added = {2009-11-24 09:59:55 -0700},
	Date-Modified = {2009-11-24 09:59:55 -0700},
	Doi = {10.1103/PhysRevE.73.048701},
	Journal = preve,
	Month = apr,
	Number = {4},
	Pages = {048701},
	Title = {Comment on ``{S}tructure of positive decompositions of exponential operators''},
	Volume = {73},
	Year = {2006},
	Abstract = {An elementary proof is shown on the necessary existence of negative coefficients in splitting methods of order $p\geq3$.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevE.73.048701}}

@article{Blanes:2006:SplittingMeth,
	Author = {Blanes, Sergio and Casas, Fernando},
	Date-Added = {2009-11-24 09:59:55 -0700},
	Date-Modified = {2009-11-24 09:59:55 -0700},
	Doi = {10.1088/0305-4470/39/19/S05},
	Journal = jphysa,
	Keywords = {geometric integration, splitting methods},
	Month = may,
	Number = {19},
	Pages = {5405--5423},
	Title = {Splitting methods for non-autonomous separable dynamical systems},
	Volume = {39},
	Year = {2006},
	Abstract = {A large number of splitting methods for autonomous separable systems exist in the literature which have been designed for many different structures of the vector field.  However, the performance of most of these methods is diminished and their orders of accuracy are frequently reduced when applied to non-autonomous problems.  Based on the formal solution obtained from the Magnus series expansion, we show how to modify a standard splitting method for autonomous problems to treat non-autonomous systems with similar or better efficiency.  We illustrate this technique to build new fourth- and sixth-order schemes whose performance is then illustrated on several numerical examples.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1088/0305-4470/39/19/S05}}

@article{Blanes:2008:LinStabilitySplit,
	Author = {Blanes, Sergio and Casas, Fernando and Murua, Ander},
	Date-Added = {2009-11-24 09:59:55 -0700},
	Date-Modified = {2009-11-24 09:59:55 -0700},
	Doi = {10.1007/s10208-007-9007-8},
	Journal = fcompm,
	Keywords = {splitting methods},
	Month = jun,
	Note = {A preprint version is available at \url{http://www.damtp.cam.ac.uk/user/na/NA_papers/NA2006_08.pdf}},
	Number = {3},
	Pages = {357--393},
	Title = {On the linear stability of splitting methods},
	Volume = {8},
	Year = {2008},
	Abstract = {A comprehensive linear stability analysis of splitting methods is carried out by means of a $2\times2$ matrix $K(x)$ with polynomial entries (the stability matrix) and the stability polynomial $p(x)$ (the trace of $K(x)$ divided by two).  An algorithm is provided for determining the coefficients of all possible time-reversible splitting schemes for a prescribed stability polynomial.  It is shown that $p(x)$ carries essentially all the information needed to construct processed splitting methods for numerically approximating the evolution of linear systems.  By conveniently selecting the stability polynomial, new integrators with processing for linear equations are built which are orders of magnitude more efficient than other algorithms previously available.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10208-007-9007-8}}

@phdthesis{Berglund:2001:PhDthesis,
	Address = {Stockholm, Sweden},
	Author = {Berglund, Gun Zara Mari},
	Date-Added = {2009-11-24 09:58:44 -0700},
	Date-Modified = {2009-11-24 09:58:44 -0700},
	Month = jun,
	School = {Royal Institute of Technology},
	Title = {Spin-Orbit Maps and Electron Spin Dynamics for the Luminosity Upgrade Project at HERA},
	Year = {2001},
	Abstract = {HERA is the high energy electron(positron)-proton collider at Deutsches Elektronen-Synchrotron (DESY) in Hamburg.  Following eight years of successful running, five of which were with a longitudinally spin polarized electron(positron) beam for the HERMES experiment, the rings have now been modified to increase the luminosity by a factor of about five and spin rotators have been installed for the H1 and ZEUS experiments.  The modifications involve nonstandard configurations of overlapping magnetic fields and other aspects which have profound implications for the polarization.  This thesis addresses the problem of calculating the polarization in the upgraded machine and the measures needed to maintain the polarization.  A central topic is the construction of realistic spin-orbit transfer maps for regions of overlapping fields and their implementation in existing software.  This is the first time that calculations with such fields have been possible.  Using the upgraded software, calculations are presented for the polarization that can be expected in the upgraded machine.  It is concluded that about 50 \% polarization should be possible.  The key issues for tuning the machine are discussed.  The last chapter deals with a separate topic, namely how to exploit a simple unitary model of spin motion to describe electron depolarization and thereby expose a misconception appearing in the literature.},
	Bdsk-Url-1 = {http://www.desy.de/~mpybar/thesisdump/mbthesis.pdf}}

@article{Benedikt:2007:DrivingTerm,
	Author = {Benedikt, Michael and Schmidt, Frank and Tom{\'a}s, Rogelio and Ursch{\"u}tz, Peter and Faus-Golfe, Angeles},
	Date-Added = {2009-11-24 09:57:35 -0700},
	Date-Modified = {2009-11-24 09:57:35 -0700},
	Doi = {10.1103/PhysRevSTAB.10.034002},
	Journal = prstab,
	Month = mar,
	Number = {3},
	Pages = {034002},
	Title = {Driving term experiments at {CERN}},
	Volume = {10},
	Year = {2007},
	Abstract = {Driving Term experiments have been performed both at small [PS (Proton Synchrotron) Booster] and large accelerators [SPS (Super Proton Synchrotron)] at CERN.  The theory of how to measure driving terms is reviewed.  A wealth of SPS experiments is shown together with a successful comparison with model calculations.  The PS Booster studies aimed at optimizing the machine performance by measuring and correcting selected driving terms.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevSTAB.10.034002}}

@techreport{Bell:1975:PolPartAccelPhys,
	Address = {Geneva},
	Author = {Bell, John Stewart},
	Date-Added = {2009-11-24 09:57:07 -0700},
	Date-Modified = {2009-11-24 09:57:07 -0700},
	Institution = {European Organization for Nuclear Research},
	Month = sep,
	Number = {75-11},
	Title = {Polarized Particles for Accelerator Physicists},
	Type = {CERN Yellow Report},
	Year = {1975},
	Abstract = {These lectures deal in an elementary way with the concept of particle polarization and its behaviour in the presence of electromagnetic fields. The first part introduces the basic notions and essential equations in a purely phenomenological way, beginning with spin-$1/2$ particles and then extending the discussion to particles of arbitrary spin. Among the topics discussed are magnetic precession and the muon $g-2$ experiment. The second part begins with an introduction to non-relativistic wave mechanics, and then develops the quantum-theoretic interpretation of the phenomenological equations for particles with spin $1/2$, $1$, and higher.}}

@book{Barenblatt:2003:Scaling,
	Address = {Cambridge, UK},
	Author = {Barenblatt, Grigory Isaakovich},
	Date-Added = {2009-11-24 09:56:20 -0700},
	Date-Modified = {2009-11-24 09:56:20 -0700},
	Publisher = {Cambridge University Press},
	Series = {Cambridge Texts in Applied Mathematics},
	Title = {Scaling},
	Year = {2003}}

@article{Bargmann:1947:IrrepsLorentz,
	Author = {Bargmann, Valentine},
	Date-Added = {2009-11-24 09:56:20 -0700},
	Date-Modified = {2009-11-24 09:56:20 -0700},
	Journal = annma2,
	Month = jul,
	Number = {3},
	Pages = {568--640},
	Title = {Irreducible Unitary Representations of the {L}orentz Group},
	Volume = {48},
	Year = {1947}}

@article{Bargmann:1959:PrecessionPP,
	Author = {Bargmann, Valentine and Michel, Louis and Telegdi, Valentine L.},
	Date-Added = {2009-11-24 09:56:20 -0700},
	Date-Modified = {2010-03-30 17:24:09 -0600},
	Doi = {10.1103/PhysRevLett.2.435},
	Journal = prevl,
	Month = may,
	Number = {10},
	Pages = {435--436},
	Title = {Precession of the Polarization of Particles Moving in a Homogeneous Electromagnetic Field},
	Volume = {2},
	Year = {1959},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevLett.2.435}}

@techreport{Barber:1986:NLSynBeta,
	Address = {Hamburg, Germany},
	Author = {Barber, Desmond P. and Mais, Helmut and Ripken, Gerhard and Willeke, Ferdinand J.},
	Date-Added = {2009-11-24 09:55:44 -0700},
	Date-Modified = {2009-11-24 09:55:44 -0700},
	Institution = {Deutsches Elektronen-Synchrotron},
	Month = jul,
	Number = {DESY 86-147},
	Title = {Nonlinear Theory Of Coupled Synchro-Betatron Motion},
	Year = {1986}}

@article{Barber:1988:CalcBell,
	Author = {Barber, Desmond P. and Mane, Sateesh R.},
	Date-Added = {2009-11-24 09:55:44 -0700},
	Date-Modified = {2010-03-30 17:22:21 -0600},
	Doi = {10.1103/PhysRevA.37.456},
	Journal = preva,
	Keywords = {spin dynamics},
	Month = jan,
	Number = {2},
	Pages = {456--463},
	Title = {Calculations of {B}ell and {L}einaas and {D}erbenev and {K}ondratenko for radiative electron polarization},
	Volume = {37},
	Year = {1988},
	Abstract = {Derbenev and Kondratenko calculated the equilibrium degree of radiative electron polarization in 1973 (Ya.S. Derbenev and A.M. Kondratenko, Zh.\ Eksp.\ Teor.\ Fiz.\ \textbf{64}, 1918 (1973) [Sov.\ Phys.---JETP \textbf{37}, 968 (1973)]), and more recently Bell and Leinaas did likewise for a more limited model, but following a different approach [J.S. Bell and J.M. Leinaas, Nucl.\ Phys.\ B \textbf{284}, 488 (1987)].  They report a different resonance structure.  In this paper the notations, formalisms, and viewpoints of the two sets of authors are compared, and the connection between their treatments is explained.  The formula for the polarization, taking into account vertical fluctuations, is derived following the Derbenev-Kondratenko approach and is generalized to strong-focusing machines.  It is also combined with the Derbenev-Kondratenko result into a unified formula.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevA.37.456}}

@inproceedings{Barber:1995:PolBmsPolarim,
	Author = {Barber, Desmond P.},
	Crossref = {HESP:1995},
	Date-Added = {2009-11-24 09:55:44 -0700},
	Date-Modified = {2009-11-24 09:55:44 -0700},
	Doi = {10.1063/1.48859},
	Pages = {211--218},
	Title = {Polarized beams and polarimeters at lepton accelerators},
	Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.48859}}

@inproceedings{Barber:1995:SpinDecoher,
	Author = {Barber, Desmond P. and B{\"o}ge, Michel and Heinemann, Klaus A. and Mais, Helmut and Ripken, Gerhard},
	Crossref = {HESP:1995},
	Date-Added = {2009-11-24 09:55:44 -0700},
	Date-Modified = {2009-11-24 09:55:44 -0700},
	Doi = {10.1063/1.48866},
	Pages = {273--279},
	Title = {Spin decoherence in electron storage rings},
	Abstract = {A simple model of spin decoherence in electron storage rings is presented and its relevance to rf spin flipping at high energy is discussed.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.48866}}

@inproceedings{Barber:1999:RBGElectrons,
	Author = {Barber, Desmond P. and Heinemann, Klaus A.},
	Crossref = {PPHE:1999},
	Date-Added = {2009-11-24 09:55:44 -0700},
	Date-Modified = {2009-11-24 09:55:44 -0700},
	Note = {Available at \url{http://www.desy.de/lp97-docs/spin/machine/barber.ps}},
	Title = {Red, blue and green electrons},
	Abstract = {If the Fokker--Planck equation for the phase space density of electrons in a storage ring is given, the corresponding equation for the polarization density has a related, simple and elegant form which can be deduced by a simple illuminating argument.}}

@techreport{Barber:1999:SpinNotes,
	Address = {Hamburg, Germany},
	Author = {Barber, Desmond P. and Heinemann, Klaus A. and Ripken, Gerhard},
	Date-Added = {2009-11-24 09:55:44 -0700},
	Date-Modified = {2009-11-24 09:55:44 -0700},
	Institution = {Deutsches Elektronen-Synchrotron},
	Month = sep,
	Note = {Second Revision},
	Number = {DESY M 92-04},
	Title = {Notes on Spin Dynamics in Storage Rings},
	Year = {1999},
	Abstract = {In the following report we present a collection of notes on spin dynamics in storage rings.  The spin motion is described in terms of a pair of real canonical spin variables $\alpha$ and $\beta$ and in four different spin dreibeins.  The orbital motion is described by using the canonical variables $x$, $p_x$, $z$, $p_z$, $\sigma = s - v_0 \cdot t$, $p_\sigma = (1/\beta_0^2) \cdot \eta$ with $\eta = \Delta E/E_0$ of the fully $6$-dimensional canonical formalism.  Action-angle variables $J_k$, $\Phi_k$ of the linear coupled orbital motion are introduced by a canonical transformation.  The equations thus obtained are valid for arbitrary velocity of the particle (below and above transition energy).  The general periodic solution for spin motion, the $\vec{n}$-axis, is determined by the method of forced solution.  Action-angle variables of spin motion and a dreibein which is a single valued function of the particle coordinates $(J_k, \Phi_k, s)$ on an arbitrary particle path are defined and the spin tune as a function of $J_k$ is calculated.  Finally, classical spin diffusion caused by radiation processes is investigated and a derivation of the depolarisation time presented.}}

@article{Barber:2004:Qperiodic,
	Author = {Barber, Desmond P. and Ellison, James A. and Heinemann, Klaus A.},
	Date-Added = {2009-11-24 09:55:44 -0700},
	Date-Modified = {2009-11-24 09:55:44 -0700},
	Doi = {10.1103/PhysRevSTAB.7.124002},
	Journal = prstab,
	Month = dec,
	Note = {An extended version is available at \url{http://arxiv.org/abs/physics/0412157}},
	Number = {12},
	Pages = {124002},
	Title = {Quasiperiodic spin-orbit motion and spin tunes in storage rings},
	Volume = {7},
	Year = {2004},
	Abstract = {We present an in-depth analysis of the concept of spin precession frequency for integrable orbital motion in storage rings.  Spin motion on the periodic closed orbit of a storage ring can be analyzed in terms of the Floquet theorem for equations of motion with periodic parameters, and a spin precession frequency emerges in a Floquet exponent as an additional frequency of the system.  To define a spin precession frequency on nonperiodic synchrobetatron orbits we exploit the important concept of quasiperiodicity.  This allows a generalization of the Floquet theorem so that a spin precession frequency can be defined in this case, too.  This frequency appears in a Floquet-like exponent as an additional frequency in the system in analogy with the case of motion on the closed orbit.  These circumstances lead naturally to the definition of the uniform precession rate and a definition of spin tune.  A spin tune is a uniform precession rate obtained when certain conditions are fulfilled.  Having defined spin tune we define spin-orbit resonance on synchrobetatron orbits and examine its consequences.  We give conditions for the existence of uniform precession rates and spin tunes (e.g., where small divisors are controlled by applying a Diophantine condition) and illustrate the various aspects of our description with several examples.  The formalism also suggests the use of spectral analysis to ``measure'' spin tune during computer simulations of spin motion on synchrobetatron orbits.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevSTAB.7.124002}}

@article{Barber:2005:QperiodicReply,
	Author = {Barber, Desmond P. and Ellison, James A. and Heinemann, Klaus A.},
	Date-Added = {2009-11-24 09:55:44 -0700},
	Date-Modified = {2009-11-24 09:55:44 -0700},
	Doi = {10.1103/PhysRevSTAB.8.089002},
	Journal = prstab,
	Month = aug,
	Number = {8},
	Pages = {089002},
	Title = {Reply to ``{C}omment on `{Q}uasiperiodic spin-orbit motion and spin tunes in storage rings'\,''},
	Volume = {8},
	Year = {2005},
	Abstract = {We reply to Lee and Mane's foregoing Comment [Phys. Rev. ST Accel. Beams \textbf{8}, 089001 (2005)]. In particular, we discuss how an adherence to certain notions of spin-orbit resonance and spin tune can limit the analysis and understanding of phenomena.  Since the Comment has very little to do with the main thrust of our paper we take the opportunity to point out the main features of the ``proper uniform 
precession rate,'' a concept introduced in our paper and based on the concept of quasiperiodicity.  We also respond to other material in the Comment.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevSTAB.8.089002}}

@article{Barber:2006:ResI,
	Author = {Barber, Desmond P. and Vogt, Mathias},
	Date-Added = {2009-11-24 09:55:44 -0700},
	Date-Modified = {2009-11-24 09:55:44 -0700},
	Doi = {10.1088/1367-2630/8/11/296},
	Journal = newjp,
	Month = nov,
	Number = {11},
	Pages = {296},
	Title = {Spin motion at and near orbital resonance in storage rings with {S}iberian {S}nakes {I}: at orbital resonance},
	Volume = {8},
	Year = {2006},
	Abstract = {In this paper, and in a sequel, we invoke the invariant spin field to provide an in-depth study of spin motion at and near low-order orbital resonances in a simple model for the effects of vertical betatron motion in a storage ring with Siberian Snakes. This leads to a clear understanding, within the model, of the behaviour of the beam polarization at and near so-called snake resonances in proton storage rings.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1088/1367-2630/8/11/296}}

@techreport{Barber:2008:TensorI,
	Address = {University of Liverpool, UK},
	Author = {Barber, Desmond P. and Malysheva, Larisa I.},
	Date-Added = {2009-11-24 09:55:44 -0700},
	Date-Modified = {2009-11-24 09:55:44 -0700},
	Institution = {Cockcroft Institute},
	Month = jun,
	Number = {Cockcroft-08-01},
	Title = {The invariant polarisation tensor field and the {B}loch equations for spin-1 particles in storage rings {I}: mathematical foundations},
	Year = {2008},
	Abstract = {We complement the concept of the invariant spin field in storage rings by defining the invariant polarisation-tensor field for spin-1 particles and we suggest how to calculate it by stroboscopic averaging or directly from the invariant spin field.  The invariant polarisation tensor field and the invariant spin field are used to construct equilibrium spin density-matrix fields, and thereby offer a clean framework for describing equilibrium spin-1 ensembles in storage rings.  We also introduce a formalism for describing the effect of noise and damping on the polarisation tensor.}}

@proceedings{BBIS:1980,
	Booktitle = {Proceedings of the Beam Beam Interaction Seminar, Stanford CA, May 22-23, 1980},
	Date-Added = {2009-11-24 09:53:46 -0700},
	Date-Modified = {2009-11-24 09:53:46 -0700},
	Note = {Available as Technical Report SLAC-R-541},
	Title = {Proceedings of the Beam Beam Interaction Seminar, Stanford CA, May 22-23, 1980},
	Year = {1980}}

@proceedings{CYC:2001,
	Address = {Woodbury, NY},
	Booktitle = {Cyclotrons and Their Applications 2001: Sixteenth International Conference, East Lansing, MI, 13--17 May 2001},
	Date-Added = {2009-01-14 15:20:12 -0700},
	Date-Modified = {2009-01-14 15:27:32 -0700},
	Editor = {Marti, Felix},
	Publisher = {AIP Press},
	Series = {AIP Conference Proceedings},
	Title = {Cyclotrons and Their Applications 2001: Sixteenth International Conference, East Lansing, MI, 13--17 May 2001},
	Volume = {600},
	Year = {2001}}

@proceedings{EPAC:2000,
	Address = {Geneva},
	Booktitle = {Proceedings of the 7th European Particle Acelerator Conference, Vienna, Austria, 26--30 June 2000},
	Date-Added = {2008-11-11 16:39:10 -0700},
	Date-Modified = {2008-11-11 16:40:41 -0700},
	Editor = {Gallo, Alessandro},
	Publisher = {European Physical Society},
	Title = {Proceedings of the 7th European Particle Acelerator Conference, Vienna, Austria, 26--30 June 2000},
	Year = {2000}}

@proceedings{EPAC:2002,
	Address = {Geneva},
	Booktitle = {Proceedings of the 8th European Particle Acelerator Conference, Paris, France, 3--7 June 2002},
	Date-Added = {2008-11-11 16:43:58 -0700},
	Date-Modified = {2008-11-11 16:45:10 -0700},
	Publisher = {European Physical Society},
	Title = {Proceedings of the 8th European Particle Acelerator Conference, Paris, France, 3--7 June 2002},
	Year = {2002}}

@proceedings{EPAC:2004,
	Address = {Geneva},
	Booktitle = {Proceedings of the 9th European Particle Acelerator Conference, Lucerne, Switzerland, 5--9 July 2004},
	Date-Added = {2008-11-11 16:41:23 -0700},
	Date-Modified = {2008-11-11 16:42:33 -0700},
	Publisher = {European Physical Society},
	Title = {Proceedings of the 9th European Particle Acelerator Conference, Lucerne, Switzerland, 5--9 July 2004},
	Year = {2004},
	Bdsk-Url-1 = {http://accelconf.web.cern.ch/AccelConf/e04/}}

@proceedings{EPAC:2006,
	Address = {Geneva},
	Booktitle = {Proceedings of the 10th European Particle Acelerator Conference, Edinburgh, Scotland, 26--30 June 2006},
	Date-Added = {2008-11-11 16:35:02 -0700},
	Date-Modified = {2008-11-11 16:43:25 -0700},
	Publisher = {European Physical Society},
	Title = {Proceedings of the 10th European Particle Acelerator Conference, Edinburgh, Scotland, 26--30 June 2006},
	Year = {2006}}

@proceedings{EPAC:2008,
	Address = {Geneva},
	Booktitle = {Proceedings of the 11th European Particle Acelerator Conference, Genoa, Italy, 23--27 June 2008},
	Date-Added = {2008-11-11 16:37:50 -0700},
	Date-Modified = {2008-11-11 16:38:50 -0700},
	Publisher = {European Physical Society},
	Title = {Proceedings of the 11th European Particle Acelerator Conference, Genoa, Italy, 23--27 June 2008},
	Year = {2008}}

@proceedings{FIC:1996:IntAlg,
	Address = {Providence, RI},
	Booktitle = {Integration Algorithms and Classical Mechanics},
	Date-Added = {2008-11-17 15:37:18 -0700},
	Date-Modified = {2008-11-17 15:42:13 -0700},
	Editor = {Marsden, Jerrold E. and Patrick, George W. and Shadwick, William F.},
	Publisher = {American Mathematical Society},
	Series = fieldsic,
	Title = {Integration Algorithms and Classical Mechanics},
	Volume = {10},
	Year = {1996}}

@phdthesis{Forest:1984:PhDthesis,
	Address = {College Park, MD},
	Author = {Forest, {\'E}tienne},
	Date-Added = {2009-01-15 10:49:46 -0700},
	Date-Modified = {2009-01-15 10:51:00 -0700},
	School = {University of Maryland},
	Title = {Lie Algebraic Methods for Charged Particle Beams and Light Optics},
	Year = {1984}}

@techreport{Forest:1986:ThCoherBmBm,
	Author = {Forest, {\'E}tienne},
	Date-Added = {2009-03-13 10:25:33 -0600},
	Date-Modified = {2009-03-19 08:59:45 -0600},
	Institution = {SSC Central Design Group},
	Month = mar,
	Number = {SSC-67},
	Title = {A Theory of the Coherent Beam Beam Effect With Long Range Interactions},
	Year = {1986},
	Abstract = {We present an extension of the Chao-Ruth treatment of the Vlasov equation which includes both the head on and the long-range collisions.  We also simplify the multiple bunches treatment by following the time evolution of a site instead of a bunch.  Analytical results are obtained for the dipole mode and some numerical results for the higher modes.}}

@inproceedings{Forest:1987:CanonInteg,
	Author = {Forest, {\'E}tienne},
	Crossref = {PHYPA:1987},
	Date-Added = {2008-12-04 10:34:15 -0700},
	Date-Modified = {2009-01-14 14:13:57 -0700},
	Pages = {1106--1136},
	Title = {Canonical integrators as tracking codes (or how to integrate perturbation theory with tracking)},
	Abstract = {This lecture is supposed to be about tracking codes.  Although you might expect me to discuss some existing codes, I have avoided discussing, or even mentioning, any of them.  This lecture is actually about the ideal single-particle code for a large circular machine.  This code must be able to track particles and produce high-order maps that can be analyzed by canonical perturbation theory.  This lecture will set guidelines for critically judging the existing codes as well as the future codes that some of you might design.}}

@article{Forest:1988:HardEdgeFringe,
	Author = {Forest, {\'E}tienne and Milutinovi{\'c}, Janko},
	Date-Added = {2009-01-15 10:27:42 -0700},
	Date-Modified = {2009-06-08 14:03:54 -0600},
	Journal = nucima,
	Month = jun,
	Number = {3},
	Pages = {474--482},
	Title = {Leading order hard edge fringe fields effects exact in $(1+\delta)$ and consistent with {M}axwell's equations for rectilinear magnets},
	Url = {http://dx.doi.org/10.1016/0168-9002(88)90123-4},
	Volume = {269},
	Year = {1988},
	Abstract = {In a circular machine, where the linear lattice functions $(\alpha,\beta,\gamma)$ and a phase advance can be defined, one expects the fringe field effects to be negligible if the change in these functions is small through the element.  However, this may not always be the case.  In such situations, it is useful to have a leading order result which is adapted to tracking and analytical analysis.  In this paper, we provide such a result for the quadrupole and we also provide a general formula for the effect of an arbitrary rectilinear multipole.

Starting from the standard multipole expansion for the $B$ field of a $2(n+1)$-pole $(n\geq 1)$, we compute the missing terms in the vector potential expansion consistent with the pure $2(n+1)$-pole symmetry.  We then compute the leading effects of the fringing fields of a multipole on the dynamics.  Finally, we apply this result to quadrupoles and reproduce the original results of Lee-Whiting, Matsuda, and Wollnik.

For the quadrupole, we show how to write a symplectic (canonical) integrator for the dynamics which can be used in a standard circular machine kick code.  For higher order multipoles, we display the implicit characteristic function solution as first proposed by Dragt.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/0168-9002(88)90123-4}}

@article{Forest:1989:NormalForm,
	Author = {Forest, {\'E}tienne and Berz, Martin and Irwin, John},
	Date-Added = {2008-12-04 10:23:45 -0700},
	Date-Modified = {2009-01-15 09:59:16 -0700},
	Journal = pacc,
	Pages = {91--107},
	Title = {Normal form methods for complicated periodic systems: A complete solution using differential algebra and {L}ie operators},
	Volume = {24},
	Year = {1989},
	Abstract = {We present two types of formal algorithms: and order-by-order and a ``superconvergent'' procedure, bringing the one-period map into a so-called normal form, which displays the harmonic content of the map.  The algorithm is arbitrary in order, number of parameters, and phase-space dimensions and covers the range of signatures of the unperturbed quadratic invariants found in circular-machine dynamics.  The normal form and the map-extraction algorithms have all been implemented using the differential-algebra software.  In fact, the work of this paper is feasible in toto because of the differential-algebra theory and software.}}

@article{Forest:1990:FourthOrder,
	Author = {Forest, {\'E}tienne and Ruth, Ronald D.},
	Date-Added = {2009-01-13 11:30:09 -0700},
	Date-Modified = {2009-01-15 10:38:17 -0700},
	Journal = physd,
	Month = may,
	Number = {1},
	Pages = {105--117},
	Title = {Fourth-order symplectic integration},
	Volume = {43},
	Year = {1990},
	Abstract = {In this paper we present an explicit fourth-order method for the integration of Hamilton's equations.  This method preserves the property that the time evolution of such a system yields a canonical transformation from the initial conditions to the final state.  That is, the integration step is an explicit symplectic map.  Although the result is first derived for a specific type of Hamiltonian, it is shown to be quite general.  In particular, the results can be applied to any Lie group.}}

@article{Forest:1990:HamFree,
	Author = {Forest, {\'E}tienne},
	Date-Added = {2008-12-04 09:40:35 -0700},
	Date-Modified = {2010-03-25 09:44:26 -0600},
	Doi = {10.1063/1.528795},
	Journal = jmathp,
	Keywords = {accelerator beam dynamics},
	Month = may,
	Number = {5},
	Pages = {1133--1144},
	Title = {A {H}amiltonian-free description of single particle dynamics for hopelessly complex periodic systems},
	Volume = {31},
	Year = {1990},
	Abstract = {A picture of periodic systems that does not rely on the Hamiltonian of the system, but on maps between a finite number of time locations, is developed.  Moser or Deprit-like normalizations are done directly on the maps, thereby avoiding the complex time-dependent theory.  Linear and nonlinear Floquet variables are redefined entirely in terms of maps.  This approach relies heavily on the Lie representation of maps introduced by Dragt and Finn [J.\ Math.\ Phys.\ \textbf{20}, 2649 (1979); J.\ Geophys.\ Res.\ \textbf{81}, 13 (1976)].  One might say that although the Hamiltonian is not used in the normalization transformation, Lie operators are used, which are themselves, in some sense, pseudo-Hamiltonians for the maps they represent.  The techniques find application in accelerator dynamics or in any field where the Hamiltonian is periodic, but hopelessly complex, such as magnetic field design in stellarators.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.528795}}

@techreport{Forest:1992:ContGuide,
	Address = {Tsukuba, Japan},
	Author = {Forest, {\'E}tienne and Hirata, Kohji},
	Date-Added = {2008-12-03 21:31:09 -0700},
	Date-Modified = {2009-01-14 14:13:41 -0700},
	Institution = {KEK},
	Month = aug,
	Number = {KEK-92-12},
	Title = {A Contemporary Guide to Beam Dynamics},
	Year = {1992},
	Abstract = {A methodological discussion is given for single particle beam dynamics in circular machines.  The discussions are introductory, but (or, even therefore) we avoid to rely on too much simplified concepts.  We treat things from a very general and fundamental point of view, because this is the easiest and rightest way to teach how to simulate particle motion and how to analyze its results.  We give some principles of particle tracking free from theoretical prejudices.  We also introduce some transparent methods to deduce the necessary information from the tracking: many of the traditional beam-dynamics concepts can be abstracted from them as approximate quantities which are valid in certain limiting cases.}}

@article{Forest:1992:SixthOrder,
	Author = {Forest, {\'E}tienne},
	Date-Added = {2009-01-13 10:45:57 -0700},
	Date-Modified = {2009-01-14 14:13:35 -0700},
	Journal = jcompp,
	Month = apr,
	Number = {2},
	Pages = {209--213},
	Title = {Sixth-order {L}ie group integrators},
	Volume = {99},
	Year = {1992},
	Abstract = {In this paper we present the coefficients of several sixth-order symplectic integrators of the type developed by R.~Ruth.  To get these results we fully exploit the connection with Lie groups.  These integrators, as well as all the explicit integrators of Ruth, may be used in any equation where some sort of Lie bracket is preserved.  In fact, if the Lie operator governing the equation of motion is separable into two solvable parts, the Ruth integrators can be used.}}

@article{Forest:1994:CorrectLocal,
	Author = {Forest, {\'E}tienne and Reusch, Michael F. and Bruhwiler, David L. and Amiry, Ali},
	Date-Added = {2008-11-16 17:13:01 -0700},
	Date-Modified = {2009-01-14 14:13:32 -0700},
	Journal = pacc,
	Pages = {65--94},
	Title = {The Correct Local Description for Tracking in Rings},
	Volume = {45},
	Year = {1994},
	Abstract = {We discuss the absolute minimum knowledge required to design a symplectic integrator for rings.  We include details about: (1) symplectic integrators for compund bends, (2) coordinate patches for bends with arbitrary entry and exit angles, (3) general fringe field effects, (4) arbitrary magnet displacements, and (5) radiation effects in electron rings.  Of course, we expect the usual automatic differentiation to be implemented in such integrators and to be linked with a perturbation theory package capable of analyzing symplectic and non-symplectic maps for the beam envelope analysis (calculation of equilibrium second-order moments).}}

@article{Forest:1994:FreedomMNF,
	Author = {Forest, {\'E}tienne and Murray, Diana},
	Date-Added = {2009-04-16 21:56:46 -0600},
	Date-Modified = {2009-04-16 22:00:15 -0600},
	Journal = physd,
	Month = jul,
	Number = {3--4},
	Pages = {181--196},
	Title = {Freedom in minimal normal forms},
	Url = {http://dx.doi.org/10.1016/0167-2789(94)90195-3},
	Volume = {74},
	Year = {1994},
	Abstract = {The purpose of this paper is to clarify the amount of freedom that is available in a complete normalization of a symplectic map.  In particular, we prove that the minimal normal form (MNF) of Kahn and Zarmi is a symplectic normal form in disguise.  We show that there is no reason to believe that the minimal normal has an extended region of good behavior despite the fact that it is better in the immediate neighborhood of the origin.  Our results apply also to multi-dimensional problems.  However, the minimal normal form of Kahn and Zarmi cannot be trivially extended to higher dimensionality without loosing analiticity, thus our discussion will clear up some of the issues raised recently by Mane and Weng.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/0167-2789(94)90195-3}}

@article{Forest:1997:DynEuclid,
	Author = {Forest, {\'E}tienne},
	Date-Added = {2008-11-16 16:26:54 -0700},
	Date-Modified = {2010-03-25 09:46:35 -0600},
	Doi = {10.1103/PhysRevE.55.4665},
	Journal = preve,
	Keywords = {accelerator beam dynamics},
	Month = apr,
	Number = {4},
	Pages = {4665--4674},
	Title = {Locally accurate dynamical {E}uclidean group},
	Volume = {55},
	Year = {1997},
	Abstract = {We derive the locally accurate representation for the dynamical symplectic group for a beam element immersed in a field-free region.  The results are expressed in terms of the displacement of a fiducial frame in the usual Euclidean space.  The method does not involve geometrical constructions of a complexity exceeding that of a usual change of basis in Euclidean space.  The extra complexity is handled by algebraic manipulations connecting the Lie representation of the usual Euclidean group with its dynamical equivalent.  This is achieved by eliminating potential divergences in the ``thin block'' representation.  Although this representation is ideally suited for large machines, it fails in the neighborhood of $180^\circ$ racetrack magnets due to these divergences.  All operations described in this paper can be fully automatized in a computer code.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevE.55.4665}}

@book{Forest:1998:BeamDyn,
	Address = {Amsterdam},
	Author = {Forest, {\'E}tienne},
	Date-Added = {2008-12-04 14:29:47 -0700},
	Date-Modified = {2009-01-14 14:13:05 -0700},
	Publisher = {Harwood Academic Publishers},
	Series = {The Physics and Technology of Particle and Photon Beams},
	Title = {Beam Dynamics: A New Attitude and Framework},
	Volume = {8},
	Year = {1998}}

@article{Forest:1998:DispLattFns,
	Author = {Forest, {\'E}tienne},
	Date-Added = {2009-01-13 11:11:16 -0700},
	Date-Modified = {2009-01-14 14:12:59 -0700},
	Journal = preve,
	Month = aug,
	Number = {2},
	Pages = {2481--2488},
	Title = {Dispersive lattice functions in a six-dimensional pseudo-harmonic-oscillator},
	Volume = {58},
	Year = {1998}}

@article{Forest:1999:MapsDistr,
	Author = {Forest, {\'E}tienne and Robin, David S.},
	Date-Added = {2009-01-13 11:02:35 -0700},
	Date-Modified = {2009-01-14 14:12:54 -0700},
	Journal = preve,
	Month = oct,
	Number = {4},
	Pages = {4793--4810},
	Title = {Maps for distributions and their time evolution},
	Volume = {60},
	Year = {1999},
	Abstract = {Many dynamical stochastic processes occur ``on top'' of a deterministic process.  We present a method which uses the trajectory of the deterministic process as basis functions for quasiarbitrary distributions.  A map for the stochastic process can then be computed.  This may have applications in electron storage rings or other devices perturbed by a small stochasticity.  In this paper we will look only at the most elementary applications of the method.}}

@techreport{Forest:2002:PTC,
	Address = {Tsukuba, Japan},
	Author = {Forest, {\'E}tienne and Schmidt, Frank and McIntosh, Eric},
	Date-Added = {2008-12-04 14:42:24 -0700},
	Date-Modified = {2009-01-14 14:12:49 -0700},
	Institution = {KEK},
	Number = {KEK-2002-3},
	Title = {Introduction to the {P}olymorphic {T}racking {C}ode},
	Year = {2002}}

@inproceedings{Forest:2006:FPP.PTC,
	Author = {Forest, {\'E}tienne and Nogiwa, Yukiko and Schmidt, Frank},
	Crossref = {ICAP:2006},
	Date-Added = {2008-12-04 14:00:46 -0700},
	Date-Modified = {2009-01-14 14:12:42 -0700},
	Pages = {17--21},
	Title = {The {FPP} and {PTC} Libraries},
	Abstract = {In this short article we summarize the FPP package and the tracking code PTC which is crucially based on FPP.  PTC is remarkable for its use of beam structures which take into full account the three dimensional structure of a lattice and its potential topological complexities such as those found in colliders and recirculators.}}

@inproceedings{Forest:2006:FPPDoc,
	Author = {Forest, {\'E}tienne and Nogiwa, Yukiko and Schmidt, Frank},
	Crossref = {ICAP:2006},
	Date-Added = {2008-12-04 13:57:16 -0700},
	Date-Modified = {2009-01-14 14:12:33 -0700},
	Pages = {191--193},
	Title = {The {FPP} Documentation},
	Abstract = {In this short article we summarize the Web documentation surrounding the FPP package.
}}

@article{Forest:2006:GeomIntegPA,
	Author = {Forest, {\'E}tienne},
	Date-Added = {2008-12-03 21:43:33 -0700},
	Date-Modified = {2010-03-25 09:22:11 -0600},
	Doi = {10.1088/0305-4470/39/19/S03},
	Journal = jphysa,
	Keywords = {accelerator beam dynamics},
	Month = may,
	Number = {19},
	Pages = {5321--5377},
	Title = {Geometric integration for particle accelerators},
	Volume = {39},
	Year = {2006},
	Abstract = {This paper is a very personal view of the field of geometric integration in accelerator physics---a field where often work of the highest quality is buried in lost technical notes or even not published; one has only to think of Simon van der Meer Nobel prize work on stochastic cooling---unpublished in any refereed journal.  So I reconstructed the relevant history of geometrical integration in accelerator physics as much as I could by talking to collaborators and using my own understanding of the field.  The reader should not be too surprised if this account is somewhere between history, science and perhaps even fiction.},
	Bdsk-Url-1 = {http://dx.doi.org/10.1088/0305-4470/39/19/S03}}

@unpublished{Forest:2007:SpinReflexions,
	Author = {Forest, {\'E}tienne},
	Date-Added = {2008-11-11 11:26:17 -0700},
	Date-Modified = {2009-01-14 14:11:42 -0700},
	Month = feb,
	Note = {Private communication},
	Title = {Random Reflexions on my Work on Spin and {PTC} inspired by {D}esmond {B}arber},
	Year = {2007},
	Abstract = {I am trying to put the BMT equation in the library PTC.  This is rather easy conceptually.  At the same time, in DESY, Dr.~Barber in the manner of a story teller, presented me with an interesting narrative about spin in accelerator physics.  This is important for me because PTC has in it FPP.  That is to say certain tools are expected by the user of PTC.  Therefore I owe it to Barber and others to provide a coherent picture within PTC that includes spin.  This means that the library FPP should have some spin tools which allow one to track ``spin lattice functions'' (whatever that means) around the ring.  This is also important for me as it provides me anchors on which to tie down my own understanding.  Others who think similarly (Bengtsson for example) might find the present expos\'e valuable.  So in my parlance theory means a normal form.

So in this private note I write down the ideas that flashed through my brain since my DESY visit.  This paper is purely a polaroid picture of my brain at this instant in time.  There is no claim of novelty and thus this is not publishable in any form.

I discuss the Invariant Spin Field, the Floquet representation, the single resonance model (I do not know what it means in standard literature so please excuse the usage here) and also the adiabatic invariant and the associated Hannay angle.

I did not discuss the spin fluctuation.  This is trivial with beam envelopes.  I intend to rewrite PTC anyway as far as fluctuations and radiation are concerned.

As I said, this paper is an attempt to establish anchor points and let others know about them since they will use my tools.}}

@proceedings{HB:2004,
	Address = {Melville, NY},
	Booktitle = {33rd ICFA Advanced Beam Dynamics Workshop on High Intensity and High Brightness Hadron Beams, Bensheim, Germany, 18--22 October 2004},
	Date-Added = {2008-11-17 12:20:21 -0700},
	Date-Modified = {2008-11-17 12:29:42 -0700},
	Editor = {Hofmann, Ingo and Lagniel, Jean-Michel and Hasse, Rainer W.},
	Publisher = {AIP Press},
	Series = {AIP Conference Proceedings},
	Title = {33rd ICFA Advanced Beam Dynamics Workshop on High Intensity and High Brightness Hadron Beams, Bensheim, Germany, 18--22 October 2004},
	Volume = {773},
	Year = {2005}}

@proceedings{HESP:1995,
	Address = {Woodbury, NY},
	Booktitle = {The 11th International symposium on high energy spin physics, Bloomington IN, 15--22 September 1994},
	Date-Added = {2009-03-17 10:16:18 -0600},
	Date-Modified = {2009-03-17 10:27:09 -0600},
	Editor = {Heller, Kenneth J. and Smith, Sandra L.},
	Publisher = {AIP Press},
	Series = {AIP Conference Proceedings},
	Title = {The 11th International symposium on high energy spin physics, Bloomington IN, 15--22 September 1994},
	Volume = {343},
	Year = {1995}}

@proceedings{ICAP:2006,
	Booktitle = {Proceedings of the 9th International Computational Accelerator Physics Conference, Chamonix, France, 2--6 October 2006},
	Date-Added = {2008-12-04 13:36:22 -0700},
	Date-Modified = {2011-05-29 13:21:37 -0600},
	Key = {Int. Conf. Accel. Phys. 2006},
	Title = {Proceedings of the 9th International Computational Accelerator Physics Conference, Chamonix, France, 2--6 October 2006},
	Year = {2006},
	Bdsk-Url-1 = {http://icap2006.web.cern.ch/icap2006/}}

@proceedings{LINAC:1966,
	Booktitle = {Proceedings of the 1966 Linear Acelerator Conference, 3--7 October 1966},
	Date-Added = {2009-07-22 16:50:37 -0600},
	Date-Modified = {2009-07-22 17:09:54 -0600},
	Editor = {McDonald, John W.},
	Month = dec,
	Note = {Available as Technical Report LA-3609, Los Alamos National Laboratory, Los Alamos, NM},
	Title = {Proceedings of the 1966 Linear Acelerator Conference, 3--7 October 1966},
	Year = {1966}}

@proceedings{PAC:1967,
	Address = {Piscataway, NJ},
	Booktitle = {Proceedings of the 1967 IEEE Particle Acelerator Conference, Washington, DC, 1--3 March 1967},
	Date-Added = {2009-07-22 17:28:06 -0600},
	Date-Modified = {2009-07-22 17:34:17 -0600},
	Editor = {Howard, Fred T.},
	Publisher = {IEEE},
	Title = {Proceedings of the 1967 IEEE Particle Acelerator Conference, Washington, DC, 1--3 March 1967},
	Year = {1967},
	Bdsk-Url-1 = {http://accelconf.web.cern.ch/AccelConf/p67/}}

@proceedings{PAC:1969,
	Address = {Piscataway, NJ},
	Booktitle = {Proceedings of the 1969 IEEE Particle Acelerator Conference, Washington, DC, 5--7 March 1969},
	Date-Added = {2009-04-17 10:12:50 -0600},
	Date-Modified = {2009-04-17 10:15:28 -0600},
	Editor = {Howard, Fred T.},
	Publisher = {IEEE},
	Title = {Proceedings of the 1969 IEEE Particle Acelerator Conference, Washington, DC, 5--7 March 1969},
	Year = {1969},
	Bdsk-Url-1 = {http://accelconf.web.cern.ch/accelconf/p69/INDEX.HTM}}

@proceedings{PAC:1971,
	Address = {Piscataway, NJ},
	Booktitle = {Proceedings of the 1971 IEEE Particle Acelerator Conference, Chicago, IL, 1--3 March 1971},
	Date-Added = {2009-04-03 16:30:39 -0600},
	Date-Modified = {2009-04-17 10:16:06 -0600},
	Editor = {Howard, Fred T.},
	Publisher = {IEEE},
	Title = {Proceedings of the 1971 IEEE Particle Acelerator Conference, Chicago, IL, 1--3 March 1971},
	Year = {1971},
	Bdsk-Url-1 = {http://accelconf.web.cern.ch/accelconf/p71/INDEX.HTM}}

@proceedings{PAC:1973,
	Address = {Piscataway, NJ},
	Booktitle = {Proceedings of the 1973 IEEE Particle Acelerator Conference, San Francisco, CA, 5--7 March 1973},
	Date-Added = {2009-04-03 16:15:50 -0600},
	Date-Modified = {2009-04-03 16:44:29 -0600},
	Editor = {Dupen, Douglas W.},
	Publisher = {IEEE},
	Title = {Proceedings of the 1973 IEEE Particle Acelerator Conference, San Francisco, CA, 5--7 March 1973},
	Year = {1973},
	Bdsk-Url-1 = {http://accelconf.web.cern.ch/accelconf/p73/INDEX.HTM}}

@proceedings{PAC:1975,
	Address = {Piscataway, NJ},
	Booktitle = {Proceedings of the 1975 IEEE Particle Acelerator Conference, Washington, DC, 12--14 March 1975},
	Date-Added = {2009-04-17 10:48:02 -0600},
	Date-Modified = {2009-04-17 10:50:00 -0600},
	Editor = {Placious, Robert C.},
	Publisher = {IEEE},
	Title = {Proceedings of the 1975 IEEE Particle Acelerator Conference, Washington, DC, 12--14 March 1975},
	Year = {1975},
	Bdsk-Url-1 = {http://accelconf.web.cern.ch/accelconf/p75/INDEX.HTM}}

@proceedings{PAC:1977,
	Address = {Piscataway, NJ},
	Booktitle = {Proceedings of the 1977 IEEE Particle Acelerator Conference, Chicago, IL, 16--18 March 1977},
	Date-Added = {2009-04-03 16:28:21 -0600},
	Date-Modified = {2009-04-03 16:30:02 -0600},
	Editor = {Cole, Frank T. and Donaldson, R.},
	Publisher = {IEEE},
	Title = {Proceedings of the 1977 IEEE Particle Acelerator Conference, Chicago, IL, 16--18 March 1977},
	Year = {1977},
	Bdsk-Url-1 = {http://accelconf.web.cern.ch/accelconf/p77/INDEX.HTM}}

@proceedings{PAC:1979,
	Address = {Piscataway, NJ},
	Booktitle = {Proceedings of the 1979 IEEE Particle Acelerator Conference, San Francisco, CA, 12--14 March 1979},
	Date-Added = {2009-04-17 10:50:54 -0600},
	Date-Modified = {2009-04-17 10:52:25 -0600},
	Editor = {Hendrickson, R.},
	Publisher = {IEEE},
	Title = {Proceedings of the 1979 IEEE Particle Acelerator Conference, San Francisco, CA, 12--14 March 1979},
	Year = {1979},
	Bdsk-Url-1 = {http://accelconf.web.cern.ch/accelconf/p79/INDEX.HTM}}

@proceedings{PAC:1981,
	Address = {Piscataway, NJ},
	Booktitle = {Proceedings of the 1981 IEEE Particle Acelerator Conference, Washington, DC, 11--13 March 1981},
	Date-Added = {2009-04-17 10:53:44 -0600},
	Date-Modified = {2009-04-17 10:54:54 -0600},
	Editor = {Placious, Robert C.},
	Publisher = {IEEE},
	Title = {Proceedings of the 1981 IEEE Particle Acelerator Conference, Washington, DC, 11--13 March 1981},
	Year = {1981},
	Bdsk-Url-1 = {http://accelconf.web.cern.ch/accelconf/p81/INDEX.HTM}}

@proceedings{PAC:1983,
	Address = {Piscataway, NJ},
	Booktitle = {Proceedings of the 1983 IEEE Particle Acelerator Conference, Santa Fe, NM, 21--23 March 1983},
	Date-Added = {2009-04-16 22:03:56 -0600},
	Date-Modified = {2009-04-16 22:07:01 -0600},
	Editor = {Taylor, Louise S.},
	Publisher = {IEEE},
	Title = {Proceedings of the 1983 IEEE Particle Acelerator Conference, Santa Fe, NM, 21--23 March 1983},
	Year = {1983},
	Bdsk-Url-1 = {http://accelconf.web.cern.ch/accelconf/p83/INDEX.HTM}}

@proceedings{PAC:1985,
	Address = {Piscataway, NJ},
	Booktitle = {Proceedings of the 1985 IEEE Particle Acelerator Conference, Vancouver, BC, Canada 13--16 May 1985},
	Date-Added = {2009-04-17 10:17:01 -0600},
	Date-Modified = {2009-04-17 10:27:40 -0600},
	Editor = {Strathdee, Ada},
	Publisher = {IEEE},
	Title = {Proceedings of the 1985 IEEE Particle Acelerator Conference, Vancouver, BC, Canada 13--16 May 1985},
	Year = {1985},
	Bdsk-Url-1 = {http://accelconf.web.cern.ch/accelconf/p85/INDEX.HTM}}

@proceedings{PAC:1987,
	Address = {Piscataway, NJ},
	Booktitle = {Proceedings of the 1987 IEEE Particle Acelerator Conference, Washington, DC, 16--19 March 1987},
	Date-Added = {2009-03-30 11:05:58 -0600},
	Date-Modified = {2009-03-30 11:17:11 -0600},
	Editor = {Lindstrom, Eric R. and Taylor, Louise S.},
	Publisher = {IEEE},
	Title = {Proceedings of the 1987 IEEE Particle Acelerator Conference, Washington, DC, 16--19 March 1987},
	Year = {1987},
	Bdsk-Url-1 = {http://accelconf.web.cern.ch/accelconf/p87/INDEX.HTM}}

@proceedings{PAC:1989,
	Address = {Piscataway, NJ},
	Booktitle = {Proceedings of the 1989 IEEE Particle Acelerator Conference, Chicago, IL, 20--23 March 1989},
	Date-Added = {2009-03-30 11:13:15 -0600},
	Date-Modified = {2009-03-30 11:16:16 -0600},
	Editor = {Bennett, Floyd and Kopta, Joyce},
	Publisher = {IEEE},
	Title = {Proceedings of the 1989 IEEE Particle Acelerator Conference, Chicago, IL, 20--23 March 1989},
	Year = {1989},
	Bdsk-Url-1 = {http://accelconf.web.cern.ch/accelconf/p89/INDEX.HTM}}

@proceedings{PAC:1991,
	Address = {Piscataway, NJ},
	Booktitle = {Proceedings of the 1991 IEEE Particle Acelerator Conference, San Francisco, CA, 6--9 May 1991},
	Date-Added = {2008-11-11 15:50:23 -0700},
	Date-Modified = {2009-04-17 10:46:19 -0600},
	Editor = {Lizama, Loretta and Chew, Joe},
	Publisher = {IEEE},
	Title = {Proceedings of the 1991 IEEE Particle Acelerator Conference, San Francisco, CA, 6--9 May 1991},
	Year = {1991},
	Bdsk-Url-1 = {http://accelconf.web.cern.ch/accelconf/p91/INDEX.HTM}}

@proceedings{PAC:1993,
	Address = {Piscataway, NJ},
	Booktitle = {Proceedings of the 1993 Particle Acelerator Conference, Washington, DC, 17--20 May 1993},
	Date-Added = {2008-11-11 15:31:19 -0700},
	Date-Modified = {2009-02-17 13:30:51 -0700},
	Editor = {Corneliussen, S. T.},
	Publisher = {IEEE},
	Title = {Proceedings of the 1993 Particle Acelerator Conference, Washington, DC, 17--20 May 1993},
	Year = {1993},
	Bdsk-Url-1 = {http://accelconf.web.cern.ch/accelconf/p93/INDEX.HTM}}

@proceedings{PAC:1995,
	Address = {Piscataway, NJ},
	Booktitle = {Proceedings of the 1995 Particle Acelerator Conference, Dallas, TX, 1--5 May 1995},
	Date-Added = {2008-11-11 15:15:30 -0700},
	Date-Modified = {2008-11-11 16:19:57 -0700},
	Editor = {Gennari, L. Trindle and Siemann, Robert H.},
	Publisher = {IEEE},
	Title = {Proceedings of the 1995 Particle Acelerator Conference, Dallas, TX, 1--5 May 1995},
	Year = {1995},
	Bdsk-Url-1 = {http://accelconf.web.cern.ch/AccelConf/p95/}}

@proceedings{PAC:1997,
	Address = {Piscataway, NJ},
	Booktitle = {Proceedings of the 1997 Particle Acelerator Conference, Vancouver, BC, Canada, 12--16 May 1997},
	Date-Added = {2008-11-11 15:02:22 -0700},
	Date-Modified = {2009-04-17 11:03:09 -0600},
	Editor = {Comyn, Martin and Craddock, Michael K. and Reiser, Martin and Thomson, J.},
	Publisher = {IEEE},
	Title = {Proceedings of the 1997 Particle Acelerator Conference, Vancouver, BC, Canada, 12--16 May 1997},
	Year = {1997},
	Bdsk-Url-1 = {http://accelconf.web.cern.ch/accelconf/pac97/}}

@proceedings{PAC:1999,
	Address = {Piscataway, NJ},
	Booktitle = {Proceedings of the 1999 Particle Acelerator Conference, New York, NY, 29 March--2 April 1999},
	Date-Added = {2008-11-13 12:20:05 -0700},
	Date-Modified = {2008-11-13 12:20:05 -0700},
	Editor = {Luccio, Alfredo U. and MacKay, William W.},
	Publisher = {IEEE},
	Title = {Proceedings of the 1999 Particle Acelerator Conference, New York, NY, 29 March--2 April 1999},
	Year = {1999},
	Bdsk-Url-1 = {http://accelconf.web.cern.ch/AccelConf/p99/procs.htm}}

@proceedings{PAC:2001,
	Address = {Piscataway, NJ},
	Booktitle = {Proceedings of the 2001 Particle Acelerator Conference, Chicago, IL, 18--22 June 2001},
	Date-Added = {2008-11-13 12:25:15 -0700},
	Date-Modified = {2008-11-13 12:25:15 -0700},
	Editor = {Lucas, Peter W. and Webber, Sara},
	Publisher = {IEEE},
	Title = {Proceedings of the 2001 Particle Acelerator Conference, Chicago, IL, 18--22 June 2001},
	Year = {2001},
	Bdsk-Url-1 = {http://accelconf.web.cern.ch/AccelConf/p01/}}

@proceedings{PAC:2003,
	Address = {Piscataway, NJ},
	Booktitle = {Proceedings of the 2003 Particle Acelerator Conference, Portland, OR, 12--16 May 2003},
	Date-Added = {2008-11-13 12:25:14 -0700},
	Date-Modified = {2008-11-13 12:29:14 -0700},
	Editor = {Chew, Joseph T. and Lucas, Peter W. and Webber, Sara},
	Publisher = {IEEE},
	Title = {Proceedings of the 2003 Particle Acelerator Conference, Portland, OR, 12--16 May 2003},
	Year = {2003},
	Bdsk-Url-1 = {http://accelconf.web.cern.ch/accelconf/p03/}}

@proceedings{PAC:2005,
	Address = {Piscataway, NJ},
	Booktitle = {Proceedings of the 2005 Particle Acelerator Conference, Knoxville, TN, 16--20 May 2005},
	Date-Added = {2008-11-13 12:25:13 -0700},
	Date-Modified = {2008-11-13 12:54:38 -0700},
	Editor = {Horak, Charlie M.},
	Publisher = {IEEE},
	Title = {Proceedings of the 2005 Particle Acelerator Conference, Knoxville, TN, 16--20 May 2005},
	Year = {2005},
	Bdsk-Url-1 = {http://accelconf.web.cern.ch/accelconf/p05/}}

@proceedings{PAC:2007,
	Address = {Piscataway, NJ},
	Booktitle = {Proceedings of the 2007 Particle Acelerator Conference, Albuquerque, NM, 25--29 June 2007},
	Date-Added = {2008-11-11 14:53:46 -0700},
	Date-Modified = {2008-11-13 13:06:09 -0700},
	Publisher = {IEEE},
	Title = {Proceedings of the 2007 Particle Acelerator Conference, Albuquerque, NM, 25--29 June 2007},
	Year = {2007},
	Bdsk-Url-1 = {http://accelconf.web.cern.ch/accelconf/p07/},
	Bdsk-Url-2 = {http://pac07.org/}}

@proceedings{PAC:2009,
	Address = {Piscataway, NJ},
	Booktitle = {Proceedings of the 2009 Particle Acelerator Conference, Vancouver, BC, 4--8 May 2009},
	Date-Added = {2008-12-06 09:03:29 -0700},
	Date-Modified = {2008-12-06 09:06:27 -0700},
	Editor = {Comyn, Martin},
	Publisher = {IEEE},
	Title = {Proceedings of the 2009 Particle Acelerator Conference, Vancouver, BC, 4--8 May 2009},
	Year = {2009},
	Bdsk-Url-1 = {http://www.triumf.info/hosted/PAC09/}}

@proceedings{PHEPA:1982,
	Address = {Woodbury, NY},
	Booktitle = {Physics of High Energy Particle Accelerators: Fermilab Summer School, Batavia, IL, 13--24 July, 1981},
	Date-Added = {2008-12-13 10:20:31 -0700},
	Date-Modified = {2008-12-13 10:34:33 -0700},
	Editor = {Carrigan, Richard A. and Huson, F. Russ and Month, Melvin},
	Publisher = {AIP Press},
	Series = {AIP Conference Proceedings},
	Title = {Physics of High Energy Particle Accelerators: Fermilab Summer School, Batavia, IL, 13--24 July, 1981},
	Volume = {87},
	Year = {1982}}

@proceedings{PHYPA:1987,
	Address = {Woodbury, NY},
	Booktitle = {Physics of Particle Accelerators},
	Date-Added = {2008-12-04 10:37:41 -0700},
	Date-Modified = {2008-12-04 10:42:44 -0700},
	Editor = {Month, Melvin and Dienes, Margaret},
	Publisher = {AIP Press},
	Series = {AIP Conference Proceedings},
	Title = {Physics of Particle Accelerators},
	Volume = {184},
	Year = {1987}}

@proceedings{PPHE:1999,
	Booktitle = {Proceedings of the Workshop on Polarized Protons at High Energies, Hamburg, Germany, 17--20 May 1999},
	Date-Added = {2008-11-17 11:16:30 -0700},
	Date-Modified = {2008-11-17 11:18:12 -0700},
	Title = {Proceedings of the Workshop on Polarized Protons at High Energies, Hamburg, Germany, 17--20 May 1999},
	Year = {1999}}

@proceedings{SC:2008,
	Address = {New York, NY},
	Booktitle = {Proceedings of the 22nd ACM International Conference on Supercomputing, Island of Kos, Greece, 7--12 June 2008},
	Date-Added = {2008-11-19 06:56:25 -0700},
	Date-Modified = {2008-11-19 07:05:56 -0700},
	Publisher = {Association for computing Machinery},
	Title = {Proceedings of the 22nd ACM International Conference on Supercomputing, Island of Kos, Greece, 7--12 June 2008},
	Year = {2008}}

@proceedings{SPIN:2004,
	Address = {Singapore},
	Booktitle = {The 16th International Spin Physics Symposium, Trieste, Italy, 10--16 October 2004},
	Date-Added = {2008-11-17 11:59:46 -0700},
	Date-Modified = {2008-11-17 12:03:19 -0700},
	Editor = {Bradamante, Franco and Bressan, Andrea and Martin, Anna and Aulenbacher, Kurt},
	Publisher = {World Scientific},
	Title = {The 16th International Spin Physics Symposium, Trieste, Italy, 10--16 October 2004},
	Year = {2005}}

@proceedings{SPMSR:1992,
	Address = {Woodbury, NY},
	Booktitle = {Proceedings of the Workshop on the Stability of Particle Motion in Storage Rings, Upton, NY, 19--24 October 1992},
	Date-Added = {2008-11-17 13:19:49 -0700},
	Date-Modified = {2008-12-13 09:22:09 -0700},
	Editor = {Month, Melvin and Ruggiero, Alessandro G. and Weng, Wu-Tsung},
	Publisher = {AIP Press},
	Series = {AIP Conference Proceedings},
	Title = {Proceedings of the Workshop on the Stability of Particle Motion in Storage Rings, Upton, NY, 19--24 October 1992},
	Volume = {292},
	Year = {1982}}

@proceedings{WSCP:1998,
	Address = {Woodbury, NY},
	Booktitle = {Workshop on Space Charge Physics in High Intensity Hadron Rings, Shelter Island, NY, 4--7 May 1998},
	Date-Added = {2008-11-17 11:33:43 -0700},
	Date-Modified = {2008-11-17 12:25:53 -0700},
	Editor = {Luccio, Alfredo U. and Weng, Wu-Tsung},
	Publisher = {AIP Press},
	Series = {AIP Conference Proceedings},
	Title = {Workshop on Space Charge Physics in High Intensity Hadron Rings, Shelter Island, NY, 4--7 May 1998},
	Volume = {448},
	Year = {1998}}

@proceedings{IPAC:2012,
	Booktitle = {Proceedings of the 3rd International Particle Accelerator Conference, New Orleans, LA, 20--25 May 2012},
	Date-Added = {2015-04-03 19:32:52 +0000},
	Date-Modified = {2015-04-03 19:32:52 +0000},
	Editor = {Eyberger, C. and Satogata, Todd and Petit-Jean-Genaz, Christine},
	Title = {Proceedings of the 3rd International Particle Accelerator Conference, New Orleans, LA, 20--25 May 2012},
	Year = {2012},
	Bdsk-Url-1 = {http://www.ipac12.org/}}