Guide to Non-linear Dynamics in Accelerator Physics/Guided Bibliography

E. Forest, "Beam Dynamics- A New Attitude and Framework" Very good source of informations. The topics are somehow mixed and sometime it is difficult to follow linearly. Here there is a selection of relevant sections order by topic: tracking: from em field to one turn map around a fixed point 3.2.2 connecting pieces 3.3.3 misaligments 8.1.4 fixed point search 10 misaligments (includes bendings) 11.3 yoshida integrators 11.3.2.2 s dependent first order integrators (maybe kick map) 12.1 Hamiltonian splittings for magnets linear one turn map: 2.4.1 2.4.2 basics of "diagonalization" 4.5 linear motions 4.5.1 symplectic 4.5.2 dissipative linear lattice functions: block matrix reduction 2.5 betaoids and tune 4.4.1 betaoids non linear motion: non linear normalization 2.3 definitions and properties 2.4.3 normal forms algorithm 3.4.3 DA equivalence between maps around fixed points and power series 4.4 dragt-finn factorization 4.4.2 normal forms algorithm 5.1.2 terms of the normalized hamiltonians, chromaciticies resonances 5.1.3 definitions 5.2 resonances basis 6.3 harmonic driving terms 6.4 resonance basis for non symplectic vector fields coasting beam 7.3.2 coasting beam, etaoids analytical perturbation theory 8.4 basics 9.1 examples (quantum as well) damping 15 radiation pag. 418 interlude (is emittance growth intrinsic or corse graining?) 15.3 etaoids betaoid with damping L. Michelotti, Intermediate Classical Dynamics with Applications to Beam Physics Includes many of the concepts used in Forest's book. Here they are spelled out a bit more explicitly. L.M. makes a point to generalize phase space to a manifold. (The subject of dynamics is described as "vector fields on a manifold"). This allows for phase space to have more complicated topology than R^n. For example, the phase space of a pendulum is a torus. The book culminates in a description of the Forest, Irwin, Berz normal form algorithm. This is described quite formally, with emphasis on commutative diagrams and solving the homological equations at each step. Although the purpose of such an algorithm (mainly to find amplitude dependent tune shift for a general one turn map) is described clearly at places, it is easy to get lost in all the symbols. Reading chapters 3 and 4 describe the models that one is to keep in mind, and the physics that is to be extracted from the general perturbation theory algorithms of chapters 5 and 6. The epilogue begins with a quote by Saul Bellow describing the breakdown of language. One can't help but feel that this is commentary on the state of non-linear dynamics in accelerator physics. The break between old methods of Hamiltonian mechanics and new left a descriptive gap in the field. Michelotti has tried valiantly to bridge that gap. Although one may feel that he isn't entirely successful in formulating the symbols and language to describe the physics and the algorithms, this book is the closest to solid ground one may find when trying to navigate some of the literature in this field. Guide to papers on non-linear dynamics http://www.slac.stanford.edu/spires/find/hep/www?irn=467014 Lie Series and Invariant Functions for Analytic Symplectic Maps A.J. Dragt , J.M. Finn . 1976 J.Math.Phys.17:2215-2227,1976 http://link.aip.org/link/?jmp/17/2215 Dragt-Finn factorization. Good introduction to Lie tools. http://www.slac.stanford.edu/spires/find/hep/www?irn=614939 Method of transfer maps for linear and nonlinear beam elements A.J. Dragt . 1979 IEEE Trans.Nucl.Sci.26:3601-3603,1979 http://accelconf.web.cern.ch/AccelConf/p79/PDF/PAC1979_3601.PDF Application of Dragt-Finn factorization to accelerators http://www.slac.stanford.edu/spires/find/hep/www?irn=398560 TRANSFER MAP APPROACH TO THE BEAM-BEAM INTERACTION Alex J. Dragt . 1979 Not found Not available , asked Fermilab Not read http://www.slac.stanford.edu/spires/find/hep/www?irn=1014870 Analysis of the Beam-Beam Interaction Using Transfer Maps. (Talk) A.J. Dragt , O.G. Jakubowicz . 1980 Stanford 1980 , Proceedings , Beam-beam Interaction Not available Not read http://www.slac.stanford.edu/spires/find/hep/www?irn=1010344 Charged Particle Beam Transport Using Lie Algebraic Methods D.R. Douglas , A.J. Dragt . 1981 IEEE Trans.Nucl.Sci.28:2522-2524,1981 http://accelconf.web.cern.ch/AccelConf/p81/PDF/PAC1981_2522.PDF Example of factorization for beam lines elements. http://www.slac.stanford.edu/spires/find/hep/www?irn=1010476 Exact Numerical Calculation Of Chromaticity In Small Rings A.J. Dragt . 1981 IEEE Trans.Nucl.Sci.28:2627-2629,1981 http://accelconf.web.cern.ch/AccelConf/p81/PDF/PAC1981_2627.PDF Determination of chromaticity from the eigenvalues of the energy dependent transfer map. Use of variational calculus is a bit cryptic. http://www.slac.stanford.edu/spires/find/hep/www?irn=1224344 Lectures On Nonlinear Orbit Dynamics. A.J. Dragt . 1981 AIP Conf.Proc.87:147-313,1982 http://link.aip.org/link/?APC/087/147 General introduction to hamiltonias and lie methods. 167 pages http://www.slac.stanford.edu/spires/find/hep/www?irn=1208250 Lie Algebraic Methods For Particle Tracking Calculations. D.R. Douglas , A.J. Dragt . 1983 LBL-16008 Not available Not read http://www.slac.stanford.edu/spires/find/hep/www?irn=1276158 Single Particle Stability M. Cornacchia et al. . 1983 Ann Arbor 1983, Proceedings, Accelerator Physics Issues For A Superconducting Super Collider Not available Not read http://www.slac.stanford.edu/spires/find/hep/www?irn=1255088 MARYLIE: The Maryland Lie Algebraic Transport and Tracking Code D.R. Douglas , A.J. Dragt . 1984 IEEE Trans.Nucl.Sci.30:2442-2444,1983 http://accelconf.web.cern.ch/AccelConf/p83/PDF/PAC1983_2442.pdf Marylie code, analysis limited to F2, F3