3 Non-linear Dynamics in Accelerators
103
In all cases care must be taken to avoid numerical problems due to the
computation techniques when a simulation over many turns is performed.
References
1. W. Herr, Mathematical and Numerical Methods for Nonlinear Dynamics Proc. CERN
Accelerator School: Advanced Accelerator Physics (2013), published as CERN Yellow
Report CERN-2014-009, arXiv:1601.07311.
2. E. Courant and H. Snyder, Theory of the Alternating Gradient Synchrotron, Ann. Phys. 3
(1958) 1.
3. A. Wolski, Beam Dynamics in High Energy Particle Accelerators, Imperial College Press
(2014).
4. H. Wiedemann, Particle Accelerator Physics—basic Principles and Linear Beam Dynamics, Springer-Verlag (1993).
5. A. Chao and M. Tigner, Handbook of Accelerator Physics and Engineering, World Scientific
(1998).
6. E. Forest, Beam Dynamics, Harwood Academic Publishers (1998).
7. A. Chao, Lecture Notes on Topics in Accelerator Physics, SLAC (2001).
8. A. Dragt, Lie Methods for Nonlinear Dynamics with Applications to Accelerator
Physics, in preparation, Univ. of Maryland (Nov. 2019). https://www.physics.umd.edu/dsat/
dsatliemethods.html.
9. E. Courant and R. Ruth, Stability in Dynamical Systems, Summer School on High Energy
Particle Accelerators, Upton, New York, July 6–16, 1983.
10. A. Dragt and E. Forest, Computation of Nonlinear Behaviour of Hamiltonian Systems
using Lie Algebraic Methods, J.Math.Phys. 24, 2734 (1983).
11. E. Forest and R. Ruth, Physica D43, (1990) 105.
12. H. Yoshida, Phys. Lett A150 (1990) 262.
13. W. Herr, Relativity, lecture at CAS-CERN Accelerator School on “Introduction to accelerator
Physics”, Budapest, Hungary (2016).
14. S. Sheehy, Motion of Particles in Electro-magnetic Fields, lecture at CAS-CERN Accelerator School on “Introduction to accelerator Physics”, Budapest, Hungary (2016).
15. A. Dragt, AIP Proc. 87, Phys. High Energy Accelerators, Fermilab, (1981) 147.
16. A. Dragt et al., Ann. Rev. Nucl. Part. Sci 38 (1988) 455.
17. A. Dragt et al, Phys. Rev. A45, (1992) 2572.
18. H. Goldstein, Classical Mechanics, Addison Wesley, (2001).
19. A. Dragt and J. Finn, J. Math. Phys., 17, 2215 (1976); A. Dragt et al., Ann. Rev. Nucl. Part.
Sci., 38, 455 (1988).
20. H. Poincare, Les Methods Nouvelles de la Mecanique Celeste, Gauthier-Villars, Paris (1892).
21. M. Berz, Particle Accelerators 24, (1989) 109.
22. W. Herr, D. Kaltchev, Effect of phase advance between interaction points in the LHC on
the beam-beam interaction, LHC Project Report 1082, unpublished, (2008).
23. T. Pieloni, A Study of Beam-Beam Effects in Hadron Colliders with a Large Number of
Bunches, PhD thesis Nr. 4211, EPFL Lausanne, (2008).
24. H.S. Dumas, J. Laskar, Phys. Rev. Lett. 70 (1989) 2975.
25. J. Laskar, D. Robin, Particle Accelerators 54 (1996)183.
26. G. Benettin et al., Phys. Rev. A14 (1976) 2338.
27. B.V. Chirikov, At. Energ. 6, (1959) 630.
103
In all cases care must be taken to avoid numerical problems due to the
computation techniques when a simulation over many turns is performed.
References
1. W. Herr, Mathematical and Numerical Methods for Nonlinear Dynamics Proc. CERN
Accelerator School: Advanced Accelerator Physics (2013), published as CERN Yellow
Report CERN-2014-009, arXiv:1601.07311.
2. E. Courant and H. Snyder, Theory of the Alternating Gradient Synchrotron, Ann. Phys. 3
(1958) 1.
3. A. Wolski, Beam Dynamics in High Energy Particle Accelerators, Imperial College Press
(2014).
4. H. Wiedemann, Particle Accelerator Physics—basic Principles and Linear Beam Dynamics, Springer-Verlag (1993).
5. A. Chao and M. Tigner, Handbook of Accelerator Physics and Engineering, World Scientific
(1998).
6. E. Forest, Beam Dynamics, Harwood Academic Publishers (1998).
7. A. Chao, Lecture Notes on Topics in Accelerator Physics, SLAC (2001).
8. A. Dragt, Lie Methods for Nonlinear Dynamics with Applications to Accelerator
Physics, in preparation, Univ. of Maryland (Nov. 2019). https://www.physics.umd.edu/dsat/
dsatliemethods.html.
9. E. Courant and R. Ruth, Stability in Dynamical Systems, Summer School on High Energy
Particle Accelerators, Upton, New York, July 6–16, 1983.
10. A. Dragt and E. Forest, Computation of Nonlinear Behaviour of Hamiltonian Systems
using Lie Algebraic Methods, J.Math.Phys. 24, 2734 (1983).
11. E. Forest and R. Ruth, Physica D43, (1990) 105.
12. H. Yoshida, Phys. Lett A150 (1990) 262.
13. W. Herr, Relativity, lecture at CAS-CERN Accelerator School on “Introduction to accelerator
Physics”, Budapest, Hungary (2016).
14. S. Sheehy, Motion of Particles in Electro-magnetic Fields, lecture at CAS-CERN Accelerator School on “Introduction to accelerator Physics”, Budapest, Hungary (2016).
15. A. Dragt, AIP Proc. 87, Phys. High Energy Accelerators, Fermilab, (1981) 147.
16. A. Dragt et al., Ann. Rev. Nucl. Part. Sci 38 (1988) 455.
17. A. Dragt et al, Phys. Rev. A45, (1992) 2572.
18. H. Goldstein, Classical Mechanics, Addison Wesley, (2001).
19. A. Dragt and J. Finn, J. Math. Phys., 17, 2215 (1976); A. Dragt et al., Ann. Rev. Nucl. Part.
Sci., 38, 455 (1988).
20. H. Poincare, Les Methods Nouvelles de la Mecanique Celeste, Gauthier-Villars, Paris (1892).
21. M. Berz, Particle Accelerators 24, (1989) 109.
22. W. Herr, D. Kaltchev, Effect of phase advance between interaction points in the LHC on
the beam-beam interaction, LHC Project Report 1082, unpublished, (2008).
23. T. Pieloni, A Study of Beam-Beam Effects in Hadron Colliders with a Large Number of
Bunches, PhD thesis Nr. 4211, EPFL Lausanne, (2008).
24. H.S. Dumas, J. Laskar, Phys. Rev. Lett. 70 (1989) 2975.
25. J. Laskar, D. Robin, Particle Accelerators 54 (1996)183.
26. G. Benettin et al., Phys. Rev. A14 (1976) 2338.
27. B.V. Chirikov, At. Energ. 6, (1959) 630.