Construction of Nonlinear Symplectic Six-Dimensional Thin-Lens Maps by Exponentiation

Details Construction of Nonlinear Symplectic Six-Dimensional Thin-Lens Maps by Exponentiation Construction of Nonlinear Symplectic Six-Dimensional Thin-Lens Maps by Exponentiation

1995-10-30

arxiv.org/abs/acc-phys/9510005v1

Physics

Accelerator Physics

57 pages, latex

Scientific paper

The aim of this paper is to construct six-dimensional symplectic thin-lens transport maps for the tracking program SIXTRACK, continuing an earlier report by using another method which consistes in applying Lie series and exponentiation as described by W. Groebner and for canonical systems by A.J. Dragt. We firstly use an approximate Hamiltonian obtained by a series expansion of the square root. Furthermore, nonlinear crossing terms due to the curvature in bending magnets are neglected. An improved Hamiltonian, excluding solenoids, is introduced in Appendix A by using the unexpanded square root mentioned above, but neglecting again nonlinear crossing terms...

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