1995/02/12 by Robert D. Ryne, Ryne, Robert D. · 1 citation
Engineering · Physics and Astronomy · #Accelerator Physics (physics.acc-ph) #FOS: Physical sciences #Gyrotron and Vacuum Electronics Research #Particle Accelerators and Free-Electron Lasers #Particle accelerators and beam dynamics #acc-phys #physics.acc-ph
paper · pdf · doi:10.48550/arxiv.acc-phys/9502001
10 pages, uuencoded gzipped PostScript (88K)
arxiv created 1995/02/12 · openalex publication_date 1995/02/12 · arxiv updated 2012/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a new method for obtaining matched solutions of the rms envelope equations. In this approach, the envelope equations are first expressed in Hamiltonian form. The Hamiltonian defines a nonlinear mapping, \cal M, and for periodic transport systems the fixed points of the one-period map are the matched envelopes. Expanding the Hamiltonian around a fiducial trajectory one obtains a linear map, M, that describes trajectories (rms envelopes) near the fiducial trajectory. Using \cal M and M we construct a contraction mapping that can be used to obtain the matched envelopes. The algorithm is quadratically convergent. Using the zero-current matched parameters as starting values, the contraction mapping typically converges in a few to several iterations. Since our approach uses numerical integration to obtain all the mappings, it includes the effects of nonidealized, z-dependent transverse and longitudinal focusing fields. We present numerical examples including finding a matched beam in a quadrupole channel with rf bunchers.