Finding matched rms envelopes in rf linacs: A Hamiltonian approach

Details Finding matched rms envelopes in rf linacs: A Hamiltonian approach Finding matched rms envelopes in rf linacs: A Hamiltonian approach

1995-02-12

arxiv.org/abs/acc-phys/9502001v1

Physics

Accelerator Physics

10 pages, uuencoded gzipped PostScript (88K)

Scientific paper

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.

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