Finding matched rms envelopes in rf linacs: A Hamiltonian approach

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.Comment: 10 pages, uuencoded gzipped PostScript (88K

Large-Scale Simulation of Beam Dynamics in High Intensity Ion Linacs Using Parallel Supercomputers

In this paper we present results of using parallel supercomputers to simulate beam dynamics in next-generation high intensity ion linacs. Our approach uses a three-dimensional space charge calculation with six types of boundary conditions. The simulations use a hybrid approach involving transfer maps to treat externally applied fields (including rf cavities) and parallel particle-in-cell techniques to treat the space-charge fields. The large-scale simulation results presented here represent a three order of magnitude improvement in simulation capability, in terms of problem size and speed of execution, compared with typical two-dimensional serial simulations. Specific examples will be presented, including simulation of the spallation neutron source (SNS) linac and the Low Energy Demonstrator Accelerator (LEDA) beam halo experiment

Lyapunov Exponents without Rescaling and Reorthogonalization

We present a new method for the computation of Lyapunov exponents utilizing representations of orthogonal matrices applied to decompositions of M or MM_trans where M is the tangent map. This method uses a minimal set of variables, does not require renormalization or reorthogonalization, can be used to efficiently compute partial Lyapunov spectra, and does not break down when the Lyapunov spectrum is degenerate.Comment: 4 pages, no figures, uses RevTeX plus macro (included). Phys. Rev. Lett. (in press

On FFT-based convolutions and correlations, with application to solving Poisson's equation in an open rectangular pipe

A new method is presented for solving Poisson's equation inside an open-ended rectangular pipe. The method uses Fast Fourier Transforms (FFTs) to perform mixed convolutions and correlations of the charge density with the Green function. Descriptions are provided for algorithms based on the ordinary Green function and for an integrated Green function (IGF). Due to its similarity to the widely used Hockney algorithm for solving Poisson's equation in free space, this capability can be easily implemented in many existing particle-in-cell beam dynamics codes

Advanced Computing Tools and Models for Accelerator Physics

This paper is based on a transcript of my EPAC'08 presentation on advanced computing tools for accelerator physics. Following an introduction I present several examples, provide a history of the development of beam dynamics capabilities, and conclude with thoughts on the future of large scale computing in accelerator physics

ADVANCED COMPUTING TOOLS AND MODELS FOR ACCELERATOR PHYSICS

Abstract This paper is based on a transcript of my EPAC'08 presentation on advanced computing tools for accelerator physics. Following an introduction I present several examples, provide a history of the development of beam dynamics capabilities, and conclude with thoughts on the future of large scale computing in accelerator physics