Use of transfer maps for modeling beam dynamics in a nonscaling fixed-field alternating-gradient accelerator

Y Giboudot,A Wolski

doi:10.1103/physrevstab.15.044001

Abstract

Transfer maps for magnetic components are fundamental to studies of beam dynamics in accelerators. In the work presented here, transfer maps are computed in Taylor form for a particle moving through any specified magnetostatic field by applying an explicit symplectic integrator in a differential algebra code. The techniques developed are illustrated by their application to study the beam dynamics in the electron model for many applications (EMMA), the first nonscaling fixed-field alternating-gradient accelerator ever built. The EMMA lattice has 4 degrees of freedom (strength and transverse position of each of the two quadrupoles in each periodic cell). Transfer maps may be used to predict efficiently the dynamics in any lattice configuration. The transfer map is represented by a mixed variable generating function, obtained by interpolation between the maps for a set of reference configurations: use of mixed variable generating functions ensures the symplecticity of the map. An optimization routine uses the interpolation technique to look for a lattice defined by four constraints on the time of flight at different beam energies. This provides a way to determine the lattice configuration required to produce the desired dynamical characteristics. These tools are benchmarked against data from the recent EMMA commissioning.

Highlights

Modeling the dynamics of particles in accelerators is essential for optimizing design and performance
One of the main goals of this section is to understand the limits on accuracy of the transfer map; the results strictly apply to the case of a single machine (EMMA), the challenges of this particular case are such that the results indicate the potential use of the technique for many other machines
The techniques presented in this study consist of the application of four independent tasks: first, construction of an accurate model of a magnetic field in a given section of accelerator beam line; second, derivation of an accurate analytical representation of the given magnetic field; third, use of an integrator in a differential algebra code to construct a transfer map in Taylor form; and use of a range of analytical techniques to extract significant features of the dynamics

Summary

Introduction

Modeling the dynamics of particles in accelerators is essential for optimizing design and performance. Determining the trajectories of particles through the magnetic fields in an accelerator is fundamental to the dynamics; a wide variety of phenomena, including beam lifetime, spin polarization, and synchrotron radiation emission depend directly on the particle trajectories. To aid the modeling process, transfer maps for standard accelerator components, such as solenoids, dipoles, quadrupoles, and higher-order multipoles, have been developed and used for almost as long as accelerators themselves (see, for example, [1]). Expressing a map in closed form for even some relatively simple accelerator components requires a number of assumptions and approximations. As accelerators begin to operate in more demanding regimes of beam quality and stability, it becomes important to provide descriptions of particle trajectories through

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