Efficient Evaluation of Arbitrary Static Fields For Symplectic Particle Tracking

TL;DR

This paper introduces a novel, efficient method for evaluating arbitrary static electromagnetic fields in source-free regions, enabling long-term symplectic particle tracking without simplifications.

Contribution

The authors present a unique approach using monopoles and spherical harmonics for fast, accurate field evaluation suitable for long-term particle tracking in static fields.

Findings

Method achieves orders of magnitude speedup in potential evaluation

Enables long-term symplectic integration in arbitrary static fields

Demonstrated successfully on a small particle accelerator

Abstract

This article describes a method devised for efficient evaluation of arbitrary static magnetic and electric fields in a source free region needed for long time tracking of charged particles. Field values given on the boundary of the region of interest are reproduced inside by an arrangement of hypothetical magnetic or electric monopoles surrounding the boundary surface. The vector and scalar potentials are obtained by summing the contributions of each monopole. The second step of the method improves the evaluation speed of the potentials and their derivatives by orders of magnitude. This comprises covering the region of interest by overlapping spheres, then calculating the spherical harmonic expansion of the potentials on each sphere. During tracking, field values are evaluated by calculating the solid harmonics and their derivatives inside a sphere containing the particle. Software has been developed to test and demonstrate the method on a small particle accelerator. To our knowledge, there is no other method of this kind, allowing long time symplectic integration in general static fields, without simplification.