Explicit symplectic integrator for particle tracking in s-dependent static electric and magnetic fields with curved reference trajectory

TL;DR

This paper introduces a symplectic particle tracking method for static electric and magnetic fields with s-dependent and curved reference trajectories, applicable even with only numerical field data.

Contribution

It presents an explicit symplectic integrator that uses series expansions of potentials derived from numerical data for accurate particle tracking.

Findings

Applicable to fields with s-dependence and curvature

Constructs potentials from numerical field data

Maintains symplectic structure during tracking

Abstract

We describe a method for symplectic tracking of charged particles through static electric and magnetic fields. The method can be applied to cases where the fields have a dependence on longitudinal as well as transverse position, and where the reference trajectory may have non-zero curvature. Application of the method requires analytical expressions for the scalar and vector potentials: we show how suitable expressions, in the form of series analogous to multipole expansions, can be constructed from numerical field data, allowing the method to be used in cases where only numerical field data are available.