Axial representation of external electromagnetic fields for particle tracking in accelerators

TL;DR

This paper introduces a power series method to represent external electromagnetic fields near an axis in accelerators, simplifying the description to two functions per azimuthal mode and verified through comparisons and examples.

Contribution

It presents a novel power series representation of electromagnetic fields near an axis, reducing complexity by using only two functions per azimuthal mode, and compares it with existing Fourier-Bessel methods.

Findings

The power series representation accurately models electromagnetic fields near the axis.

Only two real functions per azimuthal mode are needed for source-free regions.

The method is validated through multiple examples and applied to a superconducting RF gun.

Abstract

We derive a power series representation of an arbitrary electromagnetic field near some axis through the coaxial field components on the axis. The obtained equations are compared with Fourier-Bessel series approach and verified by several examples. It is shown that for each azimuthal mode we need only two real functions on the axis in order to describe the field in a source free region near to it. The representation of dipole mode in a superconducting radio-frequency gun is analyzed.