Explicit TE/TM Scheme for Particle Beam Simulations

TL;DR

This paper introduces a new explicit TE/TM splitting scheme for particle beam simulations that improves dispersion properties, simplifies implementation, and enhances stability and conservation in accelerator modeling.

Contribution

It presents a novel explicit two-level conservative scheme with tailored dispersion properties for accelerator problems, outperforming implicit methods in simplicity and speed.

Findings

The scheme is simpler and faster than implicit counterparts.

It maintains energy and charge conservation.

It is effective for rotationally symmetric structures without reducing time steps.

Abstract

In this paper we propose an explicit two-level conservative scheme based on a TE/TM like splitting of the field components in time. Its dispersion properties are adjusted to accelerator problems. It is simpler and faster than the implicit version [1]. It does not have dispersion in the longitudinal direction and the dispersion properties in the transversal plane are improved. The explicit character of the new scheme allows a uniformly stable conformal method without iterations and the scheme can be parallelized easily. It assures energy and charge conservation. A version of this explicit scheme for rotationally symmetric structures is free from the progressive time step reducing for higher order azimuthal modes as it takes place for Yee's explicit method used in the most popular electrodynamics codes.