# High Order Numerical Integrators for Relativistic Charged Particle Tracking

## TL;DR

This paper develops higher order, time-reversible numerical integrators for relativistic charged particle tracking, improving accuracy and computational efficiency in electromagnetic field simulations.

## Contribution

The paper introduces a fourth order algorithm for relativistic particle tracking, extending existing integrators to higher order accuracy with explicit testing and validation.

## Key findings

- Fourth order integrator achieves higher accuracy.
- High order integrators reduce computational cost.
- Explicit numerical examples demonstrate effectiveness.

## Abstract

In this paper, we extend several time reversible numerical integrators to solve the Lorentz force equations from second order accuracy to higher order accuracy for relativistic charged particle tracking in electromagnetic fields. A fourth order algorithm is given explicitly and tested with numerical examples. Such high order numerical integrators can significantly save the computational cost by using a larger step size in comparison to the second order integrators.