# A filtered Boris algorithm for charged-particle dynamics in a strong magnetic field

## TL;DR

This paper introduces a filtered Boris algorithm that improves numerical integration accuracy for charged particles in strong magnetic fields, achieving specific error bounds and demonstrated through numerical experiments.

## Contribution

It proposes a modified Boris algorithm with filtering techniques that attain higher accuracy in simulating charged-particle dynamics in strong magnetic fields.

## Key findings

- Achieves second-order error bounds in position and parallel velocity.
- Attains first-order error bounds in normal velocity.
- Numerical experiments confirm the improved error behavior.

## Abstract

A modification of the standard Boris algorithm, called filtered Boris algorithm, is proposed for the numerical integration of the equations of motion of charged particles in a strong non-uniform magnetic field in the asymptotic scaling known as maximal ordering. With an appropriate choice of filters, second-order error bounds in the position and in the parallel velocity, and first-order error bounds in the normal velocity are obtained with respect to the scaling parameter. The proof compares the modulated Fourier expansions of the exact and the numerical solutions. Numerical experiments illustrate the error behaviour of the filtered Boris algorithm.