# Exponential energy-preserving methods for charged-particle dynamics in a strong and constant magnetic field

## TL;DR

This paper introduces exponential energy-preserving numerical methods for charged-particle dynamics in strong magnetic fields, ensuring exact energy conservation and near conservation of magnetic moment over long times, with proven properties and numerical validation.

## Contribution

The paper develops and analyzes a novel exponential energy-preserving method that exactly conserves energy and nearly conserves magnetic moment for charged-particle simulations.

## Key findings

- Exact energy preservation in the numerical method.
- Near conservation of magnetic moment over long times.
- Numerical experiments demonstrating long-term stability.

## Abstract

In this paper, exponential energy-preserving methods are formulated and analysed for solving charged-particle dynamics in a strong and constant magnetic field. The resulting method can exactly preserve the energy of the dynamics. Moreover, it is shown that the magnetic moment of the considered system is nearly conserved over a long time along this exponential energy-preserving method, which is proved by using modulated Fourier expansions. Other properties of the method including symmetry and convergence are also studied. An illustrated numerical experiment is carried out to demonstrate the long-time behaviour of the method.