A conservative scheme for the relativistic Vlasov-Maxwell system

TL;DR

This paper introduces a conservative numerical scheme for the 1D2V relativistic Vlasov-Maxwell system that conserves energy and accurately reproduces analytical results across various plasma physics problems.

Contribution

The proposed scheme uniquely conserves energy and avoids particle loss by assuming uniform velocity within phase space cells, applicable to higher-dimensional systems.

Findings

Successfully simulates particle gyration, Weibel instability, and wakefield acceleration.

Reproduces analytical solutions accurately.

Conserves total energy during simulations.

Abstract

A new scheme for numerical integration of the 1D2V relativistic Vlasov-Maxwell system is proposed. Assuming that all particles in a cell of the phase space move with the same velocity as that of the particle located at the center of the cell at the beginning of each time step, we successfully integrate the system with no artificial loss of particles. Furthermore, splitting the equations into advection and interaction parts, the method conserves the sum of the kinetic energy of particles and the electromagnetic energy. Three test problems, the gyration of particles, the Weibel instability, and the wakefield acceleration, are solved by using our scheme. We confirm that our scheme can reproduce analytical results of the problems. Though we deal with the 1D2V relativistic Vlasov-Maxwell system, our method can be applied to the 2D3V and 3D3V cases.