Tensor network approaches for plasma dynamics

TL;DR

This paper explores applying tensor network methods, specifically Matrix Product States, to simulate plasma dynamics governed by the Vlasov-Maxwell system, demonstrating potential efficiency gains in low-dimensional and certain high-dimensional regimes.

Contribution

It introduces tensor network approaches to plasma physics, compares their performance across regimes, and extends their application to Magnetohydrodynamics.

Findings

Matrix Product States perform well in low-dimensional plasma problems.

Tensor networks can handle regimes with strong magnetic fields.

Validation against Particle-In-Cell codes shows promising results.

Abstract

The dynamics of plasmas are governed by a set of non-linear differential equations which remain challenging to solve directly for large 2D and 3D problems. Here we investigate how tensor networks could be applied to plasmas described by the Vlasov-Maxwell system of equations and investigate parameter regimes which show promise for efficient simulations. We show for low-dimensional problems that the simplest form of tensor networks known as a Matrix Product State performs sufficiently well, however in regimes with a strong permanent magnetic field or high-dimensional problems one may need to consider alternative tensor network geometries. We conclude the study of the Vlasov-Maxwell system with the application of tensor networks to an industrially relevant test case and validate our results against state of the art plasma solvers based on Particle-In-Cell codes. We also extend the application of tensor networks to the alternative plasma description of Magnetohydrodynamics and outline how this can be encoded using Matrix Product States.