Two-Scale Macro-Micro decomposition of the Vlasov equation with a strong magnetic field

TL;DR

This paper introduces a Two-Scale Macro-Micro decomposition method for the Vlasov equation under strong magnetic fields, facilitating the development of asymptotic-preserving numerical schemes for plasma physics simulations.

Contribution

It presents a novel decomposition approach that separates oscillatory components, aiding in the construction of efficient numerical schemes for the Vlasov equation with strong magnetic effects.

Findings

Decomposition separates oscillations from the main solution shape.

Provides a foundation for Two-Scale Asymptotic-Preserving Schemes.

Enhances numerical stability in plasma simulations.

Abstract

In this paper, we build a Two-Scale Macro-Micro decomposition of the Vlasov equation with a strong magnetic field. This consists in writing the solution of this equation as a sum of two oscillating functions with circonscribed oscillations. The first of these functions has a shape which is close to the shape of the Two-Scale limit of the solution and the second one is a correction built to offset this imposed shape. The aim of such a decomposition is to be the starting point for the construction of Two-Scale Asymptotic-Preserving Schemes.