From relativistic Vlasov-Maxwell to electron-MHD in the quasineutral regime

TL;DR

This paper rigorously justifies the quasineutral limit of the relativistic Vlasov-Maxwell system under analytic regularity, showing convergence to kinetic electron-MHD equations and addressing oscillatory electromagnetic effects.

Contribution

It introduces a high regularity approach to prove strong convergence of solutions from Vlasov-Maxwell to electron-MHD in the quasineutral limit, accounting for magnetic and electric oscillations.

Findings

Established uniform analytic bounds for solutions in the quasineutral limit.

Proved strong convergence to kinetic electron-MHD equations as the quasineutrality parameter tends to zero.

Addressed oscillatory electromagnetic effects with refined decomposition and dispersive correctors.

Abstract

We study the quasineutral limit for the relativistic Vlasov-Maxwell system in the framework of analytic regularity. Following the high regularity approach introduced by Grenier [44] for the Vlasov-Poisson system, we construct local-in-time solutions with analytic bounds uniform in the quasineutrality parameter $\varepsilon$. In contrast to the electrostatic case, the presence of a magnetic field and a solenoidal electric component leads to new oscillatory effects that require a refined decomposition of the electromagnetic fields and the introduction of dispersive correctors. We show that, after appropriate filtering, solutions converge strongly as $\varepsilon$ tends to zero to a limiting system describing kinetic electron magnetohydrodynamics (e-MHD). This is the first strong convergence result for the Vlasov-Maxwell system in the quasineutral limit under analytic regularity assumptions, providing a rigorous justification for the e-MHD reduction, widely used in modelling plasmas in tokamaks and stellarators.