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arXiv · 2505.11428

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

Antoine Gagnebin·Mikaela Iacobelli·Alexandre Rege·Stefano Rossi
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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.

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Antoine Gagnebin, Mikaela Iacobelli, Alexandre Rege, Stefano Rossi. 2025-05-16. From relativistic Vlasov-Maxwell to electron-MHD in the quasineutral regime. https://arxiv.org/abs/2505.11428

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