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

Antoine Gagnebin, Mikaela Iacobelli, Alexandre Rege, Stefano Rossi

16/5/25 Published in : arXiv:2505.11428

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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Phase I & II research project(s)

  • Statistical Mechanics

Phase III direction(s)

  • Differential equations of Mathematical Physics

Long-Baseline Atom Interferometry

On braided Hopf structures on exterior algebras

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