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Posts Tagged ‘Vlasov-Maxwell’

In this note, I briefly explain my recent joint work with D. Han-Kwan (CNRS, Ecole polytechnique) and F. Rousset (Paris-Sud) on the non-relativistic limit of Vlassov-Maxwell. Precisely, we consider the relativistic Vlasov-Maxwell system, modeling the dynamics of electrons with electron density distribution {f(t,x,v)}, which reads

\displaystyle \partial_t f + \hat v \cdot \nabla_x f + (E + \epsilon \hat v \times B)\cdot \nabla_v f = 0

on {\mathbb{T}^3\times \mathbb{R}^3}, with the relativistic velocity {\hat v = v/\sqrt{1+ \epsilon^2 |v|^2}}.

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What is a plasma? A plasma is an ionized gas that consists of charged particles: positive ions and negative electrons. To describe the dynamics of a plasma, let {f^\pm(t,x,v)} be the (nonnegative) density distribution of ions and electrons, respectively, at time {t\ge 0}, position {x\in \Omega \subset \mathbb{R}^3}, and particle velocity (or momentum) {v\in \mathbb{R}^3}. The dynamics of a plasma is commonly modeled by the Vlasov equations

\displaystyle \frac{d}{dt} f^\pm (t,X(t), V(t)) = 0 \ \ \ \ \ (1)

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