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