The Vlasov equation describes collisionless evolution of a phase-space distribution function in a self-consistent force field: . The force can be electromagnetic or gravitational; the Collisionless dark-matter Vlasov equation is the cosmological gravitational specialization.
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The Vlasov equation is a fundamental equation in plasma physics and kinetic theory that describes the behavior of a distribution function for a large number of charged particles under the influence of electromagnetic forces.