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  "body": "\n## Summary\n\nThe Vlasov equation describes a large system of particles that interact through long-range forces.\nExamples are charged particles in a plasma and stars in a galaxy.\nIt is a [[transport equation|PVD7VZJZ9B]] in position and velocity for the particle density $f(t, x, v)$, without a collision term.\nThe force is the mean field created by all particles together, so the equation is nonlinear.\nCoupled with the Poisson equation it gives the Vlasov–Poisson system.\n\n## Explanations\n\n### L1 human\n\nIn a plasma each electron feels the electric pull and push of billions of other charges.\nClose encounters between two particles matter little, but the combined field of all of them matters a lot.\nThe Vlasov equation follows the cloud of particles in the space of positions and velocities, as each particle moves under this averaged force.\nFor a single particle in the force $-x$ on a line, the orbits in the $(x, v)$ plane are circles.\nAny density that is constant on these circles stays the same over time.\n",
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