Vlasov Equation
The fundamental partial differential equation governing the evolution of the single-particle distribution function f(r, v, t) in a collisionless plasma.
Governing formula
∂f / ∂t + v · ∇_r f + (q / m) (E + v × B) · ∇_v f = 0
SI unit
Collisionless Kinetic Operator
In depth
Formulated by Anatoly Vlasov in 1938. Couples particle kinetics directly with self-consistent Maxwell field equations (Vlasov-Maxwell system), describing kinetic wave-particle interactions without binary collisions.
Examples in the real world
Modeling Landau damping, wave-particle resonances, and kinetic plasma instabilities in space and fusion physics.