Partial differential equation describing the evolution of the distribution function of a collisionless plasma.
The distribution function f describes the state of a fluid in terms of the position x and velocity v of every constituent particle at every time t. (i.e. f=f(x,v,t))
Differentiating f with respect to time
df/dt= δf/δt + (δx/δt)δf/δx + (δv/δt)δf/δv
In the absence of collisions the total differential df/dt is equal to zero. Note that
are the force
respectively. Furthermore, in a plasma
the force in question is the electromagnetic force
and thus the Vlasov equation may be written
δf/δt + v.δf/δx + (q/m)(E + vxB).(δf/δv)=0
are the electric
See also the Fokker-Planck equation.