text: Instead of collision-based kinetic description for interaction of charged particles in plasma, Vlasov utilizes a self-consistent collective field created by the charged plasma particles. Such a description uses distribution functions  and  for electrons and (positive) plasma ions. The distribution function  for species  describes the number of particles of the species  having approximately the momentum  near the position  at time . Instead of the Boltzmann equation, the following system of equations was proposed for description of charged components of plasma (electrons and positive ions):
  Here  is the elementary charge (),  is the speed of light,  is the mass of the ion,  and  represent collective self-consistent electromagnetic field created in the point  at time moment  by all plasma particles. The essential difference of this system of equations from equations for particles in an external electromagnetic field is that the self-consistent electromagnetic field depends in a complex way on the distribution functions of electrons and ions  and .