text: The Vlasov–Poisson equations are an approximation of the Vlasov–Maxwell equations in the non-relativistic zero-magnetic field limit:
  and Poisson's equation for self-consistent electric field:
  Here  is the particles electric charge,  is the particles mass,  is the self-consistent electric field,  the self-consistent electric potential,  is the electric charge density, and  is the electric permitivity. 
  Vlasov–Poisson equations are used to describe various phenomena in plasma, in particular Landau damping and the distributions in a double layer plasma, where they are necessarily strongly non-Maxwellian, and therefore inaccessible to fluid models.