Symmetry group of the kinetic equation and stationary distributions in a weakly turbulent plasma

A class of essentially non-equilibrium distributions characterized by the constant flux of one of the “integral of motion” (e.g. energy, number of particles or momentum) both for waves and particles is shown to exist in plasmas due to the symmetry of collision integrals (particle-wave interactions or Boltzmann's integral resp.). As a result, the non-equilibrium distributions can be obtained from a functional equation inferring that the projection of the stoss-integrand on the irreducible group representation should be equal to zero.