Exact Solutions for the Collisional Plasma Problem

Abstract

By means of the Lie group approach the symmetry of Vlasov-Fokker Planck equation (VFPE) with an arbitrary electric field of space and time are found. Mathematical forms are obtained for the electric field permit symmetry. Maxwell's equations are then used to constrain the solution further. Finally, we obtain a complete classification of all possible nontrivial similarity solutions of the VFPE plus Maxwell equations.