Green’s function for simple brownian kinetics and its application to plasma

Abstract

An analysis is outlined concerning the derivation and application of the Green’s function for a class of Fokker-Planck equations with strictly time-dependent external fields and constant viscosity-diffusion coefficients, the kinetic equation commonly used in the theory of Brownian motion. The form of Green’s function for this general class of partial differential equations is given explicit expression in terms of the collisionless time-development operator on the set of initial velocities under the influence of external fields and viscous force. Application of such a singular solution is made to simplify the formulation for the near-equilibrium kinetics of excitation of neutral atoms by electrons and to electromagnetic propagation problems where a linearized self-consistent field treatment of the electronic constituent of a three-fluid plasma is necessary.