Green's Function for the Linearized Vlasov Equation

Abstract

The Vlasov equation is considered without magnetic fields, linearized about a state with no electric fields or space and time variation. Integral representations for the Green's functions are presented for systems of one, two, and three dimensions. For the one‐dimensional stable case, two asymptotic expansions of the electric field for large time are presented. Similar expansions are given for a specific example of a one‐dimensional unstable plasma. In two and three dimensions, asymptotic expansions are exhibited for arbitrary plasmas having cylindrical or spherical symmetry.