An inhomogeneous Landau-like equation

Abstract

The problem of the mixing of two plasmas is very difficult to solve if the methods of statistical mechanics are used. When both plasmas are homogeneous in space, and the limit of weak coupling is appropriate, the Landau equation describes the motion. An equation, similar to the Landau equation, is developed for the case when one of the plasmas is initially inhomogeneous in space. The equation is a power series in time and involves wave vectors in space. The short-time-after-mixing limit is considered, which restricts the number of wave vectors. A sample problem is presented of the short time development of an infinite-temperature spike interacting with a homogeneous plasma. The spike is found to move very rapidly from the origin owing to the long range of the forces. Extension of the time development past the initial short time requires consideration of destructive wave vectors in addition to the wave vector generation considered here.