The effect of non-Markovian terms on the Landau equation

Abstract

The Landau equation can be derived as the sum of an expansion series in time provided certain non-Markovian short-time terms are neglected. The time series could be very useful for the solution of a variety of problems. It is necessary to estimate the time span over which the neglected term s are significant. The non-Markovian terms for the case of a homogeneous plasma are evaluated using a technique developed by Prigogine and Balescu. For typical values of plasma potential cut-offs the conditions under which the short-time terms may be ignored are estimated. It is found that for electrons of number density less than 1010 and protons of number density less than 1014 it may be possible to ignore the short-time effects. It is conjectured that for many situations the non-Markovian effects will be important for a time interval which has a lower bound t 0 and an upper bound several orders of magnitude greater than t .