Solutions of the Lenard-Balescu equation for drifted plasmas

Abstract

The usefulness of one-dimensional plasma models is often questioned because of the absence of lateral effects that are considered to be important in three dimensions. However, one-dimensional models are much more tractable and should yield much information about what to expect from more complicated three-dimensional descriptions especially when higher order kinetic equations are employed. To this end an investigation of the one-dimensional Lenard-Balescu equation was carried out when an external electric field is included in the formalism. Numerically exact solutions of these equations were performed with displaced Maxwellian distributions as initial conditions. The interaction term was seen to measurably affect the distributions during one plasma period. The strength of the Lenard-Balescu interaction term was found to increase with initial displacement until a maximum separation was reached beyond which the initial conditions could not satisfy the differential equations. It is conjectured what effect a three dimensional analog to these properties would have on the results of other researchers. Quantities observed were drag, diffusion and Landau damping. Also displays are given of the functions that contribute to the Lenard-Balescu interaction term.