Variational Technique for Determining Dispersion Relations in Plasma Systems

Abstract

Sturrock's variational principle seems particularly well suited to the study of small‐amplitude disturbances of plasma systems and is formulated in a sufficiently general manner so as to be applicable to relativistic as well as nonrelativistic multistream problems. The use of this variational principle is shown to be effective (in conjunction with the trial‐function method) in approximating dispersion relations. To this end the variational procedure is applied to two simple plasma problems which admit of exact solution. It is found that a first‐order error in the trial functions leads to only a second‐order error in the dispersion relation—a behavior typical of variational procedures and which renders them so useful.