Variational Formulations for Electromagnetic Field and Charged-Particle Stream Configurations and Their Linearization

Two variational formulations for electromagnetic field and charged-particle stream configurations, in which both field and particles are described by the field-like variables suited for the problems of electrodynamics, are presented. One of them is directly obtained through slight modifications of Sturrock's original procedure but has a complicated form. The other is obtained through linearization of the preceding one and has a compact form. Both formulations lend themselves to straightforward derivation of the well-known energy-momentum tensor and/or its conservation law. Specifically the latter one is of academic interest because of its compact form. Moreover, as a proof of its practical usefulness the variational principle under the small-amplitude approximation is derived from it, which is known to provide a basis for the study of certain types of instability in plasmas. It is, however, hoped that it will find main applications in the electrodynamics problems concerned with large-amplitude behavior.