A method of cyclic canonical variables for calculation of electrostatic plasma waves

Abstract

A method is derived, in which cyclic canonical variables (the generalized momenta of which are constants of the unperturbed motion) are used, for the calculation of the oscillations of a collisionless plasma in external fields. The plasma and the fields are assumed to be generally inhomogeneous. In the approximation of an electrostatic plane wave propagating in the plasma, a general dispersion equation for a weakly inhomogeneous plasma is then derived. The advantage of this method is in its great simplicity in contrast with the usual approach, where thex, v-“representation” is used. Moreover, all resuits are given in a simple, symmetric form. The application of this method is especially convenient for plasmas confined by external fields to a finite volume.