Wavemechanical formulation of plasma dynamics in longitudinal electric fields

Abstract

The macroscopic dynamics of classical many-component plasmas, in which the particles interact by the self-consistent electric field, is formulated in terms of scalar, complex wave equations. The wave equation of each component is shown to be mathematically equivalent to its nonlinear conservations equations for mass, vector momentum, and energy. Thus, the description through wave equations leads to a considerable mathematical simplification compared to the conventional many-fluid hydrodynamics. As an elementary illustration of the wave mechanical formalism, the dispersion of electrostatic waves in an electron plasma is treated.