The Cold Plasma Model

Abstract

Because a plasma is a fluid, its evolution must satisfy the equations of fluid dynamics. But because the fluid is composed of electrons and one or more species of ions, the charges on these particles act as sources of an electromagnetic field, which is governed by Maxwell’s equations. The presence of this intrinsic field leads to highly nonlinear behavior; and in fact, the dominance of long-range electromagnetic interactions over the short-range interatomic or intermolecular forces is often cited as the defining characteristic of the plasma state. In order to construct a mathematically rigorous model for the plasma which is also accessible to analysis, hypotheses must be imposed which control these nonlinearities. In Sect. 3.6 we assumed that the pressure on the plasma was zero and that magnetic forces dominated over other forces. Those hypotheses reduced the governing equations to the Beltrami equations (3.62), (3.65). In this section we impose a similar physical hypothesis: that the temperature of the plasma is zero.