Nonlinear Microwave Conductivity of a Slightly Ionized Gas for Arbitrary Collision Cross Sections

Abstract

A tractable expression for the current density in a slightly ionized gas under the influence of an electromagnetic field is obtained for arbitrary velocity dependence of the electron---heavy-particle cross section for elastic collisions. The discussion is restricted to the case of a weak field in the high-frequency approximation (frequency of the field much greater than the average collision frequency) in an isotropic plasma. For the special cases of a constant mean free path and a mean free path inversely proportional to the square root of electron temperature, the current density obtained here agrees with results previously derived by Epstein. The effect of the nonlinearity is to increase the current density in phase with the applied field if the collision frequency increases with velocity, as with hard spheres; the nonlinearity decreases the in-phase component of the current density if the collision frequency decreases with velocity, as with screened Coulomb collisions. The case of constant collision frequency results in a linear current density. Simple applications to cross modulation by pulsed microwaves and frequency mixing are discussed.