Electron Velocity Distribution in a Slightly Ionized Gas with Crossed Electric and Strong Magnetic Fields

Abstract

Assuming ${\left({\omega }_b\tau \right)}^2\gg 1$, equations that determine the electron energy distribution and drift velocity in the E×B drift frame of reference are derived, including a detailed treatment of inelastic collisions. These equations are valid when E, B, and the distribution function of the gas molecules are spacially uniform and constant in time, the component of E along B is negligible, and $E\ll B$ (in Gaussian units). The equations are suitable for numerical computations if the electron velocity distribution is assumed to be isotropic in the E×B drift frame. When the rms molecular speed in this frame is much smaller than the rms electron speed, the equations can be greatly simplified. Although the resulting equations are not new, this derivation clarifies their physical interpretation and limitations. The treatment is, of course, also applicable to cases where slightly ionized gas is moving across a magnetic field.