Electron Energy Distribution in Slightly Ionized Air under the Influence of Electric and Magnetic Fields

Abstract

We obtain numerically computed solutions to the Boltzmann equation giving the electron energy distribution in weakly ionized air under the following assumptions: (1) that there are present a static magnetic field and an electric field of constant direction (perpendicular to the magnetic field) and a constant rms value; (2) that the gas is homogeneous and the fields uniform in space; (3) that the degree of ionization is weak enough so that electron-electron and electron-ion collisions are negligible; (4) that the fields are such that the average electron energy is much larger than the thermal energy of the gas molecules, and that the heating of the gas by the electrons is negligible; (5) that processes of creation and removal of free electrons are negligible; and (6) that electrons may lose energy in elastic collisions and may also excite rotational, vibrational, and electronic degrees of freedom. To describe these energy-loss processes we use experimental cross sections. We take the constituents of the air to be ${\mathrm{N}}_{2}$, ${\mathrm{O}}_{2}$, and O, the later being included for upper atmosphere applications. We give distribution functions for a number of limiting cases and compare our solutions to others which may be obtained by less extensive calculations. We demonstrate that while the ratio of electric field to pressure is a good scaling factor for dc excitation this is not the case if either the excitation frequency or the gyro frequency is large compared to the collision frequency.