Electron conductivity of a thermally ionized gas in an electric field

Abstract

It is well known that the current carriers in a thermally ionized gas vary in composition, but that electrons [1] make the fundamental contribution to the conductivity of the gas, since their mobility is incomparably larger than that of other current-carrying particles. We shall thus be concerned only with electron conductivity. If the gas is under a high pressure in a weak electric field, then in estimating its electrical conductivity by classical means the same concepts are usually employed as those which Drude applied in the theory of metallic conduction. The Drude-Lorentz formula for electrical conductivity was subsequently perfected by Cowling and Chapman who introduced a coefficient to take into account the rate at which the particle interaction forces decrease with distance [2], For electron Coulomb interaction this coefficient takes the value 0.532 instead of 0.500 as compared with the Drude-Lorentz formula.

For high pressures and low electric field strengths the electron drift velocity in the field is vanishingly small compared with the mean velocity of random motion, and so it is logical to suppose that the electron free time is independent of the drift velocity, and this supposition leads in the end to the conclusion that Ohm's law is applicable to gases at high pressure in very weak fields.

However, we must not overlook the fact that even under the conditions mentioned the conclusion concerning the validity of Ohm's law is only an approximation which becomes less accurate, the lower the gas pressure and the greater the field strength.

In what follows the conductivity of the gas is also determined by Drude's method, but with the refinement that in determining the electron free time the drift velocity of these particles in the field is considered.