The Boltzmann equation for electrons in a uniform isothermal plasma is solved by expressing the distribution function as a series of orthogonal polynomials in velocity space with time dependent expansion coefficients. The microwave conductivity is simply related to certain coefficients. Particular attention is devoted to the case in which the plasma is subject to a constant magnetic field and a microwave electric field. By introducing an "effective" electron temperature, convergence is attained for strong as well as weak electric fields. The formulation is particularly suited for problems involving partially ionized gases which contain several species of ions and neutrals. The conductivity of a completely ionized gas is calculated with and without consideration of electron-electron collisions, and the ratio (${\gamma }_E$) of the two results is graphically illustrated as a function of microwave frequency.

• Received 28 December 1959

DOI:https://doi.org/10.1103/PhysRev.119.27