Conductivity of Plasmas to Microwaves

A relation [Eq. (13)] between the current-induced part of the distribution function ($f_1$) and the isotropic part ($f_0$), which was previously derived with limiting restrictions, is here shown to be valid at moderate electric fields for any form of $f_0$, e.g., for the case where an agency other than the passing microwaves determines it. The complex conductivity is then computed for a variety of functions $f_0$ ($\delta$ function, step function, Maxwellian distribution) and for different assumptions as to the dependence of the collision frequency on electron speed. The integrals encountered in this work are shown to be computable with good accuracy by means of a saddle-point procedure which is described.