High-Frequency Conductivity and the Emission and Absorption Coefficients of a Fully Ionized Plasma

Most previous computations of the resistivity of a fully ionized plasma assume the duration of a two-particle encounter to be shorter than any other time in the problem, and, in particular, shorter than any macroscopic time variation. In a plasma this assumption is often violated because the dominant collisional process arises from distant collisions where the encounter duration time can be of the order of the reciprocal plasma frequency, whereas the plasma is capable of sustaining macroscopic oscillations at and above the plasma frequency. It is the purpose of this paper to investigate by means of a simple model, the frequency dependence of the resistivity, and the associated processes of absorption and emission of radiation, for frequencies greater than vc = 2π/tD (tD is the cumulative 90° deflection time). The validity of this simple treatment in a large part rests upon the fact that the electron motion is inertia dominated, or in other words, to lowest approximation the current response to the driving E field is mainly reactive. Collective effects are properly included and so our results should be valid for all frequencies greater than ∼ vc (including the vicinity of the plasma frequency) for which a classical treatment is valid. Most previous results have not treated the collective aspects consistently and so are incorrect particularly near the plasma frequency. Indeed the validity of this model is borne out by an exact treatment (in the limit of infinite ion mass) stemming from the BBGKY (Bogoliubov, Born, Green, Kirkwood and Yvon) hierarchy. Further, the model has been generalized to include a uniform magnetic field and quantum effects, but these generalizations will not be discussed here