High-Frequency Conductivity of a Fully Ionized Plasma

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Abstract
A complete classical derivation of the frequency‐dependent conductivity is presented which properly takes into account collective dynamics. This treatment rests on the joint solution of the first two members of the BBGKY hierarchy, in the plasma limit, when both are able to change on the same time scale. For arbitrary frequencies this leads to an integral equation for the one‐particle distribution function which can be solved by conventional variational and/or numerical procedures. For frequencies high compared to the collision frequency, an explicit statement of the conductivity is possible. This high‐frequency limit is further examined in the limit of small electron to ion mass ratio and these limiting results are compared with those of other authors.