|Abstract:||A many body analysis is made to determine the radiation (due to current fluctuations) that emanates from a high-density, low-temperature "quantum" plasma, and in the classical limit, for a low-density, high-temperature "classical" plasma. Radiation due to field fluctuations that are independent of current fluctuations are not considered in this paper. The model is a stationary, homogeneous (possibly anisotropic) system, manifesting periodic boundary conditions, in which a quantum plasma interacts with a classical electromagnetic field. In order to insure a minimally redundant analysis, a careful gauge analysis is initially undertaken.
The system is described by noting its response to both a bare current probe (the "true" response ) and to a “dressed” current probe (the "screened" response ) . These response functions are tensors in which longitudinal and transverse effects are treated on an equal basis. The case of formulation and range of validity of the respective descriptions is contrasted. These results are related to the field and current correlation tensors in a system at thermodynamic equilibrium by invoking the Fluctuation-Dissipation theorem . The relationship is then extended to stationary, multicomponent systems (where the components may be characterized by different temperatures ) and interpreted as a superposition theorem. This allows one to find any parameter correlation tensor, once the system's single particle distribution function and a linear response function (either true or screened) is known . Within the region of mutual validity, this superposition principle is shown to agree with a comparable theorem derived by Rostoker, Eldridge and Aamodt from a Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) argument. Finally, the power spectrum that an experimenter would observe is related to the current-current correlation tensor.
As an application of the theory, the radiation arising from current fluctuations is explored for two cases: a classical, isotropic plasma and a classical, warm beam-plasma. In the latter case, coupling between the transverse and longitudinal modes occurs, providing greatly enhanced radiation at the onset of a quasi-longitudinal instability. This suggests the possibility of monitoring critical longitudinal fluctuations in an anisotropic system by examining the emitted radiation spectrum.