Plasma-electromagnetic radiation interaction

Abstract

THE WORK presented in this report was carried out at Aeronutronic under contract with AFSWC by Mr. R. S. Wright, Dr. C. A. Roberts, and the author. The effort will be reported in detail in a publication numbered TDR 62-13 1 due for release within the next two months. A narrative supplement describing the investigation has been prepared for the report and forms the notes for this paper. The general subject matter is the interaction of the electromagnetic field and a plasma. The relationship of such an investigation to opacity studies stems from a desire to understand the mechanism of communication through a plasma, for example. Our approach has been from a fundamental vantage. We include not only the Coulomb interaction as done by GUERNSEY, in a Ph.D. thesis under UHLENBECK and by BALESCU in a Physics of Fhids article, but also the transverse electromagnetic modes. The study of the properties of an ionized gas from a macroscopic point of view may be considered as involving the analysis of the reduction of the full Liouville equation to a simpler equation. It is well known that the Liouville equation governs the temporal and spatial behavior of the phase space distribution function from which, as averages, all macroscopic properties of the system under consideration may be obtained. The applicable phase space depends upon the character of the system under study; its dimensionality is that of the number of independent position and momentum degrees of freedom of the system. For a system possessing a large number of degrees of freedom (particles) the phase space distribution function is usually too detailed an entity for analysis and possesses too great a wealth of information for practical purposes. In general only a small amount of the information content of the full phase space distribution function can be handled or is required. Consequently, it is usually sufficient to consider a reduced description of the system. Such a description will contain information about only a few physical quantities of interest and will be descriptive of a small number of degrees of freedom. As an example, the pressure of a gas may be considered as an average of the more detailed information content of the full phase space distribution function. In forming this physical quantity all other system properties are integrated out to produce a reduced distribution function containing only the information of interest. Other simple physical quantities may be represented as averages in a similar fashion. The important point is that only reduced functions are required in practically all cases. The present analysis starts with the Liouville equation description of an ionized gas interacting through the medium of the electromagnetic field. Through a series of approximations and stages of analysis one is led to a simplified equation governing the one par-