Theory of fluctuations in a plasma

Abstract

A theory of electron density fluctuations in a two-component plasma of electrons and positive ions is developed within the random phase approximation. A dielectric formulation is used extensively to describe the fluctuations; investigation of various examples clarifies such facets as collective vs. individual particle aspects of fluctuations. It is shown that the collective part of the fluctuation spectrum can also be obtained from the kinetic equations derived by Pines and Schrieffer, which describe the time rate of change in the distributions of collective and individual particle modes due to the excitation of collective oscillations by fast electrons and their decay into individual particle modes. It is shown that the collective part of electron density fluctuations exhibits a huge increase as the plasma approaches from a region of stability a critical point corresponding to the onset of plasma wave instabilities; consideration of the theory of electromagnetic wave scattering leads us to predict enormously enhanced scattering of the electromagnetic radiation at certain angles, a phenomenon which is analogous to the critical opalescence for a liquid-gas phase transition. The influence of the scattering of the holes by impurities (for a plasma in a semiconductor) is studied and it is found that impurity scattering acts to shift the position of the onset of the instability, but does not alter appreciably the existence of critical fluctuations in the vicinity of the critical point. It is also shown that the electron density fluctuation spectrum obeys a certain sum rule. In the Appendix it is demonstrated that the method of super-posing the dressed particles (electrons or ions plus their associated screening clouds) is a direct consequence of the random phase approximation.