Correlation Functions and Scattering of Electromagnetic Waves by Inhomogeneous and Nonstationary Plasmas

Abstract

A rigorous formalism is given for interpreting the weak (Born) scattering of em waves by macroscopically inhomogeneous and nonstationary plasmas (plasmas whose macroscopic electron density varies within the scattering volume). This formalism does not resort to the heuristic, though useful, (coherent) assumption 〈|n(k, ω)|2〉 = |〈n(k, ω)〉|2, where n(k, ω) and 〈n(k, ω)〉 denote the (Fourier transformed) microscopic and macroscopic electron density, respectively. Rather, we determine criteria for the validity of this assumption. Generally, it is valid for only isolated regions of k and ω space—depending on the specific nature of 〈n(k, ω)〉. The derivation is based on the theorem relating space‐time correlation functions to one‐particle distribution functions. Correlation function and scattering divide into coherent (nonlinear) and incoherent parts. The coherent part |〈n(k, ω)〉|2, is due to macroscopic density variations. The incoherent part is due to (microscopic) fluctuations about the macroscopically varying density and is determined by solutions of the linearized Vlasov equation with space‐time varying background. Examples are given for plasmas with time varying Gaussian density profiles, damped oscillations, and undamped oscillations.