Solution for the Two-Electron Correlation Function in a Plasma

Abstract

The two-electron correlation function, $g$, responsible for "collisional" corrections to the correlationless (or Vlasov) description of a plasma, is investigated. It is shown that an exact solution of the integral equation for $g$ can be found for a fairly wide class of spatially homogeneous, one-electron distribution functions, $f$ (the ion dynamics being neglected). This is carried out in detail for the simplest member of the class (the resonance shape), and the Landau damping of $g$ to its asymptotic ($t\to \infty$) form is exhibited explicitly. It is shown that correlations between particles separated by more than the Debye length are damped in a time which exceeds the period of plasma oscillations, ${{\omega }_p}^{-1\mathrm{}}$, and that these make an appreciable contribution to the "collisional" rate of change of $f$. It is concluded that for rapidly varying $f$ (as in problems involving plasma oscillations) conventional treatments of the "collision" term should be replaced by a self-consistent solution of the coupled equations for $f$ and $g$.