Solution for the Two-Electron Correlation Function in a Plasma

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→∞) 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, ωₚ^-1, 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.