Two-Particle Correlation Function for an Unstable Plasma

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Abstract
The usual kinetic equation derived from the B‐B‐G‐K‐Y hierarchy for a plasma with Coulomb interparticle forces breaks down for plasmas with distribution functions which the linearized Vlasov equation would predict to be unstable. As the first step towards deriving a kinetic equation for an unstable plasma in this paper the equation for the two‐particle correlation function is solved for times for which the distribution function may be regarded as time independent. Part of the correlation function is shown to grow exponentially in time; thus the Bogoliubov adiabatic hypothesis breaks down. Taking only the fastest growing part of the correlation function, a velocity space diffusion equation is obtained for the distribution function with a time‐dependent diffusion coefficient.

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