Fluctuation of the electric field in a plasma

Abstract

The theory of electric field fluctuations in a plasma is reviewed. The fluctuations of an electric field can be assumed to be due to the Cerenkov radiation, which is emitted by single particles that satisfy the Landau wave-particle resonance conditions. This view naturally agrees with the picture that a plasma can be considered to be an aggregate of non-interacting dressed particles. A simple classical derivation of the fluctuation-dissipation theorem is presented to show that the fluctuations of the Cerenkov electric field agree with the fluctuation-dissipation theorem. A quasilinear-like solution of the Liouville equation is shown to derive an electric field fluctuation with the same form as that obtained by using the dressed particle approach. We suggest that the fluctuation can be traced to the causality that gives rise to collisionless dissipation (imaginary part of the dielectric function). Therefore, the fluctuation in a plasma has a philosophical implication in that its existence is fundamentally due to the causal principle that the effect cannot be precedent to the cause, thus defining the direction of time.