Plasma Electromagnetic Fluctuations as an Initial Value Problem

TL;DR

This paper investigates the evolution of electromagnetic fluctuations in collisionless plasmas, showing how initial fluctuations decay or evolve into stationary spectra depending on plasma stability, with implications for understanding plasma behavior.

Contribution

It formulates the fluctuations as an initial value problem and analyzes their behavior in both stable and unstable plasma states.

Findings

Stable plasma fluctuations decay exponentially over time.

Unstable two-stream systems exhibit different fluctuation dynamics.

Equilibrium plasma fluctuations match the fluctuation-dissipation spectrum.

Abstract

Fluctuations of electric and magnetic fields in the collisionless plasma are found as a solution of the initial value linearized problem. The plasma initial state is on average stationary and homogeneous. When the state is stable, the initial fluctuations decay exponentially and in the long time limit a stationary spectrum of fluctuations is established. For the equilibrium plasma it reproduces the spectrum obtained from the fluctuation-dissipation relation. Fluctuations in the unstable two-stream system are also discussed.