Generalized Langevin equation for plasma turbulence

Abstract

The generalized Langevin equation has been applied to the study of plasma turbulence. The evolution equation for the particle velocity in electrostatic plasma turbulence has been derived by the projection operator method. The time integral appearing in the equation indicates that the wave-particle interaction in a plasma is not a Markovian process. Thus, the wave-particle interaction cannot be described as instantaneous collisions between particles and wave quanta (quasi-particles), as is usually done in a conventional weak turbulence theory. Plasma particles placed in electrostatic plasma turbulence characterized by random electric fields (Gaussian process) are considered. It is found that the memory effect or the influence of the past on particle trajectories in phase space limits the particle diffusion in velocity space, in agreement with earlier observations.<>