Wave growth in a strongly turbulent plasma

An equation is derived for the average nonlinear growth (damping) rate of an electrostatic mode with wave vector k for an ensemble of electrostatically turbulent, unmagnetized plasmas. Strong turbulence alters particle orbits during the course of wave growth and hence brings particles in and out of resonance with the wave. The wave growth rate in a strongly turbulent plasma therefore depends on the initial velocity distribution of particles not only at the wave speed, but in the vicinity of this speed as well. Two orbital effects are considered: turbulence modification of ensemble average orbits and turbulence-produced orbital dispersion about the average orbits. Both contribute to a resonance broadening.