Strong Turbulence Theory of Nonlinear Stabilization and Harmonic Generation

Abstract

A nonlinear dispersion relation for dispersionless waves in a one-dimensional plasma is obtained by examining the statistical properties of particle orbits in a random potential. New techniques are developed to deal with trapped particles. It is shown that a linearly unstable plasma stabilizes when the trapping frequency is equal to the growth rate. Also, the density fluctuations set up by the trapped particles are shown to have a power-law dependence in wavenumber. The theory is able to explain many observations in recent beam-plasma experiments.