Propagation of an unstable spectrum of plasmons in the presence of random inhomogeneities

A one-dimensional stochastic kinetic equation for the propagation of unstable plasmons (Langmuir modes) in the presence of large scale random spatial fluctuations is presented, within the frame of the WKB approximation, and then solved. Using probabilistic arguments, an effective growth rate is evaluated, which turns out to be much smaller than the plasmon growth rate in the absence of fluctuations. The theory is then applied to the beam-plasma kinetic instability and to the stimulated photon-plasmon interaction. The former case exhibits a shift of the turbulent plasmon spectrum toward larger wavenumbers. The latter case shows a strong reduction in the efficiency of the stimulated process (i.e., much smaller growth rate) and the removal of the strong asymmetry inherent in this problem.