Nonlinear evolution of the decay instability in a plasma with comparable electron and ion temperatures

The nonlinear evolution of the decay instability in a plasma driven by an externally imposed pump field oscillating near the electron plasma frequency is considered. For a plasma with comparable electron and ion temperatures and for weak pump fields, nonlinear Landau damping of electron plasma waves on the ions is the dominant nonlinearity. It is demonstrated that a one-dimensional wave kinetic equation describes the dominant interactions for spectral intensities whose characteristic angular width is small. This equation is solved numerically with the exact form for the matrix element which describes the coupling. An analytical solution is found for the spectral intensity in the limit in which the (small) spontaneous emission term is neglected. The plasma wave energies obtained both numerically and analytically are in good agreement. General characteristics of the plasma wave spectrum agree with observations in the ionosphere. The enhanced dissipation rate of the pump due to the presence of the fluctuations agrees with that observed in a laboratory experiment.