Nonlinear saturation of parametric instabilities: Spectrum of turbulence and enhanced collision frequency

Abstract

The nonlinear saturated state of parametric instabilities driven by an externally applied electromagnetic pump field oscillating near the plasma frequency is considered. For short wave lengths or strong pump fields, modifications of electron and ion orbits are the dominant saturation mechanism. A calculation is made of the saturated spectrum of Langmuir waves excited by the decay instability for T e ≈ T i. The spectrum is found to be broad in angle, in the absence of a magnetic field, and this has been confirmed by computer simulations. A calculation has also been made of the enhanced collision frequency and heating rate ν*. It is found that: (a) ν* increases rapidly with pump intensity when the intensity is small, (b) ν* increases very slowly, logarithmically, with intensity when the intensity is large, and (c) ν* significantly depends on whether the ratio of matching wave number to Debye wave number is greater or less than 0.2. These predictions have all been confirmed by computer simulations and by a laboratory experiment. A previous calculation for the saturation of the decay and oscillating two-stream instabilities with T e ≥ T i was limited to just the total fluctuation energy at saturation.