Electron heating due to parametric instability turbulence

The turbulent electron heating due to laser-plasma instabilities at the critical density (laser frequency equals plasma frequency) is considered. In the regime where the laser energy is much less than the plasma thermal energy, simulations show that the wave energy spectrum takes on approximate k−2 shape concomitant with the formation of a suprathermal electron tail. Test particle calculations demonstrate that these tails are produced by velocity space diffusion due to the plasma waves. Quasilinear theory predicts a linear heating rate and an exponential shape for the electron tail, in agreement with the simulation result. The fluid equations, including mode coupling terms, are solved, and it is found that the instability saturation level and k−2 spectrum are due to mode coupling. Using the resulting fields, the electron distribution function is evolved, giving reasonable heating rates and suprathermal tail formation. Calculations in the underdense region (laser frequency greater than plasma frequency) show that the heated distribution function has fewer high energy electrons. Finally, an approximate analysis of heating in a finite interaction region is given.