The effects of laser bandwidth on the non-linearly saturated state of the two plasmon-decay instability

Broad laser bandwidth technology has emerged as a promising approach to mitigate laser-plasma instabilities (LPI) in direct-drive inertial confinement fusion. While bandwidth has been known to increase the intensity thresholds, interesting questions remain about the non-linear saturation of LPI in the cases when the bandwidth amount proves insufficient for their complete suppression.

A model for the two-plasmon decay instability is developed which takes into account the strong turbulent fluctuations present in the non-linearly saturated state. Physically, they provide an additional decorrelation mechanism to the broadband laser driver, further reducing the effective time over which the three modes maintain coherence. This effect is captured by renormalizing the plasma wave dispersion functions to include corrections from the background ion and electron fluctuation spectra. The additional turbulent decorrelation modifies the growth rate and energy injection rate of the instability from their values during the linear stage. Scalings of the fluctuation level as a function of laser bandwidth and intensity are investigated.