Inflation threshold: A nonlinear trapping-induced threshold for the rapid onset of stimulated Raman scattering from a single laser speckle

Abstract

The rapid onset, with increasing laser intensity, of levels of backward stimulated Raman scattering (BSRS) exceeding linear convective predictions, from single laser hot spots was predicted by simulations [Vu et al., Phys. Plasmas 9, 1745 (2002)], and has been observed [Montgomery et al., Phys. Plasmas 9, 2311 (2002)] in nonlinear regimes dominated by electron trapping. A theory for this inflation threshold is given here. The threshold is the result of competition between velocity diffusion and trapping, and is exceeded when the convectively amplified SRS Langmuir wave (LW) achieves an amplitude for which the coherent trapping velocity increment of electrons in the LW (the half-width of the trapping separatrix) exceeds the rms diffusion velocity (resulting from background plasma fluctuations), accumulated in one bounce time, for electrons with mean velocities near the phase velocity of the LW. The results of this theory, when the kinetic theory of the one-dimensional (1D) reduced-description particle-in-cell (RPIC) simulation is used, are in good agreement with a series of 1D RPIC simulations. The theory is naturally generalized to three dimensions, and is compatible with macroscopic laser interaction codes such as pF3d [Berger et al., Phys. Plasmas 5, 4337 (1998)]. Comparison of the LW trapping-induced inflation threshold to the LW threshold for the Langmuir decay instability provides an estimate for the transition between nonlinear saturation regimes. In an independent hot spot model of many hot spots, statistics suggests that the inflation threshold intensity will control the rapid onset of strong BSRS in laser beams smoothed by random phase plates.