Langmuir wave damping decreases slowly

The onset of stimulated Raman scatter in a single laser speckle occurs (D. S. Montgomery \textit{et al.}, Phys. Plasmas, \textbf{9}, 2311 (2002)) at lower laser intensity, $I$, than predicted by linear theory based on classical Landau damping, $\nu_{\mbox{L}}$, of the SRS daughter Langmuir wave. Does this imply that SRS onset in a speckled laser beam, propagating through long scale length plasma, is also at odds with linear theory? It has been shown (Harvey A. Rose and D. F. DuBois, Phys. Rev. Lett. \textbf{72}, 2883 (1994)) that linear convective gain in speckles with large fluctuations of $I$ about the average, $\left\langle I \right\rangle$, leads to onset at a value of $\left\langle I \right\rangle$, $I_{\mbox{c}}$, small compared to that for onset in a uniform beam. While nonlinear electron trapping effects may occur in very intense speckles, whether or not these effects are sufficient to lower the onset value of $\left\langle I \right\rangle$ below $I_{\mbox{c}}$ depends on how strongly electrons must be trapped before there is significant reduction in $\nu_{\mbox{L}}$. As the amplitude of an SRS daughter Langmuir wave increases, its $\nu_{\mbox{L}}$ decreases by the factor $\nu$/$\omega_{\mbox{b}}$, due to the competition between electron trapping, with electron bounce frequency, $\omega_{\mbox{b}}$, and escape of these trapped electrons by advection out of a speckle's side, at rate $\nu $. This result (Harvey A. Rose and David A. Russell, Phys. Plasmas, \textbf{8}, 4784 (2001)) is valid for $\nu$/$\omega_{\mbox{b}}$ $\ll$1. In this talk I present a nonlinear, transit time damping, calculation of $\nu_{\mbox{L}}$ and find that reduction by a factor of two does not occur until $\omega_{\mbox{b}}$/$\nu \approx$ 5. This slow turn on of trapping effects suggests that the linear calculation of $I_{\mbox{c}}$ is NIF relevant.