Order statistics and extreme properties of spatially smoothed laser beams in laser-plasma interaction

Abstract

The order statistics of intense speckles or “laser hot spots” are studied in the context of the so-called “optically smoothed” light beams of laser-matter interaction. We investigate theoretically and by means of numerical simulations the distribution function for the k-th most intense speckle maxima in the upper tail speckle distribution. From these distributions for each order k, a distribution function for the intense speckles as a function of their peak intensity can be established, which allows to compute their impact on nonlinear processes, like parametric instabilities. This is done for the example of stimulated Brillouin scattering, using the so-called independent hot spot model, for which the backscatter reactivity level is computed, which proves to be in very good agreements with numerical simulations. This result is of great interest for nonlinear processes, like instabilities, where extreme speckles play an important role.

Order statistics of high-intensity speckles in stimulated Brillouin scattering and plasma-induced laser beam smoothing

“…with P c = 2N c (cλ 0 /ω 0 )(n c /n 0 )n c ckT (1 − n 0 /2n c ), in which N c assumes the value of N c = 1.90 for the example of a Gaussian beam (with a corresponding definition of l ⊥ , see [18]). This is an important issue for discussion on the dominating process, namely between FSBS and SF, see section 6.…”

“…where G refers to the gain in a speckle with the average beam intensity I . In [18] order statistics of speckle fields have been investigated, which will be used in the following.…”

“…wherein the probability density follows the expression [18] obtained from the marginal probability distribution…”

Study of crossed-beam energy transfer process with large crossing angle in three-dimension

“…If the beat wave driven by a couple of two beams satisfies the dispersion relation of the ion-acoustic waves, energy transfers between the crossed beams through a three-wave coupling process (McKinstrie et al, 1996). This phenomenon, which is commonly named crossed-beam energy transfer (CBET), is a very important process because of its influence on the capsule implosion symmetry (Kruer et al, 1996) and other laser-plasma interaction (LPI) instabilities, such as stimulated Raman scattering (SRS) and simulated Brillouin scattering (SBS) (Karttunen & Salomaa, 1992;Kline & Montgomery, 2005;Sharma et al, 2009Sharma et al, , 2012Huller & Porzio, 2010;Hao et al, 2012;Vyas et al, 2014). During the latest decades, many experimental works about CBET have been carried out on the Nova and the Omega laser facilities (Wharton et al, 1998;Kirkwood et al, 2002).…”

Study of coexisting stimulated Raman and Brillouin scattering at relativistic laser power

“…In the past, a lot of theoretical and numerical works at high power laser flux has been done in which SRS and SBS are carried out separately (three wave interaction = 3WI), ignoring the interplay among them (Guérin et al, 1995;Barr et al, 1998;Mahmoud et al, 2001;Shuller et al, 2010;Paknezhad et al, 2012). However, SRS and SBS can coexist upto N cr /4 inside the plasma (SRS exists upto N cr /4 while SBS exists upto N cr ) (Kruer, 1974;Liu et al, 1994), where N cr is the electron critical density, defined as the density above which the propagation of the electromagnetic wave is not allowed.…”