Collective stimulated Brillouin backscatter

We develop the statistical theory of linear collective stimulated Brillouin backscatter (CBSBS) in spatially and temporally incoherent laser beam. Instability is collective because it does not depend on the dynamics of isolated hot spots (speckles) of laser intensity, but rather depends on averaged laser beam intensity, optic f/{\#}, and laser coherence time, T$_{c}$. CBSBS has a much larger threshold than a classical coherent beam's in long-scale-length high temperature plasma. It is a novel regime in which T$_{c}$ is too large for applicability of well-known statistical theories (RPA) but T$_{c}$ must be small enough to suppress single speckle processes such as self-focusing. Even if laser T$_{c}$ is too large for \textit{a priori} applicability of our theory, collective forward SBS$^{1}$, perhaps enhanced by high Z dopant, and its resultant self-induced T$_{c}$ reduction, may regain the CBSBS regime. We identified convective and absolute CBSBS regimes. The threshold of convective instability is inside the typical parameter region of NIF designs. Well above incoherent threshold, the coherent instability growth rate is recovered. $^{1}$ P.M. Lushnikov and H.A. Rose, Plasma Physics and Controlled Fusion, 48, 1501 (2006).