Temporal evolution of stimulated Brillouin backscatter

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Abstract
A qualitative understanding of the time dependence of stimulated Brillouin scattering (SBS) provides estimates of the amount of temporal growth that occurs in current inertial confinement fusion and short laser pulse interaction experiments when the growth is limited by the length of the experiment or by motion of the ‘‘hot spots’’ of the laser intensity pattern induced by beam smoothing. In the weak coupling limit, the instantaneous growth rate depends upon the plasma initial conditions early in time, is proportional to t−1/2 later in time, and asymptotically approaches the absolute growth rate (in the absence of damping). When the instability is strongly coupled, the growth rate depends upon the plasma initial conditions early in time but is proportional to t−1/3 later in time. When the growth rate drops to a value comparable to that of the ion acoustic frequency, the instability becomes effectively weakly coupled. The effects of damping are also discussed.