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Linear theory of multibeam parametric instabilities in homogeneous plasmas

Linear theory of parametric instabilities resulting from N overlapping laser beams with an arbitrary beam configuration and polarization in a homogeneous plasma is presented. A general dispersion relation valid for both N-beam stimulated Raman scattering (SRS) and stimulated Brillouin scattering (SBS) is derived. Analytically, we obtain the growth rate for a two-beam system and find the significance of two special geometries by sharing a common decay wave. By virtue of these geometries, the coefficient matrix of the general dispersion relation is decomposable and reducible in dimensions to give relatively simple formulae. Therefore, the most unstable mode is a trade-off among beam number, geometry, and polarization. We have also considered the spatio-temporal evolution of a highly symmetric N-beam shared scattered light (SL) mode, defined by N beams sharing a common scattered wave, and obtained convective gains for SRS and SBS. An estimation shows that both SRS and SBS in a N-beam SL mode may have significant impacts on inertial confinement fusion.