STIMULATED RAMAN, BRILLOUIN AND DUST-BRILLOUIN SCATTERING IN DUSTY PLASMAS

Stimulated scatterings of large-amplitude electromagnetic waves by Lan gmuir, dust-ion-acoustic and dust-acoustic waves in unmagnetized dusty plasmas are investigated by employing the standard methods of nonline ar three-wave interactions and by incorporating the effects of grain-c harge fluctuations, collisions of electrons and ions with dust grains, the plasma drag on a dust grain (for the case of the dust-acoustic wa ve) and the dependence of the average dust charge on the dusty plasma parameters. Distinction is made between the charging collisions, when electrons and ions are accumulated onto the grain surface; and Coulomb collisions, when electrons and ions are simply deflected from the gra in surface. We investigate the regimes for which Coulomb collisions ca n be treated under the small-angle-deflection approximation. If the in tergrain average spacing is equal to or smaller than the Debye length, the collision frequencies of plasma species with dust grains can be m uch larger than any collision frequency of the plasma species amongst themselves. In the case of Brillouin stimulated scattering, other impo rtant contributions to damping come from Landau and dust-charge fluctu ation damping. In the case of dust-Brillouin stimulated scattering, th e most important contribution to damping comes from dust-charge fluctu ation (if the intergrain average spacing is equal to or smaller than t he Debye length) and plasma drag on the dust particles (if the intergr ain average spacing is larger than the Debye length). We derive the in stability thresholds as a function of the density of the dust grains. Because of the inclusion of the new effects, in both Raman and Brillou in scatterings it is found that the instability threshold powers are d rastically increased relative to the dust-free case. In the case of du st-Brillouin scattering, a minimum for the threshold power is found in the transition region between 'dusty' and 'dust-in' plasma. Growth ra tes near thresholds are also discussed.