Stimulated Raman, Brillouin and dust–Brillouin scattering in dusty plasmas

Abstract

Stimulated scatterings of large-amplitude electromagnetic waves by Langmuir, dust–ion-acoustic and dust-acoustic waves in unmagnetized dusty plasmas are investigated by employing the standard methods of nonlinear three-wave interactions and by incorporating the effects of grain-charge fluctuations, collisions of electrons and ions with dust grains, the plasma drag on a dust grain (for the case of the dust-acoustic wave) 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 grain surface. We investigate the regimes for which Coulomb collisions can be treated under the small-angle-deflection approximation. If the intergrain average spacing is equal to or smaller than the Debye length, the collision frequencies of plasma species with dust grains can be much larger than any collision frequency of the plasma species amongst themselves. In the case of Brillouin stimulated scattering, other important contributions to damping come from Landau and dust-charge fluctuation damping. In the case of dust–Brillouin stimulated scattering, the most important contribution to damping comes from dust-charge fluctuation (if the intergrain average spacing is equal to or smaller than the Debye length) and plasma drag on the dust particles (if the intergrain average spacing is larger than the Debye length). We derive the instability thresholds as a function of the density of the dust grains. Because of the inclusion of the new effects, in both Raman and Brillouin scatterings it is found that the instability threshold powers are drastically increased relative to the dust-free case. In the case of dust–Brillouin scattering, a minimum for the threshold power is found in the transition region between ‘dusty’ and ‘dust-in’ plasma. Growth rates near thresholds are also discussed.