The phenomenon of stimulated Brillouin scattering of a large-amplitude electromagnetic wave by the electron acoustic wave has been analytically investigated in a piezoelectric semiconductor plasma in the presence of an external uniform magnetic field. The Boltzmann equation with a Krook model for the collisional term has been solved in the guiding center coordinates for the nonlinear response of the plasma electrons. It is noticed that the magnetic field enhances the growth rate of the parametric instability in contrast with the fluid-model results.

Using Vlasov-kinetic model, a dispersion relation of the low-frequency and electrostatic lower-hybrid wave is obtained accounting for the streaming of ions and dust charge fluctuations in a finite temperature and collisionless magnetized dusty plasma. It is found that the damping of this mode is the sum of the Landau damping and the charge fluctuation effect. This lower-hybrid mode can be excited when the ion streaming velocity in the direction of the magnetic field exceeds the parallel phase velocity of the mode and when the magnitude of the Landau damping exceeds the magnitude of the damping due to the dust charge fluctuation. Thus, the lower-hybrid-like mode in a dusty plasma will be damped rapidly by the unmagnetized ions compared to that due to the dust charge fluctuation process.

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