Using a kinetic description for electrons and the usual equation of motion for lattice displacement we have derived a general dispersion relation for acoustic waves in a piezoelectric semiconductor, in the presence of a strong high frequency electric field oscillating near the electron plasma frequency. Earlier hydrodynamic results valid forkλ_e≪1 (wherek is the wave number of the acoustic wave andλ_ethe electron mean free path) are rederived as a special case. Forkλ_e≫1, two instability branches are discovered and magnitudes of the threshold electric field required to drive the acoustic wave unstable in each case, are obtained.

The effect of velocity gradient across the magnetic field on the low frequency flute modes is examined in detail, using the normal mode analysis. It is shown that some new type of instabilities driven primarily by the velocitygradient arise and these excited modes eventually attain the convective saturation. The onset of plasma turbulence due to these instabilities may possibly be one of the major contributors for anomalous heating process and enhanced plasma resistivity.