Solution of the Boltzmann Equation for Electrons Interacting with Acoustic Waves in Strong Electric Fields

We have solved the Boltzmann equation to obtain the conductivity tensor for electrons interacting with acoustic waves in the presence of strong electric fields. The presence of the dc electric field leads to two new effects: the introduction of a drifted distribution function for the electrons, and of a complex electron temperature which depends on both the electric field and the acoustic wavelength. It is shown that it is the drifted distribution function which leads to the amplification of acoustic waves in the short-wavelength limit $\mathrm{ql}\gg 1$, while in the long-wavelength limit $\mathrm{ql}\ll 1$, it is the complex temperature which gives rise to the amplification.