Oscillations of a Weakly Ionized Plasma in a Strong Electric Field

The stability of a weakly ionized plasma in a strong electric field against the formation of longitudinal waves is investigated theoretically in the hydrodynamic limit $\mathrm{ql}\ll 1$ where $q$ is the wave number, and $l$ is a relaxation length related to the mean free paths of the charge carriers. Applications of the theory to semiconductors and gases are considered. The behavior of the charge carriers in response to slowly varying disturbances is dominated by their collisions with the lattice or the neutral atoms, implying that an approximate equilibrium is maintained between the local field and the local densities, drift velocities, and effective temperatures of the carriers. The mean thermal energy or effective temperature of the electrons in the steady state depends on the magnitude of the applied field and can be much greater than the lattice or neutral-atom temperature. In general, this means that the electron mobility is also field-dependent. It is shown that this field dependence and the local equilibrium condition can lead to temperature oscillations which affect the phase velocity and damping of excitations resembling ion-acoustic waves. It is predicted that when the applied field exceeds a critical value the damping constant will change sign, and the system will become unstable. The feasibility of detecting this instability is discussed, and comparisons with other instabilities are made.