Acoustic Wave Mode in a Weakly Ionized Gas

The acoustic wave mode in a weakly ionized gas, which is a perturbed version of an ordinary sound wave in a neutral gas, is investigated. At sufficiently low frequencies, $\omega \ll {\omega }_c={\Omega }_n\left(\frac{N_n}{N_i}\right)\left(\frac{T_n}{T_e}\right)$, the acoustic oscillations of the electrons, ions, and neutrals are all in phase and have equal amplitudes ($N_n=\mathrm{n}\mathrm{e}\mathrm{u}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{l}-\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{y}$, $N_i=\mathrm{i}\mathrm{o}\mathrm{n}-\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{y}$, $T_n=\mathrm{neutral}\mathrm{temperature}$, $T_e=\mathrm{electron}\mathrm{temperature}$, ${\Omega }_n=\mathrm{collision}$ frequency of a neutral particle with charged particles). However, at frequencies of the order of or larger than ${\omega }_c$, a marked phase difference between the oscillations of the different fluid components occurs. This leads to charge separation and an electro-acoustic effect, i.e., an electric-field perturbation produced by a sound wave. Previously reported wave amplification, predicted on the assumption that all particle species oscillate in phase, is found to be consistent with the dispersion relation derived here at frequencies $\omega \ll {\omega }_c$. At frequencies $\omega \ge {\omega }_c$, a reduction of the amplification takes place. As a consequence it is shown that, contrary to what previously has been believed, a decrease of the neutral-gas temperature does not always lead to an increase in the wave amplification.