Propagation of Ion Waves in Weakly Ionized Gases

Abstract

Theoretical and experimental results are presented on the propagation of longitudinal ion waves in weakly ionized gases in a frequency range extending from considerably below to well above the ion plasma frequency. The theory describes propagation in a uniform plasma on the basis of kinetic equations. First, a dispersion relation is derived and solved for the complex propagation constant; this is appropriate if the damping is weak. Second, the spatial dependence of the phase and amplitude of the disturbance excited by a pair of grids is calculated; when the damping is not weak, the amplitude does not decay exponentially with distance. The measurements are performed with grid-excited ion waves at frequencies between 0.1 and 10 MHz in hydrogen, nitrogen, argon, and krypton rf discharges with charged-particle densities of about ${10}^{9}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ and electron temperatures of the order of 50 000\ifmmode^\circ\else\textdegree\fi{}K. At frequencies well below the ion plasma frequency ${\ensuremath{\omega}}_{i}$, the phase velocity is found to be frequency-independent and is given by the Tonks-Langmuir speed. At these frequencies, the attentuation is proportional to the neutral gas pressure and is therefore primarily caused by ion-neutral collisions. At frequencies approaching ${\ensuremath{\omega}}_{i}$, the attentuation is higher than expected from collisions, and the excess is attributed to ion Landau damping. Theory and experiment agree well at $\ensuremath{\omega}$ smaller than ${\ensuremath{\omega}}_{i}$. For frequencies greater than ${\ensuremath{\omega}}_{i}$, the phase velocity increases with frequency, but not as much as expected on the basis of Maxwellian velocity distribution of the ion gas. Moreover, the ratio of imaginary to real part of the propagation constant, which is found to decrease slightly with frequency, is much smaller than expected from the theory. Better agreement between experiment and theory in this frequency range can be obtained by assuming the ionic velocity distribution to decrease more rapidly at high velocities than a Maxwellian distribution. Non-Maxwellian velocity distributions of this kind are actually expected under the conditions of the experiment. The data reported in this paper furnish the first experimental evidence of ion-wave propagation at frequencies greater than ${\ensuremath{\omega}}_{i}$.