Dispersion relation for the dust ionization and dust acoustic waves in the gas discharge complex plasma

Abstract

A theoretical approach is developed for the dust ionization (DIW) and dust acoustic waves (DAW) propagating in the cloud of microparticles in the low-pressure gas discharge under microgravity conditions. The theory explores the fluid approximation for the microparticle subsystem of complex plasma combined with the kinetic equation for the ions. In the one-dimensional approximation, the wave equation is obtained whose solution defines the dispersion relation for the waves in complex plasma involving the oscillations of microparticles. Obtained dispersion relation unifies both the dust ionization and the dust acoustic waves (DIW and DAW, respectively). According to this dispersion relation, the effect of microparticles on the recombination rate leads to a number of peculiarities. Among them are existence of the minimum frequency, above which the wave propagation is possible, a weak dependence of the DIW wave number on the frequency, and a high phase velocity of DIW as compared to DAW. It is demonstrated that no instability of DIW is possible, whereas DAW can reveal instability under proper conditions. Calculation results correlate with those obtained in a recent experiment.