The ionization instability and resonant acoustic modes suppression by charge space effects in a dusty plasma

The large wavenumber suppression of unstable modes by space charge effects of the ionization instability in a weakly ionized and unmagnetized dusty plasma is investigated. The charge losses in the initial equilibrium state are balanced by electron impact ionizations originated by both the thermal electron populations and an additional monoenergetic electron beam. The multifluid dimensionless equations are deduced by using the time and length scales for elastic collisions between ions and neutral atoms and the Poisson equation relates the plasma potential fluctuations with charged particle densities instead of the quasineutral approximation. A general dimensionless dispersion relation is obtained from the linearized transport equations, where the ratios between the characteristic velocities, as the dust ion acoustic (IA), dust acoustic (DA), ion sound, and thermal speeds permits us to evaluate the weight of the different terms. In the long wavelength limit the results obtained using the quasineutral approximation are recovered. The differences found between roots of both dispersion equations are discussed, as well as those of previous models. The unstable mode of the linear ionization instability is originated by the imbalance between ion and electron densities in the rest state caused by the negative charging of dust grains. Contrary to dust free plasmas, the unstable mode exists, even in the absence of the ionizing electron beam. The numerical calculations of the roots of the full dispersion equation present a maximum unstable wavenumber not predicted by the quasineutral approximation, which is related with the minimum allowed length for space charge fluctuations within a fluid model. This upper limit of unstable wave numbers hinders the predicted resonant coupling in the long wavenumber regime between the DA and DIA waves. (c) 2006 American Institute of Physics.