Study On Instability For Lorentzian Kappa Distributed Dusty Plasmas

A variety of experiments indicate that the ubiquitous presence of superthermal particles in laboratory and space plasmas and the plasmas are observed to have particles distributions that depart from the Maxwellian distribution. The presence of superthermal particles results in a distribution function with a high-energy tail, which can be conveniently modeled by Lorentzian kappa distribution. It was shown that the presence of a high-energy tail component in a kappa distribution considerably changes the rate of resonant energy transfer between particles and plasma waves, so that the dispersion relation, the conditions for Landau damping and plasma instabilities may be substantially different for the two distributions. Plasma waves are the collective motion modes of many particles in the plasma. The relationship of angular frequency ω and the wave vector k can determine the dispersion relations of plasma waves, which are fundamental in studying instabilities. Therefore, it is of great significance to study the dispersion relations and instability of plasma modified by non-Maxwell distribution. In this paper, we considered instability of dust acoustic wave and dust ion-acoustic wave for kappa distributed plasmas. The paper makes some work as follows:First, the instability of the dust acoustic waves driven by ions and electrons with different drift velocities in an unmagnetized, collisionless, isotropic dusty plasma is investigated by the kinetic theory. The electrons, ions, and dust particles are all modeled by the generalized Lorentzian kappa distributions. It is found that the instability growth rate depends not only on the mass, the temperature, the density ratios of the components, and ion-electron drift velocity ratio, but also on the spectral indix for each component. The effects of the indices on the instability growth rate of dust acoustic waves have been discussed in detail.Second, the dust ion-acoustic instability in an unmagnetized, collisionless, isotropic dusty plasma is investigated modeled by a Lorentzian kappa distribution for all component. Analytical expressions are derived for the dispersion relation and the instability growth rate under this condition:the phase velocity is much larger than the thermal velocity of the dust and the ions but much less than those of the electrons. We proceed by numerically evaluating and discussing the effects of spectral indices and ion-electron desenty ratio.