Dust Plasma Instability With Q-distribution In Nonextensive Statistics

Due to the non-equilibrium phenomena occur in space plasma the distribution of the hot electrons may deviate from the Maxwellian distribution. Moreover, it had been found that the electrons and ions distributions play a crucial role in characterizing the physics of nonlinear waves. In recent years, a new statistical approach, nonextensive statistics or Tsallis statistics, has attracted much attention. This statistics is believed to be a useful generalization of the conventional Boltzmann-Gibbs statistics, and suitable for the statistical description of long-range interaction systems, such as plasma systems. It has been shown that distributions very close to kappa distributions are a consequence of the generalized entropy favored by nonextensive statistics. The associated nonextensive kinetic theory has also been considered in many different branches of physics, especially in astrophysics and plasma physics. This paper uses the kinetic theory to study dust acoustic instability and dust ion acoustic instability in dust plasma in nonextensive statistics.First, for convenience, we consider a three-component plasma consisting of q-nonextensive distribution electrons, ions and dust. Using kinetic theory, we have carried out an investigation of linear dust acoustic instability in an unmagnetized collisionless plasma. The dispersion relation and the instability growth rate of dust acoustic instability are obtained. Both analytical and numerical results, the following from the solution of the dispersion relation, are presented, and a detailed comparison is made over a range of plasma parameter values. In addition, numerical solution of the instability growth rate is used to explore the effects of the spectral indices of the ions, electrons and dust, and the species’temperature and density ratios, on the instability growth rate of the waves.Second, the dispersion relation and the instability growth rate of dust ion acoustic wave are studied by using Vlasov-Poisson model for unmagnetized q-nonextensive distributed plasma containing electrons, ions and negatively charged dust. It is found that the presence of the nonextensive distribution electrons and ions significantly modify the domain of the the instability growth rate, as well as the ion-electron density ratios and drifting-thermal velocity ratio. In reverse, the index of dust grains has nearly no any effect on the instability growth rate.Furthermore, the effects of these parameters on the growth rate have also been discussed in detail.