The Applications Of Nonextensive Statistics In The Non-maxwellian Plasmas With The Power-law Distributions

Plasmas are commonly observed both in laboratory and space environment. Plasmas can support a large number of wave modes. As an important research area, the properties of plasma waves are receiving more and more interest. Many phenomena of plasmas can be obtained by the investigation of plasma waves. Spacecraft measurements for the plasma velocity distribution indicated that there was a"suprathermal"power-law tail at high energies, which can be modeled more effectively by a generalized Lorentzianκ-distribution. Such aκ-distribution is known now to be equal to the q -distribution in nonextensive statistics. As a generalization of the traditional Boltzmann-Gibbs statistics, nonextensive statistics has applied to systems with long-range interactions forces such as Newtonian gravitational forces and Coulomb electric forces which are not suitable for the description of traditional one.In this paper, we applied the nonextensive statistics to the investigation of the properties of wave modes in non-maxwellian plasmas. We consider three kinds of non-maxwellian plasmas: electron-ion plasma, dusty plasma and inter permeating plasma.After introducing some basic facts and waves modes in plasma physics, we introduce the formalism of kappa distribution commonly used in nonmaxwellian plasma. After that, we introduce the relationships between Tsallis distribution and kappa distribution. The statistical foundations of nonextensive power-law distributions are also given in this section.In section three, after introducing the properties of the standard electron-ion plasma, we study properties of ion-acoustic waves in collisionless unmagnetic field space plasma using nonextensive statistics. The generalized dispersion relation and the instability growth rate are given in the framework of nonextensive statistics. We find that the wave frequency is insensitive to the nonextensive parameterq , but the growth rate is significantly modified by q and temperature ratio. The strengthened and weakened modes for the wave growth can be interpreted, respectively, by increase of the suprathermal particles and low velocity particles.In section four, the properties of the dust ion-acoustic and dust-acoustic waves in a non-maxwellizn dusty plasma is investigated by the nonextensive kinetic theory. All the plasma components (electrons, ions and dust particles) are assumed to be the Lorentzianκ-distributions. The spectral indexesκof theκ-distributions for the three plasma components are different from each other. The obtained dispersion relations and the instability growth rates are not only depended on the physical quantities of the plasma, but also on the spectral indexes. The numerical results for theκ-effect on the instability growth rates are given by a graphical method.In section five, we applied the kappa distribution to the kinetic instability of ion-acoustic wave mode in non-maxwellian permeating plasmas. We calculate the generalized dispersion relation and instability growth rate of this wave mode. At last, we consider a simple case. We assume the ions have the same temperature and the electrons have same one too. Through a numerical method, we also give the effects of the kappa parameters of ions and electrons for the wave frequency and growth rate.