Instability Of The Ion Acoustic Waves In The Plasma In Nonextensive Statistics

In this paper, we introduce the proposition of nonextensive entropy and the application in plasma physics on the base of power law q-distributions in the frame work of Tsallis statistics. The departure point of nonextensive thermodynamics is nonextensive entropy introduced by C. Tsallis, which inherits the most characters of BG entropy except its nonextensivity. By the optimization of entropy under the confines of normalization internal energy condition, we can obtain a distribution which is obviously different from the classical BG statistics. This formalism has been proved by a series of experiments.We investigate the instability of ion acoustic waves in the collisionless magnetic-field-free plasma which is described by the nonextensive q-distributions of Tsallis statistics. Through the introduction of a relative velocity in plasma, we obtained the increase rate of the ion acoustic waves and corresponding to the stability and instability on the border of the relative velocity V on the basis of the dispersion relation of ion acoustic waves. In the limit , the results reduces to standard form in the framework of B–G statistics. By comparison, we know the relative velocity which relies on the power law q-distributions in Tsallis statistics is related to the value of q-parameter, and clearly it meet the experimental results closer. Finally, it is should be emphasized that for the systems with the long-range interactions, such as plasma and gravitational systems, where the non-equilibrium stationary states exist, and nonextensive thermodynamics might be more adequate for the description of the systems.