Nonlinear behavior of plasma: Connection with nonextensive statistics

Abstract

Nonextensive hydrodynamic equations and Zakharov equations are derived by moment equation and two time-scale methods, respectively. The conserved quantities and nonlinear entity collapse scalar law are obtained, from which we find that the conservation energy is relevant to the nonextensive parameter but momentum as well as angular momentum and the number of plasmon are not affected by the nonextensivity of system. The self-similar collapse solution of nonextensive Zakharov equations is also presented. Furthermore, we demonstrate that the nonlinear entity collapse scalar law is relevant to the nonextensive parameter and especially it allows the existence of three dimensional stable and one dimensional collapse nonlinear entity, which is significantly different from the case of Maxwellian distribution. In the extensive limit, all the results obtained in Maxwellian framework are reproduced.