The Description Of A Magnetized Plasma And Study Of Its’ Instability By ZK Equation

In the recent decades,researchers have paid more attention on plasm a instability. It plays a very role in planetary,industrial environments and nuclear fusion process. In this paper,the instability of magnetized quantum plasmas and magnetized dusty plasmas is studied,respectively,by using the reductive perturbation method.The dissertation mainly discusses the following contents:1.The instability of the electron acoustic waves is obtained in a magnetized quantum plasma under the transverse perturbation.The Zakharov-Kuznetsov (ZK) equation for the electron acoustic solitary wave is given by the reductive perturbation method We obtain the cut-off frequency of the plane soliton solution.The propagation velocity and growth rate are obtained. We find that if the wave number is small enough,the solitary wave is not stable.2.The instability of the dust acoustic waves in a two-ion temperature magnetized dusty plasma is studied under the transverse perturbation.The Zakharov-Kuznetsov (ZK)equation,modified ZK equation and Extended ZK (EZK) equation of the DAWs are given by the reductive perturbation technique.The cut-off frequency is also obtained.We find that DAWs under the transverse perturbations in a two-ion-temperature magnetized dusty plasma are instability in the region 0<k<k(?).