Modulational Instability Of Waves In Plasmas

The study of local coherent structures in plasmas is important to understanding and making use of the plasma. As one of these structures, envelope soliton is associated with many other structures' formation, whose excitation, i.e., the modulational instability, is regarded as an important approach to many coherent structures. In addition, there exist a lot of structures in the chaos of a plasma, the entrainment and migration can be achieved by the control of chaos. So, this paper is focused on the mechanism of exciting envelope soliton (i.e., the modulational instability) and control of chaos. In the study of modulational instability, oblique modulation is more realistic than parallel modulation, therefore, under the condition of oblique modulation, the modulational instability of ion-acoustic wave is investigated for several cases, it is found that a finite ion temperature, the obliqueness of modulation and the presence of nonthermal electrons are important factors affecting the ion-acoustic wave modulational instability. The modulational instability is sensitive to these factors, for a warm ion plasma with low temperature, a little difference of ion temperature may lead to great change of the critical conditions for setting on instability; with oblique modulation, the ion-acoustic wave, which is stable under parallel modulation, may become unstable; the effect of nonthermal electrons on the modulational instability is complex, it is a nonlinear process, waves which is unstable only between a range of oblique angel of modulation may evolve into solitons at every oblique angel because of the nonthermal electrons. The modulation of dust-acoustic wave is also considered, the results show that, with the dust charge variation, the modulatinal instability is quite different from the previous work, especially when the electron and ion number density differ greatly. In the study of chaos, a new approach for synchronizing chaos is proposed. The effectiveness and robustness is verified by the numerical results, and the influence of noise on this kind of synchronization is also studied numerically. It is shown that the synchronization isn't sensitive to noise. In addition, we have successfully achieved the synchronization of Liu four-scrolls and KdV-Burgers chaotic dynamical systems using Active control. These are good preparations for the forthcoming investigation of control of chaos and modulational instability in plasmas.