Nonlinear Electrostatic Waves In Magnetic Plasma

The heat nuclear fusion, space and astrophysics plasmas are the major motiv-ity to the development of plasma physics. Research on the basic plasma progress inthese three fields may be bestead and compensatory. This thesis is devoted to study-ing the linear and nonlinear physical problems in several complex magnetic plasmasystems in the dense astrophysics and tokamak fusion. Various nonlinear equationsare constructed based on the theories of hydrodynamics and electrodynamics. Usingthe traveling wave method, the multiple scale method and the special function trans-form method, a series of rich wave solutions are obtained, which can provide somemeaningful theoretical values for the realistic phenomena.The first part of the thesis, involving chapters two, three and four, is concentratedon the uniform and nonuniform quantum magnetoplasma systems in the dense astro-physics. Using the quantum hydrodynamic model, and considering that the collisionbetween ions and neutrals is dominant or minor, i.e., νindtor νindt, respec-tively, three (2+1)-dimensional nonlinear equations are constructed for the potentialvarying spatio-temporally.From these three nonlinear equations, the potential solutions are obtained to de-scribe ion acoustic waves which possesses shock, explosive and vortex structures. Re-markably, the explosive and vortex solutions are firstly found for the similar systems.Using the typical parameter conditions in the dense astrophysical environment like theatmosphere of neutron stars and magnetars, it is found that the strength of shock andthe width of explosion enhance, respectively, with the increase of density (i.e., the de-crease of quantum parameter He); enhance (νindt) or decrease (νindt) with theincrease of magnetic intensity and drift velocity (i.e., the increase of density and tem-perature gradients); and enhance (νindt) or decrease (νindt) with the increaseof the collision frequency. The electrostatic potential tends to a stable value with the increase of the spatio-temporal phase, which demonstrates that the system will reachto a stable state eventually. Besides, the vortex solutions show that the vortex potentialin the x y plane always decays in one direction, and is periodic in the other or a slopeangle direction, which shows a stable periodic vortex street. Especially, in the case ofuniform space distribution, the vortex potential may tend to stable or unstable states.It can also oscillate periodically in time.In the second and third chapters, the linear dispersion relations are derived forthe uniform and nonuniform systems when νindt. It is found that the quantum pa-rameter Hemodifies the scale length of the system; the dispersion frequency has com-plex relation with the obliqueness angle; the real frequency is proportional to the driftfrequency; and the imaginary frequency has complicated relation with the collisionfrequency between ions and neutrals, which induces damped wave. In addition, sta-bility analysis provides the generating conditions for the stable and oscillatory waves.Simultaneously, it is revealed that the quantum correction and the particle drift playvital roles in the stability of system.The second part of the thesis, involving chapter five, is focused on the coupledtwo-dimensional Hasegawa-Wakatani model. This model is applicable to the charac-terization of resistive drift-wave fluctuation and the nonuniform edge distribution in atokamak plasma. In this model, the fluctuant density and potential are cross-coupledby the adiabatic parameter. Considering the special case that the viscous term (i.e.,the high order term) is negligible, and using a special function transformation ap-proach, two groups of new analytic solutions with and without phase shift between thefluctuant density and the fluctuant potential are obtained. It is demonstrated that thefluctuant potential shares the same period and similar spatio-temporal variations withthe density. It is indicated from the solutions without phase shift that the fluctuationmay be controllable through adiabaticity and diffusion. Besides, the phase differencehas no relationship with the nonzero constants, which represents the nature characterof the system. Using the typical parameters in the quasi-adiabatic regime, the solu-tions with phase shift show that the density gradients become bigger as the contoursbecome dense toward the plasma edge in the x y plane, and the regular zonal struc-ture transforms into vortical structure; the fluctuation is periodic and exponential withradius and angular, and changes big and quickly near the plasma edge, which reveals the nonuniform distribution in the tokamak edge; and the fluctuant distribution may beperiodic and stable in spatiotemporal coordinates. Our results might be used to explainthe correlative experimental phenomena of a large level of density fluctuation and thenonuniform distribution in the tokamak plasma edge.