The Study Of The Singularity In Plasma Current

The study of current singularity is an important topic in plasma physics, because there are an amount of small scale phenomena, such as the dissipation or other dynamic and kinetic effects, in the singular region. Although Alfven resonance and magnetic reconnection. as two kinds of general singular structures in current distribution, have been studied by many researchers in the last century60’s, they still have been attractive up to now. There are two reasons. One is some attractive and important phenomena in nature, such as the corona heating, the geomagnetic storms, and substorms, and so on. The other one is the requirement on the laboratory and engineering, such as application of the wave heating, control of the sawtooth instability and the lock mode etc.. There has been considerable success in research on both Alfven resonance and magnetic reconnection which are of similar singular current structures due to inhomogeneity. However, the studies of two kinds of current structures were relatively independent. In fact, there are some similarities on equilibrium, geometry, equations and boundary conditions.In recent years, people begin to study the relationship between Alfven resonance and magnetic reconnection. Some of them proposed that the model of forced magnetic reconnection should be embedded in the Alfven resonance theory. If the resonant point is laid on the null point, the time evolution of the perturbation should be the same as the behavior of forced magnetic reconnection. The others, nevertheless, emphasized on the transition between the two processes by varying the external parameters, and gave a critical transition frequency. In effect, although these two kinds of views were reasonable somewhat, there are also certain puzzles left. First, the external frequency should be exactly equal to zero for magnetic reconnection. Second, there is no universal theory which can cover Alfven resonance and magnetic reconnection.To solve the issue mentioned above, we in this thesis study Alfven resonance and magnetic reconnection on the mentioned issue from the perspective of the property of the singularity.In Chapter Ⅰ, we make a brief introduction on the background and development of research on Alfven resonance and magnetic reconnection, respectively. The basic conceptions and methods are also referred.In Chapter Ⅱ, based on the previous view of Alfven resonance’s logarithmic and the forced reconnection’s algebraic singularity (here the singularity is specifically referred to that of perturbed displacement’s parallel component), more general equilibrium profiles are taken into account, such as the magnetic field, the density and the shear flow. Besides the Alfven resonance condition, if the high order derivative of the local Alfven velocity and perturbed phase velocity are also matched which are named sub-resonance-conditions, there are multiple roots in the equation of resonance condition. The singularity is logarithmic for a conventional equilibrium. However the algebraic singularity can exist when the root of the equation is multiple. Particularly, when the multiplicity is equal to2, the singularity is1/x which is the same as reconnection singularity.In Chapter III, according to WKB analysis, we adopt a2D Harris-like-sheet equilibrium and the five-field model, to study the eigen-function and the eigen-equation in high beta magnetic reconnection layer. Considering the ion inertial length effect, it is found that the Hall current term plays a dominant role on the dynamic process in reconnection layer, and a low frequency oblique whistler wave is generated. Then some new features which are different from the traditional whistler wave are elaborated.In Chapter IV, we adopt the same model and method as in Chapter III in Alfven resonance layer, and study the mode conversion in the Alfven resonance layer. On the scale of ion inertial length, the wave in high beta resonance layer is similar to the one in reconnection layer.In Chapter V, based on Chapter III-IV, with the frequency decreasing, the transition from Alfven resonance to forced reconnection with Hall MHD is studied. A new critical frequency is given with perturbation method. Beyond the critical frequency, the singularity is the Alfven resonance logarithmic. On the contrary, the singularity is magnetic reconnection algebraic (hereafter, except referring resonant point coinciding, it is convenient to make a definition that the logarithmic singularity is Alfven resonance singularity while the algebraic singularity is forced reconnection singularity). Going further, we show the physical picture of the transition between two kinds of singular current structures with low frequency oblique whistler wave by the results in Chapter III&IV.In Chapter VI, based on the previous research, the singularity transition is analyzed by varying externally imposed driven frequency with a2D RMHD model, and the relative physics picture is shown. With perturbation technique, the critical frequency is found. Adopted a uniform method which covers Alfven resonance and forced reconnection, a global solution is obtained to match the perturbation solution. The frequency on which the reconnection flux is maximal is also calculated. In the end of Chapter VI, the results of numerical simulation are compared with that of analytical method.Finally, the thesis is concluded with a summary and ended with discussions on future work.