Numerical Study On Theory Of Resistive Wall Mode With Resistive Layer And Linear Tearing Mode Feedback Controlling

It is well known that the resistive wall mode(RWM)and tearing mode(TM)greatly limit beta value of a tokamak device.In order to achieve a goal of long pulse discharge or steady state operation with a high plasma pressure in the future advanced tokamak device(such as ITER),research on the stabilization of the RWM and TM has become critical issue in nuclear fusion nowadays.A lot of researches show that the passive control(such as plasma toroidal rotation)or the active control(such as magnetic feedback coils)has stabilizing effects on the RWM and TM.In many numerical and analytical studies of effect of plasma rotation on RWM,the plasma is generally assumed to be ideal with vanishing plasma resistivity.In the intensive studying,it shows that the plasma resistivity near the rational surface plays a significance role for the magnetohydrodynamic instabilities.So far,research for this issue needs to make further efforts.This thesis employs the method of the energy principle to derive a dispersion relation of the RWM.The dispersion relation includes both the plasma resistive layer damping near the rational surface and the kinetic dampilng.The dispersion relation is numerically solved in order to investigate systematically the effects of the plasma resistive layer near the rational surface on the kinetic RWM stability in theory.Basically,the previous research works for the magnetic feedback control on the linear TM have been studied in slab models or in cylindrical geometries.In order to obtain a more optimized magnetic feedback control scheme about the stability of the linear TM,this thesis studies numerically the magnetic feedback control on the linear TM by using the MARS-F code.The basic contents of this thesis are as follows:In chapter ?,a briefly introduction of the background and scientific significance of this thesis,MHD equilibrium,instabilities and research methods for studying MHD instabilities are presented.We are mainly focused on the theory and research progress of the RWM and TM.In chapter ?,assuming that there is a plasma resistive layer near rational surface,the plasma in the external region of the resistive layer is still described by ideal MHD equations.A dispersion relation,which includes the resistive layer damping physics near the rational surface,is derived for the stability of the RWM by the method of energy principle.In the process of the deriving,the equivalence between the energy principle approach and the resistive layer matching approach is demonstrated.Then,the dispersion relation is numerically solved.Comparing the results of the ideal plasma fluid theory prediction with the results from the dispersion,it is found a strong reduction of the growth rate of the RWM by the plasma resistive layer energy dissipation.On the other hand,the favorable average curvature of the inner layer can further enhance the stability of the RWM.Even in a static plasma,it can excite the real frequency of the mode.In chapter III,the dispersion relations in the chapter II is further extended for the RWM,which incorporates both the resistive layer physics and the drift kinetic resonance between the mode and trapped energetic particles.The results show that the kinetic effect can further stabilize the RWM.In addition,the drift kinetic effect and plasma resistive layer damping effect work in a synergistic manner on the stability of RWM.The critical plasma rotation frequency of stabilizing the RWM is a few parts per thousand of Alfven frequency.In chapter IV,the resistive kink model of the plasma resistive layer is brief introduced.Two traditionally assumed inner layer models,the resistive kink model and the resistive tearing model,are adopted in derivation of the dispersion relation with the effect of the resistive layer for the stability of the RWM.By comparison,it is found that the resistive tearing model is better than resistive kink model on the stability of the RWM.The reason is that the favorable average curvature effect is not considered in the resistive kink model and the absolute value of the gamma function's variable is small in the resistive kink model.In chapter V,MARS-F code is briefly described.The effects of the proportional(P)and proportional derivative(PD)types of magnetic feedback control on the stability of the linear-TM are numerically studied by the MARS-F.The results show that both the two types of feedback control can reduce the growth rate of the TM.The stable effect of the proportional derivative type feedback control is better than the proportional type feedback control,so much as can stabilize the TM.The optimized feedback control scheme which is consists of the feedback coil inside resistive wall and the poloidal sensor coil is obtained.In addition,the PD type feedback control can lead to finite real frequency of the TM in a static plasma.This is due to the favorable curvature effect of the magnetic field is enhanced by the PD feedback control.In the last chapter,a brief summary and outlook of the future work are presented.