Studies On Influence Of Negative Triangularity On Ideal External Kink And Resistive Wall Modes

The external kink mode(XK)associated with the disruption of plasma,is the strongest macroscopic magnetohydrodynamic(MHD)instability.With the growth rate of an Alfvenic time scale and the global structure,XK can be completely suppressed with a closely fitting conducting wall.However,finite resistivity exists in the wall.When the confinement time of plasma exceeds the magnetic field penetration time through the wall,the XK becomes a slowly growing resistive wall mode(RWM),with the time scale of the eddy current decay in the wall.XK and RWM are driven either by plasma current or pressure gradient,which limit the plasma discharge time and the high pressure of fusion devices.In serious cases,XK and RWM lead to the disruption of plasma,interrupting of discharge,even damaging the first wall.Therefore,in order to realize a long-pulse and steady-state operation for advanced tokamak,it is of great significance to study the XK and RWM.The shape of the plasma cross-section plays crucial roles in the discharge performance of fusion devices and becomes one of the key designing parameters for the future reactor such as DEMO.In the high confinement mode of the future ITER,the edge localized modes(ELM)reduces the stored energy,affects the confinement of core plasmas and even damages the plasma facing components.In the plasma configuration with negative triangularity(NTR),the equilibrium magnetic field,associated with the characteristic of a larger fraction of good curvature regions than that of the bad curvature regions,significantly modifies the ELM properties.While the MHD beta limits of XK and RWM are often relatively low,due to the absence of a magnetic well and the pressuer gradient in the pedestal.Therefore,it is necessary to maintain good plasma performance and at the same time to properly reduce pedestal stability limit in order to avoid ELM.In this thesis,a self-consistent equilibria with NTR is used,which is designed based on the EURO DEMO and whose pressure profile is optimized,using either passive stabilization based on toroidal plasma flow damping or an active control scheme based on magnetic coils,the stabilities of XK and RWM are numerically and analytically investigated.This study may provide options for CFETR engineering design,or as an alternative to the magnetic confinement fusion DEMO reactor of China.In Chapter 1,the background of nuclear fusion energy research,the magnetic confinement fusion configuration of tokamak,major devices at home and abroad and behaviors of particles in plasma are briefly introduced,analytical methods for MHD instabilities and research progress of the unstable modes related to this thesis are also introduced.In Chapter 2,the MARS-*codes and their model used in the numerical simulation of this thesis are summarized,physical mechanisms that interact with the unstable modes in these codes are understood,the self-consistent calculations about the Coriolis force and parallel sonic viscous(ion Landau damping effect)caused by plasma rotation,the feedback control of the applied coils and the kinetic effects of the perturbation pressure tensor coupling to the linearized MHD equations are analyzed.In Chapter 3,the positive triangularity equilibria matching the NTR equilibrium is designed,and the MARS-F/K codes are used to numerically compare the effects of conductor wall,toroidal plasma rotation and kinetic contributions from trapped thermal particles on XK and RWM in the two plasma shapes.These results show that the less efficiency of wall stabilization for XK in the NTR is due to the less "external" eigenmode,and based on a similar stabilization effect of the toroidal flow on the two plasma shapes,a larger net trapping fraction in NTR does not lead to a stronger kinetic damping for XK but has a more significant effect on RWM.In Chapter 4,the MARS-F code is used to numerically study the effect of the proportional feedback control system on the XK and RWM in NTR with fluid model.The research shows that it is possible to feedback-stabilize the XK by placing both the active and sensor coils inside the vacuum vessel and the best polodial location of the active coils is still the low field side of the torus.With a single row of active coils,the presence of the conductor wall deteriorates the mode stabilization,due to cancellation of the control field by the wall eddy current;the best poloidal location of the coils is the outboard mid-plane for the best stabilization of the XK and the optimal poloidal width of the active coils is about 50° for RWM stability.With two rows of up-down symmetrically located active coils,feedback stabilization of the XK lead to a increase of the ideal wall beta limit is about 10%,asymmetry conditions lead to jumps in the closed loop growth rate of the RWM when the radial location of active coils crossed that of the sensor coils.In Chapter 5,in the multi-input-single-output(MISO)control system,the plasma response transfer function are established to analytically study feedback stabilization of the RWM.Based on the "pole-residue" method,a single-pole model of the feedback gain phasing with double-row coils is constructed,the MARS-F computed optimal gain phasing is well recovered and the optimal phasing corresponds to the one that cancels the toroidal phase of the(complex)residue factors in the plasma response transfer function;based on cylindrical circular plasma approximation,a multi-pole analytic theory is developed,the effect of the relative radial position of the active coil and the sensor coil on the closed-loop mode growth rate jumps is consistent with the numerical results,and the jumps in the single pole approximation can be eliminated by the multi-pole analytic theory when the symmetric condition of the feedback system is satisfied,that is,jumps in closed-loop growth rate of the mode are disappeared.Finally,the summary of this thesis and outlook of future work are presented.