Phase Dynamics Of Edge Magnetohydrodynamic Modes In Magnetically Confined Plasmas

High confinement mode(H-mode)is one of the key factors for achieving magnetically controlled fusion in the future Tokamaks,but it is often accompanied by spontaneous Edge Localized Mode(ELM),which will seriously damage the divertor target plate and the first wall.On the other hand,ELM plays a useful role in removing plasma impurities.Therefore,it is one of the most concerned problems in magnetically controlled fusion that how to maintain H-mode while retaining the role of ELM in removing impurities and at the same time minimizing its bad effects.In this thesis,from the perspective of phase dynamics,the nonlinear behaviors of the toroidally confined plasmas in the edge are studied,and the deep physical mechanism of the edge magnetohydrodynamics(MHD)is further understood through theoretical analysis and numerical simulation.This thesis has firstly investigated the nonlinear phase dynamics of ideal kink mode,induced byE×Bflow.Here the phase is the cross phase between perturbed stream function of velocity and magnetic field.A dimensionless parameter——the growth rate of pure kink mode toE×Bshearing rate,is defined to measure the competition between phase pinning by the current density and phase detuning by the flow shear.When their ratio is larger than one,the cross phase will be locked to a fixed value,which has an eigensolution.When their ratio is smaller than one,the cross phase enters a phase slipping or oscillating state,which does not have an eigensolution.The nonlinear phase dynamics method provides a more intuitive explanation of the complex dynamical behavior of theE×Bshear flow's stabilizing effect on kink mode.Next,the concept of vortex wave coupling in fluid dynamics is utilized to analyze the excitation of joint mode in the edge toroidally confined plasmas.In addition to the commonly observed decoupling of perturbed radial velocity and displacement by radial electric field()shear,it is found that thecurvature tends to make the perturbed radial velocity and displacement coherent,thus driving the MHD mode.As a highlighted result,this thesis analytically demonstrates thatcurvature can destabilize an otherwise stable kink mode,and so form a joint vortex-kink mode.The synergetic effects ofshear andcurvature in edge MHD dynamics will have a great impact on the stability boundary of joint vortex-peeling ballooning mode,which provides a possible transition mechanism between ELMy H mode and Quiescent(Q)H mode.At last,this thesis has investigated how the E×B shearing profile impacts the energy transport induced by MHD mode in the edge of H-mode plasmas.Under the premise that thecurvature does not change much,by enhancing the outer layer shear,the growth rate spectrum get narrower with the fastest growth rate having a lower toroidal mode number.In the nonlinear stage,the MHD fluctuations tend to reach a coherent,oscillating state,which is analogous to a QH mode state with EHO.By enhancing the inner layer shear,the low n toroidal mode is more unstable,and the growth rate spectrum gets wider.In the nonlinear stage,the edge fluctuations tend to reach an incoherent,oscillating state,which is analogous to a turbulent QH-mode state.The results obtained in this thesis have enhanced the physical understanding of the related edge MHD phenomena,and they can provide some insight and guidance for the advanced operational scenarios of the future fusion devices.