Effects Of 3D Magnetic Perturbations On Tokamak Plasmas

The edge localized mode?ELM?in tokamaks can cause great damage to the divertor target during the operation of the future large-scale tokamak device,which becomes an important factor limiting the steady state operation of tokamaks.It has been confirmed by experiments that the resonant magnetic perturbation?RMP?can effectively mitigate or even suppress the edge localized mode,thereby directly reducing the load on the divertor target plate,providing a powerful guarantee for the high-confinement operation of the large-scale tokamaks.The application of external magnetic perturbation has very rich physical phenomena in the process of interaction with plasma,such as the shielding and amplification effects of external magnetic field,the change of rotation shear and the generation of three-dimensional?3D?corrugation at the edge of the plasma.These phenomena are directly or indirectly affecting the instability of the plasma and the confinement of the tokamak.Thus,further research on the effects of 3D magnetic perturbations on plasma will provide practical guidance on the RMP application in the future large-scale devices.In this paper,the effects of3D magnetic perturbations on the plasma in tokamak are explored from three aspects:the prompt loss of fast ions,the peeling-ballooning mode instability and the non-ideal ballooning mode instability.In the simulation of the prompt loss of fast ions,we find that the resonance between the RMP and the equilibrium magnetic field,the resonance between the RMP and the unperturbed orbit,and the transition from the counter-passing orbit to the trapped orbit are the three fundamental mechanisms for the prompt loss of fast ions caused by the RMP.Firstly,the internal and vacuum magnetic fields are coupled through the Grad-Shafranov equation,and the vacuum field of the RMP is added to the analytical magnetic field configuration,resulting in a series of magnetic islands and a layer of stochastic region.Then the Hamiltonian theory is used to calculate the full orbits of the fast ions with the effect of the RMP.It is found that the RMP will cause periodic orbital drifts in the radial direction,while the drift frequency and the radial drift distance are related with the RMP resonant mechanisms.When the RMP resonates with the unperturbed orbit,the drift frequency is low and the radial drift distance is large.When the RMP resonates with the equilibrium magnetic field,the drift frequency is high and the radial drift distance is small.In addition,the RMP can also cause the transition of orbit types,and the transition from the counter-passing orbit to the trapped orbit can induce the prompt loss of fast ions located far from the edge of the plasma.What's more,the change of the prompt loss rate and the distribution of the prompt loss in the initial pitch angle-radial location plane are also calculated.It is found that the prompt loss of fast ions in the low field side is significantly larger than that in the high field side.The loss mechanism in the low field side is mostly the RMP-caused orbit transition and the resonance between the RMP and the unperturbed orbit.The main loss mechanism in the high field side is the resonance between the RMP and the equilibrium field.Since the density of fast ions in the experiment is very small near the edge of the plasma,the prompt loss induced by the RMP is mainly due to the resonance between the RMP and the unperturbed orbit,and the transition from the counter-passing orbit to the trapped orbit,which may induce prompt loss of fast ions located far from the edge.In the simulation of peeling-ballooning mode,the9)=0 magnetic perturbation is used to eliminate the influence of the magnetic resonant structures?such as magnetic islands and the stochastic regions?on the instability,and it is found that the non-resonant component of the magnetic perturbation can also mitigate the peeling-ballooning mode,and its mitigation mechanism is the multimode interactions in the non-linear phase.In the BOUT++three-field model,an9)=0 magnetic perturbation is added to simulate the effect of the magnetic perturbations on the peeling-ballooning mode.In the linear phase,the applied magnetic perturbation has no influence on the linear growth rate,because the9)=0 magnetic perturbation couldn't induce the structures of magnetic islands,and its amplitude is quite small,which is not large enough to change the plasma pressure and the parallel current profiles.In the non-linear phase,the magnetic perturbation has a strong mitigation effect on the peeling-ballooning mode.The mode analysis shows that the9)=0 magnetic perturbation can induce a multimode competition in the plasma,so that the plasma turbulence transport is weakened and the energy and particle loss are reduced.Further analysis shows that the reason why the plasma turbulent transport is weakened is that the change of the parallel gradient operator by the magnetic perturbation increases the×shear rate near the plasma edge,and the increased×shear rate suppresses the turbulent transport during the nonlinear evolution of the peeling-ballooning mode.In the simulation of plasma response to the RMP,it is found that the shielding effect of plasma will prevent the formation of the magnetic islands.This study shows that even if there were no resonant structures,the external magnetic perturbations can also mitigate the peeling-ballooning mode.In the simulation of non-ideal ballooning mode,it is found that the mechanism of the destabilization of the resistive ballooning mode is that the resistivity weakens the stabilize effect of the field line bending term on low to intermediate-n mode.Meanwhile,it is found that there is a threshold phenomenon of the RMP amplitude for non-ideal ballooning mode.The three-field reduced MHD model is used to evaluate the RMP-modified ballooning mode stability,and the ballooning mode eigenmode equation is obtained by applying the ballooning transformation technique to the reduced MHD equations.The effect of the RMP on the ballooning mode extends from the ideal case to the non-ideal case.Firstly,it is found that the RMP will destabilize the ideal ballooning mode once it can penetrate to the resonant surfaces.Secondly,destabilization of ideal ballooning modes in the presence of resistivity originates from the reduction of the field line bending stabilization.This reduced field line bending effect is more significant in low to intermediate-n mode,giving rise to a change of the growth rate spectrum pattern.Furthermore,the resistive ballooning mode may change its character from small scale fluctuations dominated by high-n modes to an MHD-like instability centralized near the intermediate-n number when?increases toward.Therefore,the resistive ballooning mode may be a potential candidate for the type-II ELMs often observed in various tokamaks with high edge collisionality.In addition,combined effects of finite resistivity and the RMP-induced local shear modulation lead to a significant change in ballooning mode stability as a function of the RMP amplitude factor.Analysis shows that the occurrence of local stability extrema is due to the competition between the averaged shear and the RMP-induced local shear modulation in high resistivity case,while it is completely decided by finite resistivity in low resistivity case.This signifies the importance of the RMP to field line bending stabilization coupled to the finite resistivity,as well as to the local shear modulation.If one considers the finite resistivity effect,it may stabilize the plasma once the threshold RMP amplitude is not high enough to induce the mode locking.This signifies that the edge stability calculation with the RMP-modified plasma equilibrium needs to take the resistivity effect into account.Through the simulations and analyses above,we found different effects of the external magnetic perturbations on plasma confinement and instability in terms of the prompt loss of fast ions,the instability of the peeling-ballooning mode and the instability of the non-ideal ballooning mode.The results of this study may provide a possible physical reference for the mitigation of the edge localized mode by the RMP in the experiment.