| The phenomenon of magnetic field penetration caused by error fields in tokamaks can reduce the confinement performance of the device and even lead to discharge disruptions.Therefore,the study of error fields has always been one of the important physics issues of ITER(International Thermonuclear Experimental Reactor).In addition,error field penetration is also a key issue in the control of Edge Localized Mode(ELM).In order to extrapolate the penetration threshold to ITER,a considerable amount of research has been conducted on the scaling relationship between error field penetration threshold and plasma parameters in most tokamak devices worldwide.However,most experimental scalings are based on Ohmic heating and do not discuss the tolerance of tokamak devices to error fields under different auxiliary heating methods.Furthermore,theoretical and numerical studies of error field penetration physics are based on the approximation of cylindrical geometry,neglecting the role of toroidal geometry effects in magnetic field penetration.On the other hand,metrics based on linear response models have been proven to be able to evaluate error field correction schemes.However,experimental results on the EAST(Experimental Advanced Superconducting Tokamak)indicate that the linear response model cannot accurately predict the dependence between the penetration threshold current of the n=1 Resonant Magnetic Perturbation(RMP)and the coil phase difference ΔφUL.Based on the aforementioned issues,the physical process of error field penetration is still not fully understood.Therefore,in order to understand the discrepancy between linear response results and experimental results,it is necessary to self-consistently simulate the nonlinear process of magnetic field penetration.This thesis utilized the experimental results of RMP penetration on EAST and employed the numerical code MARS-Q to simulate the nonlinear process of magnetic field penetration in a toroidal geometry configuration.Our focus was to investigate the influence of toroidal geometry effects on magnetic field penetration and the sensitivity of the device to error fields under different heating methods.Specifically,the study included the following aspects:(1)Plasma beta effect on the n=1 RMP field penetration in purely radio-frequency(RF)wave heated discharges has been investigated in EAST.Experimental results show that the dependence of threshold RMP coil current for field penetration,IRMP,th,on the total absorbed power Ptot scales as approximately IRMP,th∝Ptot0.30,indicating that the error field tolerance is improved with increasing RF power.This is benefited from the increased electron perpendicular flow dominated by counter current electron diamagnetic flow with increasing RF power.However,theoretical scaling in cylindrical geometry overestimates the power index.Assuming an additional term βNαβN for the normalized beta in the scaling,it is shown that the fitted αβN from the experimental observation is around-1,indicating an degradation effect of plasma beta.To clarify the underlying physics of plasma beta effect that was not included in the theoretical scaling in cylindrical geometry,the MARS-Q code with full toroidal geometry is employed for simulation of nonlinear field penetration.The MARS-Q simulation results well reproduce the βN dependence and hence the Ptot scaling of the threshold current in experimental observations.The main reason revealed that the net total torque,which is mainly contributed by the neoclassical toroidal viscosity(NTV),increases with increasing plasma βN.The result demonstrates that the nonlinear toroidal coupling effect via NTV torque plays an important role in determining field penetration even in this cases with relatively low βN∈[0.3,0.6],which is far less than no-wall beta limit.(2)Experiment on mode penetration of n=1 RMP has been carried out under low neutral beam injection torque at co-current direction(Co-NBI)in EAST.It is observed that the threshold current IRMP,th for field penetration decreases with higher Co-NBI heating power,because the plasma mode frequency(forced oscillation frequency of stable tearing mode)is at ctr-current direction and greatly reduced when the plasma toroidal rotation increases in this experiment.According to the field penetration theory and degraded effect of plasma beta,both the variations of the normalized plasma beta and mode frequency have a destabilizing influence on the field penetration.The effect of βN and mode frequency on the mode onset threshold are separately investigated by the full toroidal geometry initial value code MARS-Q.It is found that the decreasing mode frequency plays the dominant role in reduction of field penetration threshold.In addition,lower plasma rotation leads to a stronger NTV torque.Based on this,this thesis investigated the influence of toroidal plasma rotation on the penetration threshold under low momentum injection in EAST.The results indicate that,in the study of magnetic field penetration,the evaluation of the total mode frequency |fMHD| is crucial,rather than the toroidal rotation frequency fφ.Under low momentum injection heating,as the Co-NBI injection torque increases,the decrease in |fMHD| leads to an enhanced sensitivity of the device to error fields.Therefore,the error field tolerance should be paid more attention in low Co-NBI torque scenarios,in which electron diamagnetic frequency may be canceled out by Co-NBI driven toroidal plasma rotation.(3)Numerical simulations concerning the effect of RMP spectrum on field penetration threshold in EAST are presented,since the underlying physics is not well understood by linear response model.The quasi-linear full MHD model with toroidal geometry is adapted to investigate error field penetration taken into account both resonant electromagnetic force and non-resonant NTV force as plasma braking mechanisms.Nonlinear results reproduce the observed dependence of penetration threshold current on toroidal phase difference(ΔφUL)between upper and lower n=1 RMP coil.The results indicate that an increased NTV torque caused by the penetration of boundary component accelerates the occurrence of m/n=2/1 field penetration,due to the global damping of plasma rotation.Therefore,the dependence of m/n=2/1 penetration threshold on ΔφUL conforms to the spectrum of boundary resonant component,which results in a phase shift of 45 degree in linear plasma response.The physics mechanism that the mode coupling derive from adjacent resonant component has an important influence on the penetration threshold of m/n=2/1 component in toroidal plasma,may provide a new insight for ELM control.This paper presents a study based on experimental results from EAST and utilizes the numerical simulation code MARS-Q to investigate the influence of toroidal geometry effects on magnetic field penetration in tokamak.The research aims to deepen the physical understanding of the locking mode phenomenon induced by error fields.The numerical simulation results obtained in this study have important implications for the assessment of error field tolerance,error field correction,and ELM suppression in future fusion experimental reactors. |
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