Investigation on the roles of equilibrium toroidal rotation during edge-localized mode mitigated by resonant magnetic perturbations

The effects of equilibrium toroidal rotation during edge-localized mode(ELM)mitigated by resonant magnetic perturbation(RMP)are studied with the experimental equilibria of the EAST tokamak based on the four-field model in the BOUT++code.As the two main parameters to determine the toroidal rotation profiles,the rotation shear and magnitudes were separately scanned to investigate their roles in the impact of RMPs on peeling-ballooning(P-B)modes.On one hand,the results show that strong toroidal rotation shear is favorable for the enhancement of the self-generated E×B shearing rate<ω_(E×B)>with RMPs,leading to significant ELM mitigation with RMP in the stronger toroidal rotation shear region.On the other hand,toroidal rotation magnitudes may affect ELM mitigation by changing the penetration of the RMPs,more precisely the resonant components.RMPs can lead to a reduction in the pedestal energy loss by enhancing the multimode coupling in the turbulence transport phase.The shielding effects on RMPs increase with the toroidal rotation magnitude,leading to the enhancement of the multimode coupling with RMPs to be significantly weakened.Hence,the reduction in pedestal energy loss by RMPs decreased with the rotation magnitude.In brief,the results show that toroidal rotation plays a dual role in ELM mitigation with RMP by changing the shielding effects of plasma by rotation magnitude and affecting<ω_(E×B)>by rotation shear.In the high toroidal rotation region,toroidal rotation shear is usually strong and hence plays a dominant role in the influence of RMP on P-B modes,whereas in the low rotation region,toroidal rotation shear is weak and has negligible impact on P-B modes,and the rotation magnitude plays a dominant role in the influence of RMPs on the P-B modes by changing the field penetration.Therefore,the dual role of toroidal rotation leads to stronger ELM mitigation with RMP,which may be achieved both in the low toroidal rotation region and the relatively high rotation region that has strong rotational shear.

Effects of resonant magnetic perturbations on the loss of energetic ions in tokamak pedestal

Resonant magnetic perturbations(RMPs) are extensively applied to mitigate or suppress the edge localized mode in tokamak plasmas, but will break the axisymmetric magnetic field configuration and increase the loss of energetic ions. The mechanism of RMPs induced energetic ion loss has been extensively studied, and is mainly attributed to resonant effects. In this paper,in the perturbed non-axisymmetric tokamak pedestal, we analytically derive the equations of guiding center motion for energetic ions including the bounce/transit averaged radial drift velocity and the toroidal precession frequency modified by strong radial electric field. The loss time of energetic ions is numerically solved and its parametric dependence is analyzed in detail.We find that passing energetic ions cannot escape from the plasma, while deeply trapped energetic ions can escape from the plasma. The strong radial electric field plays an important role in modifying the toroidal precession frequency and resulting in the drift loss of trapped energetic ions. The loss time of trapped energetic ions is much smaller than the corresponding slowdown time in DIII-D pedestal. This indicates that the loss of trapped energetic ions in the perturbed non-axisymmetric pedestal is important, especially for the trapped energetic ions generated by perpendicular neutral beam injection.

Effects of resonant magnetic perturbations on radial electric fields in DIII-D tokamak

Gyrokinetic simulations of DIII-D tokamak equilibrium find that resonant magnetic perturbation(RMP)drives a neoclassical non-ambipolar electron particle flux,which causes a rapid change of equilibrium radial electric fields consistent with experimental observations during the suppression of the edge localized mode(ELM).The simulation results provide a support for the conjecture that RMP-induced changes of radial electric fields lead to the enhanced turbulent transport at the pedestal top during the ELM suppression(Taimourzadeh et al 2019 Nucl.Fusion59046005).Furthermore,gyrokinetic simulations of collisionless damping of zonal flows show that resonant responses to the RMP decrease the residual level of the zonal flows and damp the geodesic acoustic mode.

Study on divertor heat flux under n=3 and n=4 resonant magnetic perturbations using infrared thermography diagnostic in EAST

Resonant magnetic perturbations(RMPs)with high toroidal mode number n are considered for controlling edge-localized modes(ELMs)and divertor heat flux in future ITER H-mode operations.In this paper,characteristics of divertor heat flux under high-nRMPs(n=3 and 4)in H-mode plasma are investigated using newly upgraded infrared thermography diagnostic in EAST.Additional splitting strike point(SSP)accompanying with ELM suppression is observed under both RMPs with n=3 and n=4,the SSP in heat flux profile agrees qualitatively with the modeled magnetic footprint.Although RMPs suppress ELMs,they increase the stationary heat flux during ELM suppression.The dependence of heat flux on q_(95)during ELM suppression is preliminarily investigated,and further splitting in the original strike point is observed at q 495=during ELM suppression.In terms of ELM pulses,the presence of RMPs shows little influence on transient heat flux distribution.

Gyrokinetic simulation of magnetic-island-induced electric potential vortex mode

Ion temperature gradient(ITG)-driven turbulence with embedded static magnetic islands is simulated by utilizing a gyrokinetic theory-based global turbulence transport code(GKNET)in this work.Different from the traditional equilibrium circular magnetic-surface average(EMSA)method,an advanced algorithm that calculates the perturbed magnetic-surface average(PMSA)of the electric potential has been developed to precisely deal with the zonal flow component in a non-circular magnetic surface perturbed by magnetic islands.Simulations show that the electric potential vortex structure inside islands induced by the magnetic islands is usually of odd parity when using the EMSA method.It is found that the odd symmetry vortex can transfer into an even one after a steep zonal flow gradient,i.e.the flow shear has been built in the vicinity of the magnetic islands by adopting the PMSA algorithm.The phase of the potential vortex in the poloidal cross section is coupled with the zonal flow shear.Such an electric potential vortex mode may be of essential importance in wide topics,such as the turbulence spreading across magnetic islands,neoclassical tearing mode physics,and also the interaction dynamics between the micro-turbulence and MHD activities.

Impact of resonant magnetic perturbation on blob motion and structure using a gas puff imaging diagnostic on the HL-2A tokamak

The impact of resonant magnetic perturbation(RMP)on blob motion and structure in the SOL of the HL-2A tokamak is studied using a gas puff imaging diagnostic.Ellipse fitting is applied to study the structure and motion of blobs quantitatively.The radial locations,amplitudes and scale sizes of blobs are obtained based on the fitted ellipse.Furthermore,based on the measurement of blob location,the radial and poloidal velocities of blobs are calculated.With the application of RMP,the edge poloidal shear flow is significantly weakened and the wave number spectrum changes from quasisymmetric to significantly up-down asymmetric.The application of RMP also causes the detected blob location to be much further into the far scrape-off layer(SOL)and increases the blob amplitude.Blob poloidal velocity in the SOL is slowed.Larger-size and longer-lifetime blobs are observed with RMP.With the application of RMP,stronger-amplitude and larger-size blobs are detected in the far SOL and they may cause a more serious erosion problem to the first wall.

Design of new resonant magnetic perturbation coils on the J-TEXT tokamak

The resonant magnetic perturbation(RMP)system is a powerful auxiliary system on tokamaks.On the J-TEXT tokamak,a set of new in-vessel coils is designed to enhance the amplitude of the RMP.The new coils are designed to be two-turn saddle coils.These two-turn saddle coils have been optimized in terms of their structure,support,and protection components to overcome the limitations of the narrow in-vessel space,resulting in a compact coil module that can be accommodated in the vessel.To verify the feasibility of this design,an electromagnetic simulation is performed to investigate the electrical parameters and the generated field of the coils.A multi-field coupled simulation is performed to investigate the capacity of heat dissipation.As a result of these efforts,the new RMP coils have been successfully installed on the J-TEXT tokamak.It has significantly enhanced the RMP amplitude and been widely applied in experiments.

Effect of the relative phase between pre-existing 2/1 and 3/1 magnetic islands on the suppression of runaway electrons on J-TEXT

In the experiments of actively triggering plasma disruption by massive gas injection, the externally applied resonant magnetic perturbation has been used to mitigate the hazard of runaway electron(RE). Motivated by the experiment of multimode coupling to suppress REs on J-TEXT, some typical simulation cases with non-ideal MHD with rotation-open discussion(NIMROD) code are carried out to explore the influential mechanism of different relative phases between m/n =2/1 and m/n = 3/1 magnetic islands on the confinement of REs. Results show that the RE confinement is drastically affected by the relative phase between 2/1 and 3/1 magnetic islands. When the O point phase of 2/1 and 3/1 magnetic islands is toroidal 330°, REs can be effectively lost. The fitting curve of the remaining ratio of REs vs. the relative toroidal phase is predicted to approximate a sine-like function dependence. Further studies indicate that the phase difference between coexisting 2/1 and 3/1 islands can affect the radial transport of impurities. The loss of runaway electrons is closely related to the deposition effect of impurity. The impurity is easier to spread into the core region with smaller poloidal phase difference between the radial velocity of impurity and the impurity quantity of Ar.

Preliminary Study of the Magnetic Perturbation Effects on the Edge Density Profiles and Fluctuations Using Reflectometers on EAST

The resonant magnetic perturbation （RMP） coils have been successfully designed and installed on the Experimental Advanced Superconducting Tokamak （EAST）. Using the reflectometer systems, the density profile and the density fluctuations during magnetic perturbations （MPs） phase have been investigated. During the experiments, two different cases are studied separately： steady MPs and rotating MPs. In both cases, a strongly density pump-out has been observed. In the steady MPs cases, an enhancement of the low frequency （〈60 kHz） density fluctuations in H-mode phase has been observed. The plasma density boundary out-shifts 5~ caused by the MPs. The pedestal density gradient is reduced by 50%, while the radial location nearly stays unchanged. In the rotating MPs, the line-averaged density, the D~ emission at the divertor region and the spectrum of the density fluctuations are modulated. The results suggest that the low frequency （〈60 kHz） density fluctuations may contribute to the strong density pump-out.

Numerical simulation of plasma response to externally applied resonant magnetic perturbation on the J-TEXT tokamak

Nonlinear magnetohydrodynamic（MHD） simulations of an equilibrium on the J-TEXT tokamak with applied resonant magnetic perturbations（RMPs） are performed with NIMROD（non-ideal MHD with rotation,open discussion）.Numerical simulation of plasma response to RMPs has been developed to investigate magnetic topology,plasma density and rotation profile.The results indicate that the pure applied RMPs can stimulate 2/1 mode as well as 3/1 mode by the toroidal mode coupling,and finally change density profile by particle transport.At the same time,plasma rotation plays an important role during the entire evolution process.

The effect of resonant magnetic perturbation with different poloidal mode numbers on peeling-ballooning modes

The effect of resonant magnetic perturbation(RMP)with different poloidal mode numbers on peeling-ballooning(P-B)modes is simulated with the BOUT++code.In order to investigate the physical mechanism of edge-localized mode mitigated by RMP,a series of RMPs with different poloidal mode numbers are applied into the four-field P-B mode simulation module separately.The results indicate that RMP has a better reducing effect on the energy loss from the pedestal when the resonant position is near the bottom and top of pedestal rather than near the middle.The RMP could influence P-B modes through the following effects:on the one hand,the E×B shearing rate is significantly stronger when the RMP(resonant surface locates at the top of the pedestal)is added,which can suppress the radial propagation of the negative pressure perturbation and reduce energy loss from the pedestal.On the other hand,the coupling of toroidal modes in the nonlinear phase is enhanced when RMPs are added,which motivated the growth of multiple toroidal modes,and the turbulence fluctuation level is weaker with the RMP when the resonant surface is located at the bottom of the pedestal.

Perturbed magnetic field of an infinite plate with a centered crack

Deforming a cracked magnetoelastic body in a magnetic field induces a perturbed magnetic field around the crack. The quantitative relationship between this perturbed field and the stress around the crack is crucial in developing a new generation of magnetism-based nondestructive testing technologies. In this paper, an analytical expression of the perturbed magnetic field induced by structural deforma- tion of an infinite ferromagnetic elastic plate containing a centered crack in a weak external magnetic field is obtained by using the linearized magnetoelastic theory and Fourier transform methods. The main finding is that the perturbed magnetic field intensity is proportional to the applied tensile stress, and is dominated by the displacement gradient on the boundary of the magnetoelastic solid. The tangential component of the perturbed magnetic-field intensity near the crack exhibits an antisymmetric distribution along the crack that reverses its direction sharply across its two faces, while the normal component shows a symmetric distribution along the crack with singular points at the crack tips.

Gap opening and tuning in single-layer graphene with combined electric and magnetic field modulation

The energy band structure of single-layer graphene under one-dimensional electric and magnetic field modulation is theoretically investigated. The criterion for bandgap opening at the Dirac point is analytically derived with a two-fold degeneracy second-order perturbation method. It is shown that a direct or an indirect bandgap semiconductor could be realized in a single-layer graphene under some specific configurations of the electric and magnetic field arrangement. Due to the bandgap generated in the single-layer graphene, the Klein tunneling observed in pristine graphene is completely suppressed.

Revisiting the elastic solution for an inner-pressured functionally graded thick-walled tube within a uniform magnetic field

In this paper, the mechanical responses of a thick-walled functionally graded hollow cylinder subject to a uniform magnetic field and inner-pressurized loads are studied. Rather than directly assume the material constants as some specific function forms displayed in pre-studies, we firstly give the volume fractions of different constituents of the functionally graded material(FGM) cylinder and then determine the expressions of the material constants. With the use of the Voigt method, the corresponding analytical solutions of displacements in the radial direction, the strain and stress components, and the perturbation magnetic field vector are derived. In the numerical part, the effects of the volume fraction on the displacement, strain and stress components, and the magnetic perturbation field vector are investigated. Moreover, by some appropriate choices of the material constants, we find that the obtained results in this paper can reduce to some special cases given in the previous studies.

Thermomagnetic viscoelastic responses in a functionally graded hollow structure

This paper presents an analytical solution for the interaction of electric potentials, electric displacements, elastic deformations, and thermoelasticity, and describes electromagnetoelastic responses and perturbation of the magnetic field vector in hollow structures （cylinder or sphere）, subjected to mechanical load and electric potential. The material properties, thermal expansion coefficient and magnetic permeability of the structure are assumed to be graded in the radial direction by a power law distribution. In the present model we consider the solution for the case of a hollow structure made of viscoelastic isotropic material, reinforced by elastic isotropic fibers, this material is considered as structurally anisotropic material. The exact solutions for stresses and perturbations of the magnetic field vector in FGM hollow structures are determined using the infinitesimal theory of magnetothermoelasticity, and then the hollow structure model with viscoelastic material is solved using the correspondence principle and Illyushin＇s approximation method. Finally, numerical results are carried out and discussed.

Study of the spectrum effect on the threshold of resonant magnetic perturbation penetration on J-TEXT

The spectrum effect on the penetration of resonant magnetic perturbation(RMP) is studied with upgraded in-vessel RMP coils on J-TEXT.The poloidal spectrum of the RMP field,especially the amplitudes of 2/1 and 3/1 components,can be varied by the phase difference between the upper and lower coil rows,ΔΦ=Φ_(top)-Φ_(bottom),where Φ_(top)and Φ_(bottom)are the toroidal phases of the n=1 field of each coil row.The type of RMP penetration is found to be related to ΔΦ,including the RMP penetration of either 2/1 or 3/1 RMP and the successive penetrations of 3/1 RMP followed by the 2/1 RMP.For cases with penetration of only one RMP component,the penetration thresholds measured by the corresponding resonant component are close for variousΔΦ.However,the 2/1 RMP penetration threshold is significantly reduced if the 3/1 locked island is formed in advance.The changes in the rotation profile due to 3/1 locked island formation could partially contribute to the reduction of the 2/1 thresholds.

Effect of edge magnetic island on carbon screening in the J-TEXT tokamak

The effect of externally applied resonant magnetic perturbation(RMP)on carbon impurity behavior is investigated in the J-TEXT tokamak.It is found that the m/n=3/1 islands have an impurity screening effect,which becomes obvious while the edge magnetic island is generated via RMP field penetration.The impurity screening effect shows a dependence on the RMP phase with the field penetration,which is strongest if the O point of the magnetic island is near the low-field-side(LFS)limiter plate.By combining a methane injection experimental study and STRAHL impurity transport analysis,we found that the variation of the impurity transport dominates the impurity screening effect.The impurity diffusion at the inner plasma region(r/a<0.8)is enhanced with a significant increase in outward convection velocity at the edge region in the case of the magnetic island’s O point near the LFS limiter plate.The impurity transport coefficient varies by a much lower level for the case with the magnetic island’s X point near the LFS limiter plate.The interaction of the magnetic island and the LFS limiter plate is thought to contribute to the impurity transport variation with the dependence on the RMP phase.A possible reason is the interaction between the magnetic island and the LFS limiter.

A brief review of the development and optimization of the three-dimensional magnetic configuration system in the J-TEXT tokamak

The three-dimensional(3D) magnetic configuration system in the J-TEXT tokamak has featured in many experimental studies.The system mainly consists of three subsystems:the static resonant magnetic perturbation(SRMP) system,the dynamic resonant magnetic perturbation(DRMP) system and the helical coil system.The SRMP coil system consist of two kinds of coils,i.e.three six-loop coils and two five-loop coils.It can suppress tearing modes with a moderate strength,and may also cause mode locking with larger amplitude.The DRMP coil system consists of 12 single-turn saddle coils(DRMP1) and 12 double-turn saddle coils(DRMP2).Its magnetic field can be rotated at a few kHz,leading to either acceleration or deceleration of the tearing mode velocity and the plasma rotation.The helical coil system consists of two closed coils,and is currently under construction to provide external rotational transform in J-TEXT.The 3D magnetic configuration system can suppress tearing modes,preventing and avoiding the occurrence of major disruption.

A brief review:effects of resonant magnetic perturbation on classical and neoclassical tearing modes in tokamaks

This paper reviews the effects of resonant magnetic perturbation(RMP)on classical tearing modes(TMs)and neoclassical tearing modes(NTMs)from the theory,experimental discovery and numerical results with a focus on four major aspects:(i)mode mitigation,where the TM/NTM is totally suppressed or partly mitigated by the use of RMP;(ii)mode penetration,which means a linearly stable TM/NTM triggered by the externally applied RMP;(iii)mode locking,namely an existing rotating magnetic island braked and finally stopped by the RMP;(iv)mode unlocking,as the name suggests,it is the reverse of the mode locking process.The key mechanism and physical picture of above phenomena are revealed and summarized.

Stress and Thermal Analysis of the In-Vessel Resonant Magnetic Perturbation Coils on the J-TEXT Tokamak

A set of four in-vessel saddle coils was designed to generate a helical field on the J- TEXT tokamak to study the influences of the external perturbation field on plasma. The coils are fed with alternating current up to 10 kA at frequency up to 10 kHz. Due to the special structure, complex thermal environment and limited space in the vacuum chamber, Jt is very important to make sure that the coils will not be damaged when undergoing the huge electromagnetic forces in the strong toroidal field, and that their temperatures don＇t rise too much and destroy the in- sulation. A 3D finite element model is developed in this paper using the ANSYS code, stresses are analyzed to find the worst condition, and a mounting method is then established. The results of the stress and modal analyses show that the mounting method meets the strength requirements. Finally, a thermal analysis is performed to study the cooling process and the temperature distribution of the coils.