Alfvén continuum in the presence of a magnetic island in a cylinder configuration

In this work,the effect of a magnetic island on Alfvén waves is studied.A physical model is established wherein Alfvén waves propagate in the presence of a magnetic island in a cylindrical geometry.The structure of the Alfvén wave continuum is calculated by considering only the coupling caused by the periodicity in the helical angle of the magnetic island.The results show that the magnetic island can induce an upshift in the Alfvén continuum.Moreover,the coupling between different branches of the continuous spectrum becomes more significant with increasing continuum mode numbers near the boundary of the magnetic island.

Identification of the magnetic island structure in the HL-2A tokamak

The identification of the magnetic island structure in the HL-2A tokamak is presented. First, the perturbation current as a source for the perturbation flux can be determined by using Mirnov probe measurements. By superposing the perturbation flux and the equilibrium flux reconnected by equilibrium fitting, the structure and the width of the magnetic islands can be estimated. The method has been used in the HL-2A experiments.

Numerical study of fast ion behavior in the presence of magnetic islands and toroidal field ripple in the EAST tokamak

A peculiar first orbit loss type was found apart from the normal ones when we use ORBIT code to simulate fast ion orbits in the EAST tokamak. Fast ion orbits were studied in the presence of toroidal field （TF） ripple and magnetohydro- dynamic （MHD） perturbations. We analyzed the properties of the drifted orbits in detail and compared their differences, finding that the combined effects of ripple and magnetic islands are much greater than the effects of either one of them alone. Then we investigated the orbitdeviations as a function of pitch angle in different radial positions. The modeling results demonstrate that the loss of trapped particles is mainly caused by the ripple, while MHD＇perturbation mainly plays an important role in the passing particles. Furthermore we modeled the loss rate using different equilibriums. Results prove that a higher beta can indeed improve the confinement of fast ions, while a little change in the q profile can make the topologies of magnetic islands become quite different and results in quite different total particle losses.

Development of a real-time magnetic island reconstruction system based on PCIe platform for HL-2A tokamak

A real-time magnetic island reconstruction(MIR)system based on PCI express platform for HL-2 A tokamak is introduced.The front-end analog circuit and high performance analog-to-digital converters complete high-precision synchronous sampling of 18 channel Mirnov signals,and the application of PCIe platform and direct memory access technology enables high speed data transmission between graphics processing unit and field programmable gate array(FPGA).FPGA,as a mainstream high speed parallelizable computing tool,was used to implement the MIR algorithm,while a parameter table is established in an external double data rate SDRAM to improve the computational efficiency.The software of the MIR system is developed with Compute Unified Device Architecture 8.0 in Centos 6 system,which mainly realizes driver development,data transmission,network communication,parameter calculation and system control.This system has been tested in HL-2 A plasma discharge experiment,and the reconstructed magnetic island structure can achieve a spatial resolution of 1.02 cm while the time resolution can reach 2 ms.

Electron acceleration during magnetic islands coalescence and division process in a guide field reconnection

The magnetic merging process related to pairwise magnetic islands coalescence is investigated by two-dimensional particle-in-cell simulations with a guide field.Owing to the force of attraction between parallel currents within the initial magnetic islands,the magnetic islands begin to approach each other and merge into one big island.We find that this newly formed island is unstable and can be divided into two small magnetic islands spontaneously.Lastly,these two small islands merge again.We follow the time evolution of this process,in which the contributions of three mechanisms of electron acceleration at different stages,including the Fermi,parallel electric field,and betatron mechanisms,are studied with the guide center theory.

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.

Ion-Banana-Orbit-Width Efect on Bootstrap Current for Small Magnetic Islands

A simple and direct theoretical method has been proposed to investigate the so- called ion-banana-orbit-width （IBW） effect on the bootstrap current in the region of magnetic islands generated by the neoclassical tearing mode （NTM）. The result shows that, when the IBW approaches the island width, the （ion） bootstrap current can be partly restored inside the island while the pressure profile is flattened. This can lead to the reduction of the bootstrap current drive on the NTM. The strength of the IBW effect on the NTM is related to the safety factor and the inverse aspect ratio on the rational surface.

Measurement of Magnetic Island Width by Multi-Channel ECE Radiometer on HT-7 Tokamak

A 16-channel electron cyclotron emission （ECE） radiometer has been employed to observe the （m, n） = （2, 1） magnetic island structure on HT-7 tokamak, where m and n represent the poloidal and toroidal mode number respectively. The results indicate that the island width is about 7 cm when the magnetic island is saturated during the m/n = 2/1 mode. The location of resonance surface can be determined by plotting the contour of ECE relative fluctuation. This method could be applied to the HT-7 and EAST campaigns in the future for the research of neoclassical tearing modes （NTMs）.

MHD Equilibrium with Reversed Current Density and Magnetic Islands Revisited:the Vacuum Vector Potential Calculus

The solution of Grad-Shafranov equation determines the stationary behavior of fusion plasma inside a tokamak. To solve the equation it is necessary to know the toroidal current density profile. Recent works show that it is possible to determine a magnetohydrodynamic （MHD） equilibrium with reversed current density （RCD） profiles that presents magnetic islands. In this work we show analytical MHD equilibrium with a RCD profile and analyze the structure of the vacuum vector potential associated with these equilibria using the virtual casing principle.

Magnetic Islands Observed by a Fast-Framing Tangentially Viewing Soft X-Ray Camera on LHD and TEXTOR

The formation of magnetic islands within plasmas confined magnetically within the tori has significant influence upon their confinement and stability. To obtain an experimental insight into the formation and dynamics of such island structures we employed a fast framing camera viewing the plasma tangentially in the toroidal direction. The toroidal viewing direction gives the advantage in that the islands are viewed almost tangentially and this greatly facilitates the reconstruction of the local data from the line integrated ones. We discuss an effective method to do inversion. To study the fluctuations seen in the video images we perform a singular value decomposition, and then we use a truncated least square method to infer their pictures in space.

The Implementation of Magnetic Islands in Gyrokinetic Toroidal Code

The implementation of magnetic islands in gyrokinetic simulation has been verified in the gyrokinetic toroidal code（GTC）.The ion and electron density profiles become partially flattened inside the islands.The density profile at the low field side is less flattened than that at the high field side due to toroidally trapped particles in the low field side,which do not move along the perturbed magnetic field lines.When the fraction of trapped particles decreases,the density profile at the low field becomes more flattened.

Real-Time Detection for Magnetic Island of Neoclassical Tearing Mode in EAST Plasma Control System

Accurate detection of a magnetic island in real time is one of the important issues for the tearing mode（TM） and neoclassical tearing mode（NTM） control.This paper presents a real-time detection system for the magnetic island of NTM control in the EAST Plasma Control System（PCS）.Diagnosis is based on magnetic periodic perturbation and electron temperature fluctuation caused by the magnetic island.Therefore,a Mirnov measurement has been selected to calculate the island＇s parameters,such as island width,frequency of island rotation,and toroidal number.The electron cyclotron emission（ECE） system can detect the island position,which is calculated by two fast detection algorithms called correlation analysis and Hilbert transform.For future NTM control,real-time equilibrium reconstruction（rt-EFIT） is needed to locate the rational q-surface where the island is detected.This fast detection system is able to detect an island within 3 ms.It can be integrated into PCS to provide effective parameters of the island for NTM control by using EC resonance heating（ECRH） in the next experiment of EAST.

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.

RCD Large Aspect-Ratio Tokamak Equilibrium with Magnetic Islands:a Perturbed Approach

Solutions of Grad-Shafranov （CS） equation with Reversed Current Density （RCD） profiles present mag- netic islands when the magnetic flux is explicitly dependent on the poloidal angle. In this work it is shown that a typical cylindrical （large aspect-ratio） RCD equilibrium configuration perturbed by the magnetic field of a circular loop （simulating a divertor） is capable of generate magnetic islands, due to the poloidal symmetry break of the GS equilibrium solution.

Magnetic-island-induced ion temperature gradient mode： Landau damping, equilibrium magnetic shear and pressure flattening effects

Characteristics of the magnetic-island-induced ion temperature gradient （MITG） mode are studied through gyrofluid simulations in the slab geometry, focusing on the effects of Landau damping, equilibrium magnetic shear （EMS）, and pressure flattening. It is shown that the magnetic island may enhance the Landau damping of the system by inducing the radial magnetic field. Moreover, the radial eigenmode numbers of most MITG poloidal harmonics are increased by the magnetic island so that the MITG mode is destabilized in the low EMS regime. In addition, the pressure profile flattening effect inside a magnetic island hardly affects the growth of the whole MITG mode, while it has different local effects near the O-point and the X-point regions. In comparison with the non-zero-order perturbations, only the quasi-linear flattening effect due to the zonal pressure is the effective component to impact the growth rate of the mode.

Stability impacts from the current and pressure profile modifications within finite sized island

The stability(or instability)of finite sized magnetic island could play a significant role in disruption avoidance or disruption mitigation dynamics.Especially,various current and pressure profile modifications,such as the current drive and heating caused by electron cyclotron wave,or the radiative cooling and current expulsion caused by the shattered pellet injection could be applied within the island to modify its stability,thus changing the ensuing dynamics.In this study,we calculate the mode structure modification caused by such profile changes within the island using the perturbed equilibrium approach,thus obtain the change of stability criterion Δ′ and assess the corresponding quasi-linear island stability.The positive helical current perturbation is found to always stabilize the island,while the negative one is found to do the opposite,in agreement with previous results.The pressure bump or hole within the island has a more complicated stability impact.In the small island regime,its contribution is monotonic,with pressure bump that tends to stabilize the island while pressure hole destabilizes it.This effect is relatively weak,though,due to the cancellation of the pressure term’s odd parity contribution in the second derivatives of the mode structure.In the large island regime,such cancellation is broken due to the island asymmetry,and the pressure contribution to stability is manifested,which is non-monotonic.The stability analysis in this paper helps to more accurately clarify the expected island response in the presence of profile modifications caused by disruption avoidance or mitigation systems.

Identification and Analysis of Magnetic Structures on HL-2A

A method for the identification and analysis of magnetic islands is presented based on the calculation of the perturbative current and magnetic field in plasmas. A cylindrical approximation is adopted and the toroidal effect on plasma equilibrium is also included. This method has been used on the HL-2A tokamak for analysing the magnetic island structures.

Review of Divertor Studies in LHD

In the Large Helical Device （LHD）, two different divertor configurations, i.e. helical divertor （HD） and local island divertor （LID）, are utilized to control the edge plasma. The HD with two X-points is an intrinsic divertor for heliotron devices, accompanied with a relatively thick ergodic layer outside the confinement region. Edge and divertor plasma behavior from low density to high density regimes is presented, referring to the divertor detachment. The effect of the ergodic layer on the edge transport is also discussed. On the other hand, the LID is an advanced divertor concept which realizes a high pumping efficiency by the combination of an externally induced magnetic island and a closed pumping system. Experimental results to confirm the fundamental divertor performance of the LID are presented.

Topology of toroidal helical fields in non-circular cross-sectional tokamaks

The ordinary differential magnetic field line equations are solved numerically; the tokamak magnetic structure is studied on Hefei Tokamak-7 Upgrade （HT-TU） when the equilibrium field with a monotonic q-profile is perturbed by a helical magnetic field. We find that a single mode （m, n） helical perturbation can cause the formation of islands on rational surfaces with q=m/n and q=（m±1,±2,±3,...）/n due to the toroidicity and plasma shape （i.e. elongation and triangularity）, while there are many undestroyed magnetic surfaces called Kolmogorov-Arnold-Moser （KAM） barriers on irrational surfaces. The islands on the same rational surface do not have the same size. When the ratio between the perturbing magnetic field Br（r） and the toroidal magnetic field amplitude Bφ0 is large enough, the magnetic island chains on different rational surfaces will overlap and chaotic orbits appear in the overlapping area, and the magnetic field becomes stochastic. It is remarkable that the stochastic layer appears first in the plasma edge region.

Neoclassical tearing mode stabilization by electron cyclotron current drive for HL-2M tokamak

Investigation of neoclassical tearing mode and its suppression by electron cyclotron current drive(ECCD)has been carried out in HL-2 M tokamak.The current driving capability of the electron cyclotron wave is evaluated.It is found that the deposition location can be effectively controlled by changing the poloidal angle.The validation of electron cyclotron wave heating and current driving has been demonstrated for the upper launcher port.We show that 3.0 MW and2.5 MW modulated ECCD can completely stabilize(2,1)and(3,2)NTMs,respectively.The non-modulated ECCD,radial misalignment as well as current profile broadening have deleterious effect on the NTM stabilization.The time required for suppression of(3,2)mode is shorter than that required for the suppression of(2,1)mode.Moreover,the time needed for complete stabilization at different initial island width has been quantitatively presented and analyzed.