Application of three-dimensional MHD equilibrium calculation coupled with plasma response to island divertor experiments on J-TEXT

The application of resonant magnetic perturbation (RMP) coils could break the initial axisymmetry and change the magnetic topology in tokamak systems. To understand the plasma equilibrium response to the RMP fields, three-dimensional (3D) non-linear magnetohydrodynamics equilibrium calculations have been carried out using the HINT code for an RMP field-penetration experiment on J-TEXT. The HINT code does not assume perfectly nested flux surfaces, and is able to consider directly the change of magnetic topology due to the RMP field penetrations. Correlations between 3D equilibrium calculations and experimental observations are presented. The magnetic topologies calculated by HINT were compared with the field topologies obtained from a vacuum approximation method. It turns out that the effects of redistribution of plasma pressure and current due to the formation of magnetic islands at various resonant rational surfaces should be considered self-consistently for understanding the change of magnetic structure. Such changes include changes in the shape and size of magnetic islands, and the distribution of stochastic fields around the magnetic islands and at the plasma boundary, which plays an important role for plasma-wall interactions.

<sec>Resonant magnetic perturbation (RMP), generated by externally applied magnetic perturbation coils, is an important method of controlling plasma edge localized mode. Many experiments have shown that RMP can effectively mitigate/suppress edge localized mode, but its intrinsic physical mechanism is not completely clear. The response of plasma to RMP is the key to understanding the RMP physics. In the presence of RMP, the circumferential symmetry of the tokamak magnetic field will be broken, forming a new three-dimensional(3D) equilibrium, and this process is called the plasma response to RMP. Currently, the parameter range and control effect of RMPs to control edge localized mode on different devices are quite different, implying that the plasma response to RMPs has different response results in different parameter ranges on different devices. Therefore, it is necessary to study the RMP response characteristics of specific devices.</sec><sec>In this work, the effect of the plasma rotation frequency on the linear response process of plasma to the resonant magnetic perturbations is investigated in the framework of MARS-F in the HL-2A configuration, and the physical reasons are analyzed in detail. It is found that the shielding and amplification effects in plasma response do not change linearly with plasma rotation frequency, since the plasma resistivity plays an important role. The shielding effect for the magnetic perturbation on the rational surface is enhanced with the increase of the rotation frequency in the high rotation frequency range. However, this rule no longer holds true in the low rotation frequency range due to the deviation of the strongest shielding position from the rational surface caused by the plasma resistivity. As for the amplification effect, the resistivity weakens the amplification effect of plasma response due to the dissipation of induced current. The variation trend of the amplification effect with the rotation frequency and resistivity is consistent with that of the core-kink response, which indicates that the amplification effect of the magnetic perturbation is mainly caused by the core-kink response.</sec>

KSTAR has clarified a set of unresolved 3D physics issues utilizing the ITER-like in-vessel, three-row, resonant magnetic perturbation (RMP) configurations. Since RMP-driven, edge-localized-modes (ELMs)-crash control elevates the divertor heat flux peak through its impact on edge plasma parameters and transport, a series of intentionally misaligned RMP configurations (IMCs) have been explored to investigate the relationship between RMP ELM control and divertor heat fluxes, while searching for an ideal IMC that could be favorable in both aspects. First of all, the contrasting influence of kink vs anti-kink phasing on the ELM-crash suppression has been articulated, demonstrating the synergistic benefit of ‘kink’ phasing on ELM-crash-suppression. On the other hand, the three-row IMC in the anti-kink phasing becomes more insensitive to the ELM-crashes at the sub-marginal level of RMP, consistent with theory. Meanwhile, the divertor ‘wetted’ area of ELM-crash-suppression gets narrower than that of ELM-crash-mitigation, suggesting that ELM-crash-mitigation remains advantageous over ELM-crash-suppression in terms of time-averaged divertor thermal loading. In comparison, based on a set of two-row IMCs, no evidence of divertor heat flux broadening was found during ELM-crash-suppression, supporting a hypothesis that the dispersal of the divertor heat flux in three-row IMCs cannot be driven by helically structured two-row RMPs alone. Among ITER-like three-rows, lower two-row RMPs have been found to be much more effective in suppressing the ELM-crashes than upper two-row RMPs. Although it is quite preliminary, the up/down asymmetric dependence of RMP coupling may be generically attributed to lower-single-null plasmas. Such a holistic understanding of RMP-driven, ELM-crash-control in KSTAR is expected not only to elucidate various subtle points in the vicinity of ELM-crash-suppression, but also to clarify the relevant divertor thermal loading issues for ITER and beyond.

The effects of changes in core density on divertor electron temperature, density and heat flux when resonant magnetic perturbations (RMPs) are applied are presented, notably a reduction in RMP induced secondary radial peaks in the electron temperature profile at the target plate is observed when the core density is increased, which is consistent with modeling. RMPs is used here to indicate non-axisymmetric magnetic field perturbations, created using in-vessel control coils, which have at least one but typically many resonances with the rotational transform of the plasma (Evans et al 2006 Phys. Plasmas 13 056121). RMPs are found to alter inter-ELM heat flux to the divertor by modifying the core plasma density. It is shown that applying RMPs reduces the core density and increases the inter-ELM heat flux to both the inner and outer targets. Using gas puffing to return the core density to the pre-RMP levels more than eliminates the increase in inter-ELM heat flux, but a broadening of the heat flux to the outer target remains. These measurements were made at a single toroidal location, but the peak in the heat flux profile was found near the outer strike point where simulations indicate little toroidal variation should exist and tangentially viewing diagnostics showed no evidence of strong asymmetries. In experiments where divertor Thomson scattering measurements were available it is shown that local secondary peaks in the divertor electron temperature profile near the target plate are reduced as the core density is increased, while peaks in the divertor electron density profile near the target are increased. These trends observed in the divertor electron temperature and density are qualitatively reproduced by scanning the upstream density in EMC3-Eirene modeling. Measurements are presented showing that higher densities are needed to induce detachment of the outer strike point in a case where an increase in electron temperature, likely due to a change in MHD activity, is seen after RMPs are applied.

Control of neutral fueling and helium exhaust to NSTX-U plasmas by means of three-dimensional magnetic control fields

Edge localized modes (ELMs) are a concern for future devices, such as ITER, due to the large transient heat loads they generate on the divertor surfaces which could limit the operational lifetime of the device. This paper discusses the application of resonant magnetic perturbations (RMPs) as a mechanism for ELM control on Mega Amp Spherical Tokamak (MAST). Experiments have been performed using an n = 3 toroidal mode number perturbation and measurements of the strike point splitting performed. The measurements have been made using both infrared and visible imaging to measure the heat and particle flux to the divertor. The measured profiles have shown clear splitting in L-mode which compares well with the predication of the splitting location from modelling including the effect of screening. The splitting of the strike point has also been studied as a function of time during the ELM. The splitting varies during the ELM, being the strongest at the time of the peak heat flux and becoming more filamentary at the end of the ELM (200 µs after the peak midplane Dα emission). Variation in the splitting profiles has also been seen, with some ELMs showing clear splitting and others no splitting. A possible explanation of this effect is proposed, and supported by modelling, which concerns the relative phase between the RMP field and the ELM filament location.

In order to consider the nonlinear three-dimensional (3D) equilibrium response of the resonant magnetic perturbation field, the nonlinear 3D equilibrium is discussed for the 3D perturbed tokamak. To model the magnetic topology, a nonlinear 3D equilibrium calculation code, which has been developed in stellarator research, is applied to the perturbed tokamak. That code does not assume the existence of perfectly nested flux surfaces. In the nonlinear 3D equilibrium calculation, the change of the magnetic topology is due to the nonlinear 3D equilibrium response, which is the lowest order plasma response appearing in the 3D steady state. The parallel current flow along perturbed field lines three-dimensionally drives the perturbed field to break the magnetic topology. This effect is significant along the separatrix and must be considered to interpret the experimental observations.

KSTAR has demonstrated divertor heat flux broadening during edge-localized mode (ELM) crash suppression using ITER-like three-row resonant magnetic perturbation (RMP) for the first time. To address a couple of critical issues in ITER RMP, robust ELM-crash-suppression methodology has been explored at low q95 and established in KSTAR using low-n RMPs. Taking full advantage of the ITER-like three-row in-vessel control coils (IVCC) in KSTAR, a set of intentionally misaligned RMP configurations (IMC) was tested to investigate whether or not IMC could be compatible with ELM crash suppression, while minimizing electromagnetic loads on RMP coils. As a result, the ITER-like three-row IMCs were found not only to have been compatible with the ELM crash suppression, but also to have broadened the divertor heat fluxes in the vicinity of the outer strike point. In comparison, the two-row RMPs have rarely affected the near scrape-off layer (SOL) heat flux despite slightly broadened profile change in the far-SOL. Since the divertor heat flux broadening reflects the dispersal of the peaked near-SOL heat flux, the experimental outcome is quite favorable to the ITER choice of three rows, instead of two rows. Nonetheless, since the IMC-driven broadening observed in the attached plasmas in KSTAR might appear substantially different in the partially detached plasmas in ITER, additional investigation has been conducted to see if RMP-driven, ELM crash suppression could be compatible with detached plasmas. Although no detached plasmas have been identified with ELM crash suppression yet, significantly reduced divertor heat flux was confirmed in high density, ELM-crash-suppressed plasmas at q95 = 3.4 using n = 2 RMPs. These new findings elevate the confidence level about the ITER RMP system, while the remaining uncertainties need to be further clarified using the three-row IVCCs in KSTAR.

Controlling the splitting divertor heat flux caused by resonant magnetic perturbations (RMPs) is a topic of concern for fusion devices. As a fundamental prerequisite, it is necessary to understand the characteristics of the heat flux distribution under the applied RMP field, which will be studied in this paper. The nonlinear phenomenon of strike point splitting was found to be strongly dependent on the plasma response under RMP. These splitting heat flux distributions are qualitatively explained by the simulated magnetic footprints. The RMP phase scanning experiment shows that scanning in a certain range of relative phase can maintain good ELM mitigation and simultaneously sweep the striations of heat flux on divertor target. Additionally, even in upper single null (USN) configurations, heat stripes are observed on the lower outer divertor (LO-div), attributed to RMP-induced additional magnetic connections to the LO-div, as confirmed by magnetic topology simulations. A dedicated investigation into the impact of the discrepancy between lower and upper separatrix radii mapped to the low field side mid-plane (〖dR〗_sep) reveals its significant influence on both ELM control and heat flux distribution. Within a certain range of 〖dR〗_sep, the heat flux distribution is improved while ELM suppression is maintained. These findings contribute to divertor heat flux understanding under RMP conditions in tokamak operations.

The orientation of 3D equilibria in the Madison Symmetric Torus (MST) [R. N. Dexter et al., Fusion Technol. 19, 131 (1991)] reversed-field pinch can now be controlled with a resonant magnetic perturbation (RMP). Absent the RMP, the orientation of the stationary 3D equilibrium varies from shot to shot in a semi-random manner, making its diagnosis difficult. Produced with a poloidal array of saddle coils at the vertical insulated cut in MST's thick conducting shell, an m = 1 RMP with an amplitude br/B ∼ 10% forces the 3D structure into any desired orientation relative to MST's diagnostics. This control has led to improved diagnosis, revealing enhancements in both the central electron temperature and density. With sufficient amplitude, the RMP also inhibits the generation of high-energy (>20 keV) electrons, which otherwise emerge due to a reduction in magnetic stochasticity in the core. Field line tracing reveals that the RMP reintroduces stochasticity to the core. A m = 3 RMP of similar amplitude has little effect on the magnetic topology or the high-energy electrons.

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-n RMPs (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 during ELM suppression is preliminarily investigated, and further splitting in the original strike point is observed at during ELM suppression. In terms of ELM pulses, the presence of RMPs shows little influence on transient heat flux distribution.

<sec> The fast ion transport associated with resonant magnetic perturbation (RMP) contains rich physical spanning single particle motion of fast particle and plasmas response physics with RMP and their interaction. Full numerical simulation considering such physical ingredients should be performed in a long run for clarifying the underlying physical features of the fast ion confinement with RMP. Thus, the appropriate application of RMP is not only to avoid the detrimental effects but also to serve as an actuator to exert targeted control over the energetic particle profile. To achieve this goal, a comprehensive knowledge of the effects of RMP including plasma response on fast ions is necessary. </sec> <sec> In this work, the plasma response to RMP in HL-2A device is simulated by the MARS-F code under different parameters including finite resistivity, toroidal rotation frequency and toroidal mode number, and the three-dimensional (3D) magnetic field topology considering RMP is obtained. Then, Boris algorithm is used to track the ion orbit under these 3D fields, and the physical mechanism of ion orbit characteristics changed by the perturbed field is explored in detail. It is found that with the increase of finite resistivity, the average value of perturbed magnetic field decreases, and the orbit radial expansion turns smaller. The variation of toroidal rotation frequency can change the distribution of perturbed magnetic field, resulting in different orbit radial expansions for different kinds of orbits. What is more, if the toroidal mode number increases, the amplitude of perturbed magnetic field after response decreases obviously, thus resulting in little effect on orbit radial expansion. In a word, the plasma responded RMP field enhances the orbit radial expansion, and the maximum orbital radial expansion increases with the augment of average value of perturbed magnetic field on the orbit. Meanwhile, the amplitude of orbit expansion increases significantly when the ions pass through the region where the perturbed magnetic field is strongly amplified. This effect can explain the increase of ion prompt loss and enhancement of plasma radial transport in edge localized mode mitigation experiments by RMP. </sec>

Suppression and mitigation of a high-frequency Alfvén-like mode (HFAM) between type-I edge localized modes (ELMs) during ELM mitigation by resonant magnetic perturbation (RMP) is observed for the first time in the EAST tokamak. This mode is located near the edge pedestal region. The modeling result of the Alfvén continuum shows that the HFAM is located near the elipical Alfvén eigenmode (EAE) gap. During the application of n = 1 RMP for ELM mitigation, the HFAM can be fully suppressed when the RMP amplitude exceeds a threshold, below which the HFAM is mitigated. The suppression is caused by a reduction of pedestal height induced by RMP. In the case using n = 3 RMP, the mode is localized toroidally at specific phase depending on the phase of applied RMP, i.e. locked in the three-dimensional equilibrium formed by RMP. The dominant toroidal mode number of HFAM is around n = −6 and it reduces to −3 during the application of n = 3 RMP, which indicates the existence of possible nonlinear coupling between the HFAM and RMP. Here the negative mode number denotes that the mode rotates in electron diamagnetic drift direction. The observation reported here improves the understanding of pedestal dynamics and its stability in RMP ELM control.

A critical issue for fusion-plasma research is the erosion of the first wall of the experimental device due to impulsive heating from repetitive edge magneto-hydrodynamic instabilities known as 'edge-localized modes' (ELMs). Here, we show that the addition of small resonant magnetic field perturbations completely eliminates ELMs while maintaining a steady-state high-confinement (H-mode) plasma. These perturbations induce a chaotic behaviour in the magnetic field lines, which reduces the edge pressure gradient below the ELM instability threshold. The pressure gradient reduction results from a reduction in the particle content of the plasma, rather than an increase in the electron thermal transport. This is inconsistent with the predictions of stochastic electron heat transport theory. These results provide a first experimental test of stochastic transport theory in a highly rotating, hot, collisionless plasma and demonstrate a promising solution to the critical issue of controlling edge instabilities in fusion-plasma devices.

The effects of resonant magnetic perturbation (RMP) field on impurity radiation, divertor footprint distribution, and core plasma transport are investigated in the detachment discharges of the Large Helical Device (LHD). The RMP with m/n = 1/1 mode creates an edge magnetic island in the stochastic layer, which enhances the impurity emission from low charge states, C2+ and C3+, and then triggers a detachment transition. Emission from the higher charge states, C4+ and C5+, implies enhanced penetration of impurities during the detachment phase with RMP. The toroidal divertor particle flux distribution exhibits n = 1 mode structure in both the attached and detached phases, but with a large toroidal phase shift between the two phases. The distribution in the attached phase is well correlated with the magnetic footprint of field line connection length calculated by the vacuum approximation. During the detached phase, however, the phase shift is not well explained by the vacuum approximation, where a significant plasma response to the external RMP is observed. The energy confinement time becomes systematically shorter with RMP application due to the shrinkage of plasma volume caused by the edge magnetic island. On the other hand, the pressure profile during detachment with RMP is found to be more peaked than without RMP. The analysis using the core transport code TASK3D, considering the heating profiles of neutral beam injection, shows no significant transport degradation during detachment with RMP application, even with the enhanced radiation, reduced divertor flux, and possible impurity penetration.