Resonant Magnetic Perturbation Field Research Articles

Impact of increasing plasma-wall gap on plasma response to RMP fields in ITER

The impact of increasing plasma-wall gap on controlling edge-localized modes (ELMs) is numerically evaluated for the ITER 5 MA/2.65 T H-mode scenarios with full tungsten wall, based on the MARS-F computed plasma response to the applied n= 3–5 (n is the toroidal mode number) resonant magnetic perturbation (RMP) fields. Three new scenarios, referred to as standard, clearance and outergap, are considered assuming different plasma-wall gap sizes over a range on which vertically stability can be maintained by in-vessel coils in ITER. The latter are shown to have both direct and indirect effects on the plasma response and hence ELM control in ITER. The indirect and also primary influence occurs via change of the equilibrium edge safety factor q95 , which decreases with increasing the plasma-wall gap (at fixed plasma current and toroidal field), leading to a multi-peaking structure in the plasma response as measured by the plasma displacement near the X-point or the edge-localized resonant radial magnetic field perturbation. The direct, albeit secondary effect, is the reduction of local peak amplitudes with increasing the plasma-wall gap thus weakening the RMP field efficiency for ELM control with a given current in the control coils. A slight reduction of the plasma current, from 5 MA to 4.77, 4.92 and 4.65 MA for the standard, clearance and outergap scenarios, respectively, is found to be sufficient to access the q 95 window for the best ELM control with the n= 3 RMP. The n= 4 coil current configuration with the n= 5 sideband is also found favorable for ELM control in ITER, by producing RMP fields with mixed toroidal spectra compared to n = 3.

A new type of resonant magnetic perturbation for controlling edge localized modes

A new type of resonant magnetic perturbation (RMP), generated by helical coils, is proposed for controlling the edge localized mode (ELM) in H-mode tokamak plasmas. The helical coil optimization utilizes the MARS-F code (Liu et al 2000 Phys. Plasmas 7 3681) computed linear resistive fluid response of the plasma to the applied RMP field. The optimal helical coils are found to be located near the outboard mid-plane of the torus, with relatively simple shape but tilted towards the equilibrium magnetic field line pitch. Compared to the window-frame ELM control coils, the optimal helical coils require 2–4 times less current, in order to achieve the same ELM control performance specified by various figures of merit adopted in this work. The results from the present study show a promising path forward in achieving ELM control with RMP fields in tokamak plasmas.

Effects of resonant magnetic perturbations on turbulence and flows in the edge of HL-2A plasmas

The influence of resonant magnetic perturbations (RMPs) on the dynamics of turbulence and flows at the edge of the HL-2A tokamak is analyzed utilizing transfer entropy technique. The results have shown that the RMP damps the poloidal flows as well as the E × B shearing rate, whereas enhances the toroidal flows and leads to a broadened particle spectrum with increased small scale turbulence transport. The causality analysis indicates that the regulation impact of poloidal flow on turbulent fluctuations and particle flux is weakened, while that of the toroidal rotation on the latter is strengthened by the RMP field. The impact of the changes in poloidal flow dominates over that of the modified toroidal flow on turbulent transport in the edge. The magnetic perturbation and the flows generally show predator–prey oscillations, where the causal effect between the former and the toroidal flow transits to a synchronization relation in the presence of RMP. In addition, the RMP field will weaken the causal effect on poloidal Reynolds stress while strengthening the parallel-radial component simultaneously. The present findings provide a possible explanation on the effects of external fields on the edge transport, which is suggested to be dominated by the complex interactions among external perturbations, flows, and ambient microturbulence.

Effect of resonant magnetic perturbation on edge–core turbulence spreading in a tokamak plasma

Turbulence spreading from the edge to the core region of a tokamak with a resonant magnetic perturbation (RMP) is investigated using an electromagnetic Landau-fluid model in a toroidal geometry. As a RMP field with an appropriate amplitude is applied, long-wavelength fluctuations around the resonance surface can be excited due to forced magnetic reconnection. Strong shear flow at the magnetic island separatrix is observed, which can break the radially elongated vortex structures of the turbulent fluctuation. Inward turbulence spreading can be blocked by this shear flow, and the saturation level of turbulence intensity in the core region declines.

Overview of the Recent Experimental Research on the J-TEXT Tokamak

Abstract The J-TEXT capability is enhanced compared to two years ago with several upgrades of its diagnostics and the increase of electron cyclotron resonance heating (ECRH) power to 1 MW. With the application of electron cyclotron wave (ECW), the ECW assisted plasma startup is achieved; the tearing mode is suppressed; the toroidal injection of 300 kW ECW drives around 24 kA current; fast electrons are generated with toroidal injected ECW and the runaway current conversion efficiency increases with ECRH power. The mode coupling between 2/1 and 3/1 modes are extensively studied. The coupled 2/1 and 3/1 modes usually lead to major disruption. Their coupling can be either suppressed or avoided by external resonant magnetic perturbation (RMP) fields and hence avoids the major disruption. It is also found that the 2/1 threshold of external field is significantly reduced by a pre-excited 3/1 mode, which can be either a locked island or an external kink mode. The disruption control is studied by developing prediction methods capable of cross tokamak application and by new mitigation methods, such as the biased electrode or electromagnetic pellet injector. The high-density operation and related disruptions are studied from various aspects. Approaching the density limit, the collapse of the edge shear layer is observed and such collapse can be prevented by applying edge biasing, leading to an increased density limit. The density limit is also observed to increase, if the plasma is operated in the poloidal divertor configuration or the plasma purity is increased by increasing the pre-filled gas pressure or ECRH power during the start-up phase.

Acceleration of plasma toroidal rotation driven by non-axisymmetric magnetic perturbation fields in the EAST tokamak

Plasma toroidal rotation acceleration in the co-current direction introduced by the n = 1 (toroidal mode number) static resonant magnetic perturbation (RMP) has been observed in the EAST tokamak. It strongly depends on the RMP coil configuration, which is manifested by its dependence on δϕUL (phase difference between upper and lower coils) and RMP current. Modeling results from NTVTOK based on the linear plasma response modeled by MARS-F shows that the Neoclassical Toroidal Viscosity (NTV) torque is in the co-current direction because of the dominant contribution from electrons with the condition that the electron normalized collisionality is much lower than that of ions in this experiment. The modeled dependence of core integrated NTV torque modulated by the magnitude of core magnetic perturbation on δϕUL is consistent with the experimental observations. Threshold condition related to normalized collisionality to achieve the transition from rotation braking to acceleration is obtained in the NTV modeling and agrees well with experimental observations. It is shown in the modeling that the discharges with rotation acceleration are located at the regime that electron contribution to NTV is dominant and the torque is in co-current direction, while others with rotation braking are located at the regime that ion contribution to NTV torque is dominant and the torque is in countercurrent direction. Though the modeling results are in qualitative agreement with the experimental results, there is quantity difference between the modeled NTV torque based on linear plasma response and the experimental values. Possible reason is that the 3D fields are underestimated by linear modeling, particularly in the case of RMP field penetration, as demonstrated by the RMP current threshold for the rotation acceleration observed in the experiments.

Validation of MARS-F modeling of plasma response to RMPs using internal measurements on DIII-D

The linear resistive plasma response model is validated against the plasma internal measurement data from DIII-D edge-localized mode (ELM) control experiments with applied resonant magnetic perturbation (RMP). Considered are DIII-D discharges where the n = 1, 2, and 3 (n is the toroidal mode number) RMP field was applied. Experimental data for the plasma boundary displacement, as well as the three-dimensional (3D) pressure perturbation in the edge pedestal region, are deduced from the vertical Thomson scattering (TS) system and the horizontal charge exchange recombination (CER) system on DIII-D. The linear response model produces results that are in reasonable quantitative agreement with the DIII-D internal measurements. The plasma boundary displacement of up to 15 mm is modeled, with the pedestal pressure perturbation reaching 3 kPa. As an important insight, the larger plasma displacement measured by the vertical TS system, as compared to that measured by the horizontal CER system, is due to the contribution from the tangential component of the plasma displacement to the former. This mixing of displacement components is also found to influence the sensitivity of the CER measurement comparisons. The results of this study provide further confidence in the linear resistive plasma response model for analyzing ELM control experiments.

The effect of plasma toroidal rotation on n = 1 resonant magnetic perturbation field penetration under low neutral beam injection torque in EAST

An experiment was conducted to study the mode penetration of resonant magnetic perturbation (RMP) in EAST under low neutral beam injection torque in the co-current direction (Co-NBI). The experimental results indicate that the threshold current for field penetration decreases with higher input torque . Furthermore, it is observed that the plasma mode frequency at counter-current direction is greatly reduced when the plasma toroidal rotation frequency increases. The theoretical scaling of mode frequency predicted by the field penetration theory is in good agreement with the experimental observation (). The role of and on the mode onset threshold was separately investigated using the full toroidal geometry initial value code MARS-Q (Liu et al 2013 Phys. Plasmas 20 042503). The numerical scaling based on the experimental mode frequency is consistent with the experimental and theoretical ones. Numerical results suggest that evaluating the total mode frequency is crucial in field penetration analysis, in contrast to toroidal rotation frequency . With the increase of , the decreasing leads to a reduction in the field penetration threshold. This suggests that more attention should be paid to error field tolerance in low Co-NBI torque scenarios, where the electron diamagnetic frequency may be canceled out by NBI-driven toroidal plasma rotation.

Penetration properties of applied resonant magnetic perturbation in HL-2A tokamak

Any arbitrary perturbation on a magnetic field separatrix can cause a structure named homoclinic tangle in tokamaks. Both an edge localized mode (ELM) and a resonant magnetic perturbation (RMP) can lead to a perturbation of the magnetic field on the separatrix. Under the appropriate circumstances, RMP could alleviate or even completely suppress a rapid collapse process of an ELM. The simulation results using the CLTx code, the extended version of the three-dimensional toroidal magnetohydrodynamic (MHD) code (CLT (Ci-Liu-Ti, which means MHDs in Chinese)) with a scrape-off layer, show the structure of the homoclinic tangle with a borderline stochastic region resulting from RMP in HL-2A tokamak. Strongly distorted magnetic field lines with the homoclinic tangle could connect to the tokamak divertors. The footprints of these magnetic field lines on the divertors are consistent with the energy deposit spots in the experiment. From Poincaré plots of escaped magnetic field lines, it is found that the depth of the plasma edge region penetrated by these field lines depends on the RMP coil current, the rotation frequency of the RMP field, and the plasma resistivity.

Effect of resonant magnetic perturbations including toroidal sidebands on magnetic footprints and fast ion losses in HL-2M

Externally applied resonant magnetic perturbations (RMPs), generated by magnetic coils located outside the plasma (referred to as RMP coils), provide an effective way to control the edge localized mode (ELM) in tokamak devices. Due to the discrete nature of the toroidal distribution of these window-frame coils, toroidal sidebands always exist together with the fundamental harmonics designed for ELM control. In this work, the MARS-F code (Liu et al 2000 Phys. Plasmas 7 3681) is applied to investigate the detailed features of the RMP spectra considering both the dominant harmonic (n = 2) and the associated sideband (n = 6), and the impact of the combined fields on magnetic footprints as well as on the fast ion losses for a reference double-null scenario in the HL-2M device. It is found that the sum of the n = 2 and n = 6 RMP fields splits the footprint and widens the footprint area, as compared to the single-n (n = 2) harmonic case. The resistive plasma response breaks the up–down symmetry of the footprint pattern on the outer divertor plates, which is otherwise symmetric assuming vacuum RMP fields. Considering fast ion losses, a threshold value exists for the initially launched radial position of test particles, as well as for the RMP coil current, before the loss occurs. When the threshold criterion is satisfied, the combined n = 2 and n = 6 RMP fields enhance the fast ion loss rate by , as compared to that of the n = 2 component alone. These results illustrate the important role of the sideband of RMP fields on the magnetic footprints and fast ion losses in tokamak plasmas.

Reduction of the external resonant magnetic perturbation threshold for 2/1 locked mode excitation by the pre-excited mode on J-TEXT

A significant reduction of the external resonant magnetic perturbation (RMP) required for exciting the locked mode (LM) has been observed experimentally due to the presence of an existing LM on J-TEXT. In a plasma with edge safety factor q a slightly smaller than 3, 3/1 and 2/1 modes are observed to be destabilized successively by a rotating RMP field. The 3/1 mode is excited first and identified as an external kink mode, whose excitation threshold decreases with the operating q a increasing from 2.67 to 2.8 with the absence of a 3/1 rational surface. Shortly after excitation of the 3/1 external kink mode, 2/1 field penetration occurs and the 2/1 mode is excited, as identified by the phase between the 2/1 magnetic response and the RMP field jumping by π. The 2/1 mode is excited with a dominant kink structure and then converts into tearing mode for a duration of several milliseconds. During the excitation of the 2/1 mode, the phase difference between the 2/1 and 3/1 modes evolves from π to around 0 and the 2/1 mode amplitude grows to a saturation value comparable with that of the 3/1 mode. The presence of the 3/1 mode leads to a remarkable reduction of the external RMP current required for the 2/1 mode excitation, which can be explained by the contribution of a 2/1 resonant field from the 3/1 mode via the toroidal coupling effect. The larger 3/1 mode amplitude can lead to a greater reduction. This work reveals that the mode can be excited more easily with a reduced amplitude of RMP or error field due to the impact of the pre-existing mode and this might be a new consideration for error field correlation predictions and active magnetohydrodynamics control actuator designs.

The effect of the plasma response on peeling–ballooning modes during edge localized modes mitigated by resonant magnetic perturbations

The effects of resonant magnetic perturbation (RMP) fields on peeling–ballooning (P–B) modes are studied with the experimental equilibria of EAST based on the four-field model in BOUT++ code. As the two basic types of plasma responses, the magnetic and the transport response to RMP are considered in our simulation to reveal the roles of the plasma response during edge localized mode mitigation. On the one hand, the results show that RMP can reduce the linear growth rates of the P–B modes and the pedestal energy loss in the nonlinear process by directly coupling with the P–B modes. The magnetic response can weaken the impacts of RMPs on the P–B modes by partially screening the applied RMP fields more precisely the resonant components. On the other hand, RMP can further reduce the linear growth rates of the P–B modes and the pedestal energy loss by changing the equilibrium pressure profiles through the transport response. More detailed analysis suggests that, compared with other resonant components of RMPs, the components whose corresponding rational surfaces are located at the top of the pedestal can lead to stronger reductions in the linear growth rates of the P–B modes, and can reduce pedestal energy loss more significantly by enhancing multi-mode coupling in the nonlinear process. Finally, the multi-mode coupling increases with the strength of the resonant components, so one can change the RMP poloidal spectrum by adjusting the phase difference between the upper and low RMP coils from to , and hence obtain the optimal coil phase difference that leads to the strongest reductions in the linear growth rates of the P–B modes and the pedestal energy loss through maximizing the strength of resonant components, especially the resonant components whose corresponding rational surfaces are located at the top of the pedestal.

The effect of plasma beta on error-field penetration in radio-frequency wave heated plasmas in EAST

The plasma-beta effect on the n = 1 resonant magnetic perturbation (RMP) field penetration in purely radio-frequency (RF) wave heated discharges has been investigated in EAST. The experimental results show that the dependence of the threshold RMP coil current for field penetration, , on the total absorbed power P tot scales as approximately , indicating that the error-field tolerance is improved with increasing RF power. This is benefited by the increased electron perpendicular flow dominated by a counter-current electron diamagnetic flow with increasing RF power. However, theoretical scaling in cylindrical geometry overestimates the power index. Assuming an additional term for the normalized beta in the scaling, it is shown that the fitted from the experimental observation is around −1, indicating a degradation effect of plasma beta. To clarify the underlying physics of the 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 (Liu et al 2013 Phys. Plasmas 20 042503). The MARS-Q simulation results reproduce the dependence well, and hence the P tot scaling of the threshold current in experimental observations. The main reason for this is that the net total torque, which is mainly contributed by the neoclassical toroidal viscosity (NTV), increases with increasing plasma . The results demonstrate that the nonlinear toroidal coupling effect via NTV torque plays an important role in determining field penetration, even in cases with relatively low , which is far less than the no-wall beta limit.

Prevention of mode coupling by external applied resonant magnetic perturbation on the J-TEXT tokamak

Toroidal coupling between m/n = 2/1 and m/n = 3/1 modes frequently occurs in the J-TEXT, where m (n) is the poloidal (toroidal) mode number. These coupled modes destabilize each other, leading to confinement degradation and even triggering a major disruption. This paper presents two control strategies for preventing the mode coupling through the application of a proper static resonant magnetic perturbation (RMP) field. Experimental results demonstrate that moderate 2/1 RMP can suppress the small, rotating 2/1 mode thus prevent coupling between the 2/1 and 3/1 modes. The 3/1 static RMP can excite a large 3/1 locked island while leave the small 2/1 mode rotating at 8 kHz. Enlarging the frequency difference between 2/1 and 3/1 modes makes mode coupling more difficult. Both strategies can break the frequency coupling condition between the 2/1 and 3/1 modes, and hence avoid coupling and mutual destabilizing.

Turbulence characterization during the suppression of edge-localized modes by magnetic perturbations on ASDEX Upgrade

We study localized edge turbulence in the ASDEX Upgrade tokamak that appears if resonant magnetic perturbations (RMP) are applied to suppress edge localized modes (ELMs) in the high confinement mode. The concomitant density fluctuations are detected by microwave reflectometry at the outboard midplane. Two modes can be distinguished, (a) a broadband fluctuation below a threshold of the RMP field amplitude, and (b) a narrow-band quasi-coherent mode (QCM) above the threshold. The broadband fluctuation is toroidally spread out but disappears at the toroidal position of maximum E × B shear in the gradient region. Temporal and spatial correlation along field lines of the midplane density fluctuation and the divertor particle flux suggests that this mode is producing significant particle transport across the gradient region and into the divertor, hence contributing to the plasma density reduction that is often observed when applying RMP fields (the so-called ‘pump-out’ effect). The QCM is also toroidally localized, its radial extent grows with increasing RMP field amplitude, and leads to further increased divertor particle flux compared to the broadband mode. Our observations suggest that both modes not only play an important role in keeping the plasma density stationary in the absence of ELMs but also to reduce the plasma pressure such that the plasma edge becomes stable against ELMs.

Drift kinetic effects on plasma response to resonant magnetic perturbation for EU DEMO design

A systematic investigation of the plasma response to an externally applied resonant magnetic perturbation (RMP) field, for the purpose of controlling edge localized modes, is carried out for an EU DEMO reference plasma. Particular emphasis is placed on the role of kinetic effects associated with both thermal particles and fusion-born alphas. The single fluid, resistive model predicts a large peak amplification of the n= 1 (n is the toroidal mode number) plasma response to the target equilibrium, which is found to be close to the Troyon no-wall limit. A more advanced response model, including kinetic resonances between the RMP perturbation and drift motions of thermal and energetic particles, on the other hand, finds a strong suppression of the n= 1 field amplification. A major role is played by the precessional drift resonance of fusion-born alphas. A strong parallel sound wave damping model is found to well reproduce the full kinetic response results for the DEMO plasma, in terms of both the resonant field response amplitude and the plasma displacement. Finally, both fluid and kinetic models produce similar responses for the n = 2 and 3 RMP fields for the considered DEMO plasma, whilst kinetic effects again become important for the n = 4 RMP due to proximity of the reference plasma to the no-wall limit for the n = 4 ideal kink instability.

Effect of aspect ratio on plasma response to resonant magnetic perturbations in tokamak devices

A systematic numerical study is carried out, computing and comparing the plasma response to the resonant magnetic perturbation (RMP) field, applied for controlling edge localized modes (ELMs), in a series of tokamak plasmas with varying aspect ratio and utilizing the MARS-F code. The aspect ratio is scanned either by varying the plasma major radius at a fixed minor radius or by varying the latter while fixing the former. Both approaches yield similar results when compared in terms of quantities with proper normalizations. In general, a non-monotonic dependence of the resonant response field (normalized by the vacuum counterpart) near the plasma edge is found with varying aspect ratio, indicating that a given ELM control coil current configuration strongly favors plasmas with a certain aspect ratio. This optimal aspect ratio, on the other hand, depends on the toroidal as well as poloidal (i.e., coil phasing) spectra of the applied RMP field. The equilibrium (edge) safety factor, the plasma shape, and the plasma toroidal flow are all fixed to ensure that the effects identified here are predominantly due to the plasma aspect ratio.

The spectrum analysis of RMP coils with multiple connection modes and the design of high field side coils on J-TEXT

The phase difference Δξ between locked islands (2/1 and 3/1) has been found to influence the heat transport on the thermal quench during disruptions by numerical modeling [Hu Q et al 2019 Nucl. Fusion 59, 016005]. To verify this experimentally, a set of resonant magnetic perturbation (RMP) coils is required to excite coupled magnetic islands with different Δξ. The spectrum analysis shows that the current RMP coils on J-TEXT can only produce sufficient 2/1 and 3/1 RMP fields with a limited phase difference of Δξ∈[−75°, 75°]. In order to broaden the adjustable range of Δξ, a set of coils on the high field side (HFS) is proposed to generate 2/1 and 3/1 RMP fields with Δξ = 180°. As a result, RMPs with adjustable Δξ∈[−180°, 180°] and sufficient amplitudes could be achieved by applying the HFS coils and the low field side (LFS) coils. This work provides a feasible solution for flexible adjustment of the phase difference between m and m + 1 RMP, which might facilitate the study of major disruptions and their control.

Stochastic fluctuation and transport of tokamak edge plasmas with the resonant magnetic perturbation field

We present that a statistical method known as the complexity–entropy analysis is useful to characterize a state of plasma turbulence and flux in the resonant magnetic perturbation (RMP) edge localized mode (ELM) control experiment. The stochastic pedestal top temperature fluctuation in the RMP ELM suppression phase is distinguished from the chaotic fluctuation in the natural ELM-free phase. It is discussed that the stochastic temperature fluctuation can be originated from the narrow layer of the field penetration on the pedestal top. The forced magnetic island can emit the resonant drift wave of comparable sizes (relatively low-k) in the RMP ELM suppression phase, and it can result in the generation of stochastic higher wavenumber fluctuations coupled to tangled fields around the island. The analysis of the ion saturation current measurement around the major outer striking point on the divertor shows that it also becomes more stochastic as the stronger plasma response to the RMP field is expected.

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 various Δϕ. 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.