Resonant Magnetic Perturbations Research Articles

Comparison of transport coefficients before and after density pump-out induced by resonant magnetic perturbation using a BOUT++ six-field model on the EAST tokamak

Many experiments have demonstrated that resonant magnetic perturbation (RMP) can affect the turbulent transport at the edge of the tokamak. Through the Experimental Advanced Superconducting Tokamak (EAST) density modulation experiment, the particle transport coefficients were calculated using the experimental data, and the result shows that the particle transport coefficients increase with RMP. In this study, the six-field two-fluid model in BOUT++ is used to simulate the transport before and after density pump-out induced by RMP, respectively referred as the case without RMP and the case with RMP. In the linear simulations, the instabilities generally decreases for cases with RMP. In the nonlinear simulation, ELM only appears in the case without RMP. Additionally, the particle transport coefficient was analyzed, and the result shows that the particle transport coefficient becomes larger for the case with RMP, which is consistent with the experimental conclusion. Moreover, its magnitude is comparable to the results calculated from experimental data.

Chasing the multi-modal plasma response in MAST-U

Achieving edge localized modes (ELMs) suppression in spherical tokamaks by applying resonant magnetic perturbations (RMPs) has proven challenging. The poloidal spectrum of the applied RMP is a key parameter that has an impact on the capability to mitigate and eventually suppress ELMs. In this work the resistive magnetohydrodynamic code MARS-F (Liu et al 2000 Phys. Plasmas 7 3681) is used to evaluate the possibility of directly measuring the plasma response in MAST-U, and particularly its variation as function of the applied poloidal spectrum, in order to guide the experimental validation of the predicted best RMP configuration for ELM suppression. Toroidal mode number n = 2 RMP is considered to minimize the presence of sidebands, and to avoid the deleterious core coupling of n = 1. Singular Value Decomposition is used to highlight linearly independent structures in the simulated magnetic 3D fields and how those structures can be measured at the wall where the magnetic sensors are located. Alternative ways to measure the multimodal plasma response and how they can be used to infer the best RMP configuration to achieve ELM suppression are also presented, including the plasma displacement and the 3D footprints at the divertor plates.

Neoclassical tearing mode stabilization by electron cyclotron current drive in EAST tokamak experiments

Abstract The stabilization of the m/n=2/1 neoclassical tearing mode (NTM) by electron cyclotron current drive (ECCD) has been carried out in EAST H-mode discharges, where m/n is the poloidal/toroidal mode number. The major experimental results are reported for the first time in this paper. To facilitate the experimental study, the magnetic island (NTM) is generated by a sufficiently large amplitude of the externally applied resonant magnetic perturbation (RMP). After switching off the RMP, the NTM exists due to the bootstrap current perturbation, with the magnetic island width being about 5 cm for the local equilibrium bootstrap current fraction being larger than 10 %. By applying the localized ECCD later, the NTM is fully suppressed if the radial misalignment between the magnetic island and the ECCD location is sufficiently small. The stabilizing effect depends on both the radial misalignment and the applied electron cyclotron wave power. More importantly, it is found that the NTM can be avoided when applying ECCD earlier during the ramp-up phase of the RMP amplitude, if ECCD is localized around the O-point of the magnetic island, indicating an efficient way for avoiding locked modes that can lead to the major disruptions of tokamak plasmas.

Simulation of neoclassical heavy impurity transport in ASDEX Upgrade with applied 3D magnetic fields using the nonlinear MHD code JOREK

Accumulation of heavy impurities in the tokamak core is detrimental for its performance and can lead to disruption of the plasma. In small to medium-sized tokamaks the effective neoclassical transport in the pedestal is typically oriented radially inward. In larger tokamaks—e.g., ITER—where the temperature gradient is higher and density gradients are lower due to the need to operate in a radiative divertor regime, the neoclassical transport is predicted to be outwards. The models are derived for axisymmetric quasi-steady-state plasmas. Applied 3D magnetic fields, i.e., Resonant Magnetic Perturbation (RMPs) as they are used to suppress Edge Localized Modes (ELMs), have experimentally been observed in AUG to enhance the outflow of heavy impurities in the pedestal. There is no model that can predict neoclassical heavy impurity transport in these ergodized 3D magnetic fields self-consistently. In this contribution, we present our kinetic tungsten transport simulation for an ASDEX Upgrade plasma with applied RMPs. Our model based on Hoelzl et al. [Nucl. Fusion 61, 065001 (2021)], van Vugt et al. [Phys. Plasmas 26, 042508 (2019)], and Korving et al. [Phys. Plasmas 30, 042509 (2023)] utilizes a full-orbit pusher, ionization, recombination, effective line, and continuum radiation and neoclassical collisions with the background plasma. The effective collisional radiative rates are from the OpenADAS database, the neoclassical collision operator uses the framework of Homma et al. [J. Comput. Phys. 250, 206–223 (2013)] and Homma et al. [Nucl. Fusion 56, 036009 (2016)]. We show that the adopted collision operator produces neoclassical transport within a satisfactory degree of accuracy. A sufficiently high RMP current causes an increase in tungsten diffusion in the pedestal by a factor of 2. We compare the average radial transport between axisymmetric and 3D RMP scenarios in the pedestal region. RMPs enhance the pedestal permeability for impurities, which results in enhanced transport. In addition to the enhanced transport, some of W is found to be trapped in 3D potential wells in the scrape-off layer. Due to the lack of suitable diagnostics for W in the pedestal, we investigate and suggest that argon can be an adequate substitute in experiments for model validation and further understanding impurity transport in scenarios with applied 3D magnetic fields. With the newly developed neutral model [Korving et al., Phys. Plasmas 30, 042509 (2023)], we can combine the interaction in the divertor with the 3D RMPs to model the tungsten transport from the divertor toward the core of the plasma.

Overview of recent experimental results on the EAST tokamak

Abstract Since the 2021 IAEA FEC, EAST experiments have been carried out in support of high-performance steady-state operation and physics understanding for ITER and CFETR. The first demonstration of reproducible 403 s long-pulse steady-state H-mode plasma with H98y2>1.3, βP~2.5, βN~1.6, ne/nGW~0.7 and a good control of impurity and heat exhaust have been achieved on EAST using the pure radio frequency (RF) power heating and current drive. In support of ITER and CFETR long pulse operation, a thousand-second time scale (~1056 s) fully non-inductive plasma has been achieved. The EAST operational regime of high βP has been significantly extended (H98y2>1.3, βP~4.0, βN~2.4 and ne/nGW~1.0) using RF and neutral beam (NB). The full edge localized mode suppression using the n = 4 resonant magnetic perturbations (RMP) has been achieved in ITER-like standard type-I ELMy H-mode plasmas with q95 ≈ 3.1 on EAST, extrapolating favorably to the ITER baseline scenario. The sustained large ELM control and stable partial detachment have been achieved with Ne seeding. The plasma-beta effect for error field penetration is investigated with n = 1 RMP. Breakdown and plasma initiation at low toroidal electric fields (<0.3 V/m) with EC pre-ionization is developed. The transport and control of high-Z impurity of tungsten is investigated.

Radiatively tamed divertor thermal loading in resonant magnetic perturbation (RMP)-driven, ELM-crash-suppressed plasmas

Edge-localized-modes (ELMs) suppression by non-axisymmetric resonant-magnetic-perturbation (RMP) provides the way to reach high performance fusion plasmas without a threatening level of transient heat fluxes to the walls of fusion devices. The application of RMP, however, strongly modifies the heat flux pattern onto in-vessel components in contact with the plasma (especially the divertor) leading to local ‘hot spots’. Radiative dissipation by partially ionized species (impurities and deuterium) lowers the heat flux peaks on the walls but has been poorly compatible with such RMP-driven, ELM-crash-suppression. Here, we show how KSTAR has radiatively tamed divertor thermal loading down to more than a factor of 7 in the off-separatrix region without losing ELM-crash-suppression using ITER-like, three-row, RMP configurations, demonstrating its sustainment even in a partially detached plasma in the outer strike point, as required for ITER.

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.

Dynamic characteristics of edge plasma profiles during the opening of edge islands on the J-TEXT tokamak

Abstract On the J-TEXT tokamak, the dynamics of edge magnetic topology during the opening of the edge magnetic islands induced by the external Resonant Magnetic Perturbation (RMP) are investigated. The edge island chain is pushed outward by increasing plasma toroidal current to intersect the poloidally and toroidally localized divertor plate, forming an open magnetic island in the Scrape-Off Layer (SOL). The location of the strike points on the divertor plate predicted by the HINT code is in agreement with the experimental observations. The influence of the magnetic topology on edge plasma profiles has also been investigated using Langmuir probes. The properties of edge T e , n e , P e and E r profiles are studied as function of three magnetic structures in q a -dependence experiments and two magnetic structures in RMP configuration-dependence experiments. Some common features are observed. Inside the edge closed and SOL remnant islands, flat P e but non-flat T e and n e profiles are detected. When transitioning from the edge closed island to the partially open island with remnant island, the local flat P e profile is shifted outward accompanied by a narrower flattened P e region. The steep slopes of T e , n e and P e are measured in the SOL regions characterized by a long connection length L c , and the longer L c , the steeper slopes. E r exhibits a negative well inside the remnant island with infinite L c and in the SOL regions where L c significantly exceeds than the electron mean free path λ e , but develops a positive value in the SOL regions where L c is relatively short.

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.

Effects of edge-localized electron cyclotron current drive on edge-localized mode suppression by resonant magnetic perturbations in DIII-D

According to recent DIII-D experiments (Logan et al 2024 Nucl. Fusion 64 014003), injecting edge localized electron cyclotron current drive (ECCD) in the counter-plasma-current (counter-I p) direction reduces the n = 3 resonant magnetic perturbation (RMP) current threshold for edge-localized mode (ELM) suppression, while co-I p ECCD during the suppressed ELM phase causes a back transition to ELMing. This paper presents nonlinear two-fluid simulations on the ECCD manipulation of edge magnetic islands induced by RMP using the TM1 code. In the presence of a magnetic island chain at the pedestal-top, co-I p ECCD is found to decrease the island width and restore the initially degraded pedestal pressure when its radial deposition location is close to the rational surface of the island. With a sufficiently strong co-I p ECCD current, the RMP-driven magnetic island can be healed, and the pedestal pressure fully recovers to its initial ELMing state. On the contrary, counter-I p ECCD is found to increase the island width and further reduce the pedestal pressure to levels significantly below the peeling-ballooning-mode limited height, leading to even stationary ELM suppression. These simulations align with the results from DIII-D experiments. However, when multiple magnetic island chains are present at the pedestal-top, the ECCD current experiences substantial broadening, and its effects on the island width and pedestal pressure become negligible. Further simulations reveal that counter-I p ECCD enhances RMP penetration by lowering the penetration threshold, with the degree of reduction proportional to the amplitude of ECCD current. For the ∼1 MW ECCD in DIII-D, the predicted decrease in the RMP penetration threshold for ELM suppression is approximately 20%, consistent with experimental observations. These simulations indicate that edge-localized ECCD can be used to either facilitate RMP-driven ELM suppression or optimize the confinement degradation.

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.

Statistical analysis of locked mode induced disruption in EAST

The effects of key parameters on locked mode induced disruption (LMiD) are investigated in EAST experiments. The experimental data for locked mode are collected from 2015 to 2022 when the externally applied resonant magnetic perturbation is successfully employed in EAST. In this dataset, ∼42% of the total shots are LMiD, while the remaining 58% are LM without disruption. To better analyze the LMiD, an intuitive physical process is proposed. The LMiD process can be divided into two stages, the evolution of magnetic islands and the loss of plasma stored energy. The LMiD can also be related to the evolution of the other 8 physical quantities. On the basis of this physical process analysis, the time scale and the influencing factors for LMiD are investigated using statistical analysis. It is found that the density (ne), the distance from the magnetic island outer boundary to the plasma last closed surface (dedge), the loop-voltage (Vloop), and the plasma core electron temperature (Te), which are consistent with the intuitive physical model, are key parameters to LMiD. In addition, other potentially important parameters, the relevant reasons, and statistical analysis on the parameter intervals where rapid disruption with greater harmfulness occurred have also been investigated.

Small resonant magnetic perturbations result in three-dimensional material transport in the fusion plasma edge

Erosion patterns in a 3D magnetic topology are significantly altered when compared to an axisymmetric scenario due to differences in the impurity transport in a plasma environment. When resonant magnetic perturbations are applied in L-Mode discharges, eroded impurities can buildup in regions where an axisymmetric plasma would otherwise lead to zones of net erosion across the full toroidal length of the divertor. The reduction on the local and integrated erosion observed across a parametric study of the anomalous diffusion and impurity content in a plasma, can lead to the extension of divertor lifetimes in low power scenarios when 3D fields are applied. By contrast, in axisymmetric scenarios, most of the carbon eroded from the divertor are carried away to the far scrape-off layer.

Influence of the far non-resonant components of high-n resonant magnetic perturbations on energetic passing ions loss

The influence on the loss of energetic passing ions by the n = 4 resonant magnetic perturbation (RMP) is investigated through numerical simulations (here, n is the toroidal mode number of the RMP field). Dedicated efforts have been made to uncover how the plasma response modifies the loss fractions and underlying mechanisms. The stochastization of the drift surfaces and the particle loss fractions increase significantly under the response field, in which the resonant component is significantly shielded. In order to better understand how the response field contributes a considerable drift island width, the respective effect of each poloidal component mb on the outermost drift island mp/n=9/4 are compared (here, mb and mp are poloidal mode numbers of the RMP components and drift island, respectively). Contrary to the intuition that the components with mb=mp±1 should dominate the sideband resonance, some of the components which fulfill |mp−mb|≫1 have the dominant contributions under the response field. There are mainly two reasons accounting for this phenomenon, i.e. the drift motion of particles and the enhancement of amplitudes of non-resonant high-m components by the plasma response near the edge due to the resonant field amplification (RFA) effect. The former made it possible for particles to resonate with the far non-resonant components, and the latter significantly enhanced the perturbation field experienced by particles. The above results imply that the RFA effect is more critical than the stochastization of magnetic topology in the fast ion losses under RMP.

Effect of hyper-resistivity on ballooning modes with resonant magnetic perturbations

The impact of hyper-resistivity on non-ideal ballooning modes (BMs) is studied in the presence of resonant magnetic perturbation (RMP) through considering the hyper-resistivity, resistivity and diamagnetic effect in the BM model with an equilibrium distorted by RMP, which is stable for ideal BMs. Similar to the resistivity, the hyper-resistivity is also destabilizing for the BMs, but RMPs make the mode spectrum of the BMs destabilized by the hyper-resistivity move towards the low toroidal mode number side on the flux surface with a safety factor slightly larger than the RMP resonance safety factor, where the growth rates of the BMs destabilized by the resistivity decrease due to RMP. When both the hyper-resistivity and the resistivity are considered, there is a sort of competitive relationship between them in determining the properties of BMs. If either of the hyper-resistivity term and the resistivity term is much larger than the other one, the instability of BMs is mainly determined by the larger one, and the effect of the smaller one is masked. The destabilizing mechanisms of the hyper-resistivity and the resistivity on BMs are similar, namely, the diffusion and dissipation of current and magnetic field weaken the stabilizing effect of magnetic field line bending. The research results may be important for understanding the enhancement of plasma transport and the mechanism of small edge localized mode (ELM) during ELM control with RMP.

Soft H-L back transitions by applying resonant magnetic perturbations in the low q 95 EAST plasmas

Controlled ‘soft’ H-L transitions with a simultaneous ramp-down of plasma density and stored energy, generated by applying resonant magnetic perturbations (n = 2 RMPs), relevant to the control of ITER terminations, are achieved in the EAST tokamak. These H-mode plasmas are run at median electron densities and a low safety factor q 95 ( q95=3.5 –4.0) under neutral beam injection (NBI) dominant heating. During a slow ramp in the RMP current the internal transport barrier for the electron density collapses at the beginning and the edge transport barrier for the electron density collapses later. Before the controlled H-L back transitions, the plasma stored energy W MHD is linearly correlated with the core line-averaged density ⟨ne⟩ . These controlled H-L back transitions ensue from the collapse of the edge transport barrier and at a similar energy confinement time τeH-L∼48 ms. These H-L transitions are not sensitive to the NBI power but are very sensitive to the fueling rate and ramp-up rate of the RMP current.

Isochronous island bifurcations driven by resonant magnetic perturbations in tokamaks.

Recent evidence shows that heteroclinic bifurcations in magnetic islands may be caused by the amplitude variation of resonant magnetic perturbations in tokamaks. To investigate the onset of these bifurcations, we consider a large aspect ratio tokamak with an ergodic limiter composed of two pairs of rings that create external primary perturbations with two sets of wave numbers. An individual pair produces hyperbolic and elliptic periodic points, and its associated islands, that are consistent with the Poincaré-Birkhoff fixed-point theorem. However, for two pairs producing external perturbations resonant on the same rational surface, we show that different configurations of isochronous island chains may appear on phase space according to the amplitude of the electric currents in each pair of the ergodic limiter. When one of the electric currents increases, isochronous bifurcations take place and new islands are created with the same winding number as the preceding islands. We present examples of bifurcation sequences displaying (a) direct transitions from the island chain configuration generated by one of the pairs to the configuration produced by the other pair, and (b) transitions with intermediate configurations produced by the limiter pairs coupling. Furthermore, we identify shearless bifurcations inside some isochronous islands, originating nonmonotonic local winding number profiles with associated shearless invariant curves.