Resistive Wall Mode Research Articles

MST resistive wall tearing mode simulations

The Madison Symmetric Torus (MST) is a toroidal device that, when operated as a standard tokamak, does not have major disruptions. Unlike most tokamaks, the MST plasma is surrounded by a close fitting highly conducting wall, with a resistive wall penetration time two orders of magnitude longer than in JET or DIII-D, and three times longer than in ITER. The MST can operate with edge , unlike standard tokamaks. Simulations presented here indicate that the MST is unstable to resistive wall tearing modes (RWTMs) and resistive wall modes (RWMs). They could in principle cause disruptions, but the predicted thermal quench (TQ) time is much longer than the experimental pulse time. If the MST TQ time were comparable to measurements in JET and DIII-D, theory and simulations predict that disruptions would have been observed in MST. This is consistent with the modeling herein, predicting that disruptions are caused by RWTMs and RWMs. In the low regime of MST, the RWTM asymptotically satisfies the RWM dispersion relation. The transition from RWTM to RWM occurs smoothly at , where are poloidal and toroidal mode numbers.

Destabilizing effects of edge infernal components on resistive wall modes in advanced tokamak scenarios

The stability of the n = 1 resistive wall modes (RWMs) dominated by the pressure-driven infernal components is investigated using the ideal magnetohydrodynamics (MHD) code AEGIS for the advanced tokamak scenarios. Here, n is the toroidal mode number. In the advanced tokamak scenarios, due to the large fraction of bootstrap current contribution, the profile of safety factor q is deeply reversed in magnetic shear in the central core region and locally flattened within the edge pedestal. Consequently, the pressure-driven infernal components develop in the corresponding flat-q regions of both core and edge. However, the edge infernal components dominate the n = 1 RWM structure and lead to lower βN limits for the advanced tokamak scenarios. In the framework of ideal MHD, the edge rotation is found the most critical to the stabilization due to the dominant influence of the edge infernal components, which should be maintained sufficiently large in magnitude and range in order for the rotation alone to fully suppress the n = 1 RWM in typical advanced tokamak scenarios.

Occam's razor on the mechanism of resistive-wall-mode-induced β limits in diverted tokamaks.

External kink modes, believed to be the drive of the β-limiting resistive wall mode, are strongly stabilized by the presence of a separatrix. We thus propose a novel mechanism explaining the appearance of long-wavelength global instabilities in free boundary high-β diverted tokamaks, retrieving the experimental observables within a physical framework dramatically simpler than most of the models employed for the description of such phenomena. It is shown that the magnetohydrodynamic stability is worsened by the synergy of β and plasma resistivity, with wall effects significantly screened in an ideal, i.e., with vanishing resistivity, plasma with separatrix. Stability can be improved by toroidal flows, depending on the proximity to the resistive marginal boundary. The analysis is performed in tokamak toroidal geometry, and includes averaged curvature and essential separatrix effects.

Simultaneous stabilization and control of the n = 1 and n = 2 resistive wall mode

DIII-D experiments demonstrate simultaneous stability measurements and control of resistive wall modes (RWMs) with toroidal mode numbers n = 1 and n = 2. RWMs with n > 1 are sometimes observed on DIII-D following the successful feedback stabilization of the n = 1 mode, motivating the development of multi-n control. A new model-based multi-mode feedback algorithm based on the VALEN physics code has been implemented on the DIII-D tokamak using a real-time GPU installed directly into the DIII-D plasma control system. In addition to stabilizing RWMs, the feedback seeks to control the stable plasma error field response, enabling compensation of the typically unaddressed DIII-D n = 2 error field component. Experiments recently demonstrated this algorithm’s ability to simultaneously control n = 1 and n = 2 perturbed fields for the first time in a tokamak, using reactor relevant external coils. Control was maintained for hundreds of wall-times above the n = 1 no-wall pressure limit and approaching the n = 1 and n = 2 ideal-wall limits. Furthermore, a rotating non-zero target was set for the feedback, allowing stability to be assessed by monitoring the rotating plasma response (PR) while maintaining control. This novel technique can be viewed as a closed-loop extension of active MHD spectroscopy, which has been used to validate stability models through comparisons of the PR to applied, open-loop perturbations. The closed-loop response measurements are consistent with open-loop MHD spectroscopy data over a wide range of β N approaching the n = 1 ideal-wall limit. These PR measurements were then fit to produce both VALEN and single-mode stability models. These models allowed for important plasma stability information to be determined and have been shown to agree with experimentally observed RWM growth rates.

Disruption event characterization and forecasting in tokamaks

Disruption prediction and avoidance is a critical need for next-step tokamaks, such as ITER. Disruption Event Characterization and Forecasting (DECAF) research fully automates analysis of tokamak data to determine chains of events that lead to disruptions and to forecast their evolution allowing sufficient time for mitigation or complete avoidance of the disruption. Disruption event chains related to local rotating or global magnetohydrodynamic (MHD) modes and vertical instability are examined with warnings issued for many off-normal physics events, including density limits, plasma dynamics, confinement transitions, and profile variations. Along with Greenwald density limit evaluation, a local radiative island power balance theory is evaluated and compared to the observation of island growth. Automated decomposition and analysis of rotating tearing modes produce physical event chains leading to disruptions. A total MHD state warning model comprised of 15 separate criteria produces a disruption forecast about 180 ms before a standard locked mode detector warning. Single DECAF event analyses have begun on KSTAR, MAST, and NSTX/-U databases with thousands of shot seconds of device operation using from 0.5 to 1 × 106 tested sample times per device. An initial multi-device database comparison illustrates a highly important result that plasma disruptivity does not need to increase as βN increases. Global MHD instabilities, such as resistive wall modes (RWMs), can give the briefest time period of warning before disruption compared to other physics events. In an NSTX database with unstable RWMs, the mode onset, loss of boundary and current control, and disruption event warnings are found in all cases and vertical displacement events are found in 91% of cases. An initial time-dependent reduced physics model of kinetic RWM stabilization created to forecast the disruption chain predicts instability 84% of the time for experimentally unstable cases with a relatively low false positive rate. Instances of the disruption event chain analysis illustrate dynamics including H–L back transitions for rotating MHD and global RWM triggering events. Disruption warnings are issued with sufficient time before the disruption (on transport timescales) to potentially allow active profile control for disruption avoidance, active mode control, or mitigation.

Control of resistive wall modes in the spherical tokamak

In this work, the MARS-F/K codes (Liu et al 2000 Phys. Plasmas 7 3681; Liu et al 2008 Phys. Plasmas 15 112503) are utilized to model the passive and active control of the n= 1 (n is the toroidal mode number) resistive wall mode (RWM) in a spherical tokamak (aspect ratio A = 1.66). It is found that passive stabilization of the RWM gives a relatively small increase in normalized beta above the no-wall limit, relying on toroidal plasma flow and drift kinetic resonance damping from both thermal and energetic particles. Results of active control show that with the flux-to-voltage control scheme, which is the basic choice, a proportional controller alone does not yield complete stabilization of the mode. Adding a modest derivative action, and assuming an ideal situation without any noise in the closed-loop, the RWM can be fully stabilized with the axial plasma flow at 5% of the Alfvén speed. In the presence of sensor signal noise, success rates exceeding 90% are achieved, and generally increase with the proportional feedback gain. On the other hand, the required control coil voltage also increases with feedback gain and with the sensor signal noise.

Vertical displacement oscillatory modes in tokamak plasmas

Vertical displacement normal modes in shaped tokamak plasmas are studied analytically, based on the reduced ideal-magnetohydrodynamic model. With the help of quadratic forms, and using the appropriate eigenfunction for vertical displacements with toroidal mode number $n=0$ and dominant elliptical-angle mode number $m=1$ , a dispersion relation is derived, including the effects of ideal or resistive walls through a single parameter, $D_w(\gamma )$ , which is, in general, a function of the complex eigenfrequency $\gamma = -{\rm i}\omega$ . For the resistive-wall case, the dispersion relation is cubic in $\gamma$ . One root corresponds to the well-known, non-rotating resistive-wall vertical mode, growing on the resistive-wall time scale. The other two roots are weakly damped by wall resistivity, but oscillate with a frequency below the poloidal Alfvén frequency, which makes them immune to continuum damping, but subject to possible instability due to resonant interaction with fast ions.

Numerical study on influences of parallel sonic wave damping, precession, and bounce resonances on resistive wall modes in CFETR

Adopting an 11 MA steady-state reversed magnetic shear equilibrium of the China Fusion Engineering Test Reactor, the influence of parallel sonic wave damping, precession, and bounce resonances on the resistive wall mode (RWM) at different plasma pressures and plasma toroidal rotations is numerically investigated using the MARS-K code. We find that the parallel sonic wave damping, precession, and bounce resonances have damping effects on the RWM. The RWM is stabilized by the parallel sonic wave damping at low plasma pressure. At the two q = 3 rational surfaces, the RWM is the most unstable, but the precession resonance mainly occurs at one of the q = 3 rational surfaces, so the RWM cannot be stabilized. In addition, the precession resonance and bounce resonance occur simultaneously, and there are two roots. One is the precession resonance root, and another is the bounce resonance root. The bounce resonance has a stabilizing effect on the RWM.

Comment on “Certain clarifications on the resistive wall mode theorem and extensions” [Phys. Plasmas 29, 024502 (2022)

Comment on “Certain clarifications on the resistive wall mode theorem and extensions” [Phys. Plasmas <b>29</b>, 024502 (2022)

Experimental characterization and modelling of the resistive wall mode response in a reversed field pinch

Model-based control algorithms have potential advantages for resistive wall mode (RWM) feedback control. In this study, a physics model of the RWM response to externally applied perturbation fields is validated against experiments in a reversed field pinch (RFP). The experimental characterization of the RWM plasma response is performed in the EXTRAP T2R device by the excitation of nonaxisymmetric perturbation magnetic fields utilizing an external array of saddle coils for RWM control. The modelling and experimental validation is carried out with an extended sensor array, resolving a wider spectrum of RWM compared to earlier studies, covering the relevant poloidal and toroidal modes for this high aspect ratio RFP device. In addition to the nonresonant unstable modes, which are the primary target of RWM feedback control, this spectrum also includes a wide range of resonant modes. The validated resistive magnetohydrodynamics (MHD) model includes the passive stabilization effect on these modes from intrinsic plasma rotation. The inclusion of resistivity and plasma rotation in the present model provides a substantially better agreement between modelled and experimental growth rates than that observed in earlier studies using the ideal MHD model. The present model provides a realistic description of the plasma response for both nonresonant and resonant modes, which is both relatively simple and compatible with the computing capabilities and latency limitations encountered in practical implementations of model-based control algorithms.

Loss of energetic particles due to resistive wall mode instability in ITER

Effects of an unstable n = 1 (n is the toroidal mode number) resistive wall mode (RWM) on the energetic particle (EP) confinement and loss are numerically investigated, for an ITER steady state scenario with 10 MA plasma current and 5.3 T toroidal field. The eigenfunction of the RWM is computed, with the associated three-dimensional magnetic field perturbation superposed with the 2D equilibrium field for tracing the EP drift orbits. Considered are mono-energetic EPs at 0.5 MeV and 1 MeV for deuterium ions, and 3.5 MeV for fusion-born alphas, with a range of distribution in the particle pitch angle. Modeling finds that less than 20% of EPs can be lost to the limiting surface in ITER assuming a source distribution uniform in minor radius, due to an unstable RWM that produces 100 Gauss poloidal field perturbation at the outboard mid-plane just inside the (effective) resistive wall surface. On top of the initial prompt drift orbit loss for counter-current EPs, the RWM induced particle loss occurs on a one second time scale, which is comparable to the RWM growth time in ITER. The ‘wetted’ area, due to the lost EPs striking the limiting surface, is generally found to be large due to the RWM. This is a favorable prediction for ITER. The loss distribution in the poloidal angle is more uniform for co-current EPs. Counter-current EPs experience outward orbit drift when launched from the low-field side, and tend to more often hit the bottom region of the limiting surface.

Numerical study of the effect of kinetic damping on resistive wall modes with plasma toroidal rotation in CFETR

Herein, the effect of kinetic damping on the resistive wall mode (RWM) instability in the China nuclear fusion engineering test reactor (CFETR) is numerically studied using the magnetohydrodynamic resistive spectrum-kinetic (MARS-K) code. A CFETR hybrid equilibrium with a plasma current of Ip = 13 MA is adopted. The sum of the electron diamagnetic, plasma rotation, and mode frequencies increases at q = 2 rational surface with increasing plasma rotation frequency. When the sum of the frequencies is less than 0, kinetic damping has a stabilizing effect on RWM. In contrast, when the sum of the frequencies is greater than 0, the kinetic damping has a destabilizing effect on RWM, causing a second unstable branch to appear. Additionally, the effects of plasma pressure and wall distance on the two unstable branches are investigated. The mode frequency is excited with increasing plasma pressure and wall distance. Consequently, the first branch is stabilized and the second branch is destabilized.

Stabilization of resistive wall mode and improved plasma performance in a low‐aspect‐ratio reversed field pinch by a single mode control power supply system

AbstractStabilization of resistive wall modes (RWMs) is one of the important issues in magnetic fusion research. In the reversed field pinch (RFP), the number of unstable RWMs becomes smaller by lowering the aspect ratio (A), the ratio of the minor to major radius of the device. In REversed field pinch of Low‐Aspect ratio eXperiment (RELAX), whose aspect ratio is 2, unstable m/n = 1/2 RWM was stabilized by a single mode control power supply system with improvements of discharge performance. In this paper we report new results with modified power supply system in which magnetic boundary condition near the poloidal gaps is controlled. The modified power supply system is designed to stabilize the most unstable m/n = 1/2 mode by use of the saddle coil array covering the whole torus with eight (8) power supplies. The results show that the discharge duration is improved from ~ 3.0 ms to ~ 4.0 ms, limited by the capability of the iron core in RELAX device. Stabilization of the dominant RWM with the resultant improved plasma performance by a single mode control power supply system shows one of the advantages of a low‐aspect‐ratio RFP concepts.

Stabilization of Resistive Wall Mode and Improved Plasma Performance in a Low-aspect-ratio Reversed Field Pinch by a Single Mode Control Power Supply System

Stabilization of resistive wall modes (RWMs) is one of the important issues in magnetic fusion research. In the reversed field pinch (RFP), the number of unstable RWMs becomes smaller by lowering the aspect ratio (A), the ratio of the minor to major radius of the device. In REversed field pinch of Low-Aspect ratio eXperiment (RELAX), whose aspect ratio is 2, unstable m/n = 1/2 RWM was stabilized by a single mode control power supply system with improvements of discharge performance. In this paper we report new results with modified power supply system in which magnetic boundary condition near the poloidal gaps is controlled. The modified power supply system is designed to stabilize the most unstable m/n = 1/2 mode by use of the saddle coil array covering the whole torus with eight (8) power supplies. The results show that the discharge duration is improved from ∼ 3.0 ms to ∼ 4.0 ms, limited by the capability of the iron core in RELAX device. Stabilization of the dominant RWM with the resultant improved plasma performance by a single mode control power supply system shows one of the advantages of a low-aspect-ratio RFP concepts.

Certain clarifications on the resistive wall mode theorem and extensions

In a previous paper by V. D. Pustovitov [Phys. Plasmas 24, 112513 (2017)], it is claimed that the proofs of the “Resistive-Wall-Mode theorem” by Pfirsch and Tasso [Nucl. Fusion 11, 259 (1971)] and extensions of that theorem for time dependent wall resistivity and equilibrium plasma flow are not detailed and that there are limitations restricting their applicability. In response, we provide here pertinent detailed derivations, showing that the proofs of the above-mentioned theorems are rigorous and complete, unlike the considerations of V. D. Pustovitov [Phys. Plasmas 24, 112513 (2017)], which ignore the self-adjointness of the operator ∇×∇× and the fact that the force operator in the linearized ideal MHD momentum equation remains self-adjoint in the presence of equilibrium flows.

Predicting resistive wall mode stability in NSTX through balanced random forests and counterfactual explanations

Recent progress in the disruption event characterization and forecasting framework has shown that machine learning guided by physics theory can be easily implemented as a supporting tool for fast computations of ideal stability properties of spherical tokamak plasmas. In order to extend that idea, a customized random forest (RF) classifier that takes into account imbalances in the training data is hereby employed to predict resistive wall mode (RWM) stability for a set of high beta discharges from the NSTX spherical tokamak. More specifically, with this approach each tree in the forest is trained on samples that are balanced via a user-defined over/under-sampler. The proposed approach outperforms classical cost-sensitive methods for the problem at hand, in particular when used in conjunction with a random under-sampler, while also resulting in a threefold reduction in the training time. In order to further understand the model’s decisions, a diverse set of counterfactual explanations based on determinantal point processes (DPP) is generated and evaluated. Via the use of DPP, the underlying RF model infers that the presence of hypothetical magnetohydrodynamic activity would have prevented the RWM from concurrently going unstable, which is a counterfactual that is indeed expected by prior physics knowledge. Given that this result emerges from the data-driven RF classifier and the use of counterfactuals without hand-crafted embedding of prior physics intuition, it motivates the usage of counterfactuals to simulate real-time control by generating the β N levels that would have kept the RWM stable for a set of unstable discharges.

Resistive wall mode stability and resonant field amplification in MAST high beta plasma

The n = 1 (n is the toroidal mode number) resistive wall mode (RWM) instability and the resonant field amplification (RFA) due to a stable RWM response are numerically investigated for an MAST high-pressure plasma scenario, utilizing the MARS-F Liu et al (2000 Phys. Plasmas 7 3681) and MARS-K Liu et al (2008 Phys. Plasmas 15 112503) codes, for the purpose of understanding the potential RWM behavior in MAST-U plasmas. Ideal kink stability analysis identifies a target plasma, with parameters similar to that of the reference equilibrium reconstructed from an MAST high-pressure discharge, that accesses the RWM regime. The unstable n = 1 RWM for the target equilibrium is subject to strong damping by the plasma toroidal flow and/or the drift kinetic effects from thermal particles. As a result, the mode is found to be stable under the experimental flow conditions, or even without flow stabilization if drift kinetic stabilization is included. The stability prediction is robust against variation of the assumed resistive wall minor radius. Active magneto-hydrodynamic (MHD) spectroscopy modeling, using the magnetic coils designed for controlling the edge localized modes (ELMs) in MAST-U as the antenna, shows strong RFA due to a stable RWM response in the target plasma. Maximal amplification, of 6–7 times larger than the applied vacuum field within the plasma, is obtained assuming a coil phasing of 120–180 degrees between the upper and lower rows of the ELM control coils. The MHD-kinetic hybrid model predicts generally higher RFA than the fluid model, in particular near the low-field and high-field sides of the plasma boundary surface. The MARS-F/K modeling thus shows that the RWM in MAST-U is subject to strong flow and kinetic stabilization, but can nevertheless be detected by active MHD spectroscopy.

Intermediate n mode stability in the negative triangularity tokamaks

There is renewed interest in negative triangularity (or reversed triangularity) tokamaks after the TCV and DIII-D experiments have shown that the low-mode confinement in the negative triangularity configuration can achieve the high-mode-level confinement without edge localized modes. This particularly addresses the divertor heat load issue for tokamak high beta confinement. Previous investigations have found, in agreement with experimental observations, that the beta limit for low-n (macroscopic) modes is somewhat lower in the negative triangularity case than in the positive one. In this work, we study higher-n (mesoscopic) modes. Using equilibria modeling of those used in the DIII-D negative triangularity experiment, the numerical results show that the intermediate-n modes with the resistive wall are actually more stable for the negative triangularity case than the positive triangularity case. This is consistent with the experimental observations of the lower level of turbulence transport in the frequency range of resistive wall modes in the negative triangularity case and can also be explained physically.

Impact of negative triangularity plasma shaping on the n = 0 resistive wall mode in a tokamak

The axisymmetric (n = 0) resistive wall mode instability is numerically investigated for the negative triangularity plasma shape, which has shown several benefits in terms of improved confinement time and fusion engineering. To evaluate the shape effects, we modified a MHD instability code AVSTAB (Axisymmetric Vertical STABility), which calculates the marginally controllable elongation in a simplified feedback capability parameter. The plasma characteristics (poloidal beta and internal inductance) as well as the geometric effects (wall shape and plasma location) are important to determine the instability. In contrast to positive triangularity, the higher poloidal beta provides more instability drive for the negative triangularity because of the higher Shafranov shift and the higher elongation of the inner flux surface of the MHD equilibrium. Non-conformal wall shapes to the plasmas (positive triangularity wall and negative triangularity plasma) are found to be rather helpful to stabilize the n = 0 mode, unless the plasma is too close to the walls at the nulls for the opposite triangularity.

Suppression of MHD modes with active phase-control of probe-injected currents

Active phase-control of probe-injected current is shown to both suppress and amplify long-wavelength rotating magnetohydrodynamic instabilities in the HBT-EP tokamak. Four probes are connected in quadrature and energized to drive non-axisymmetric currents through the edge of the tokamak, creating magnetic perturbations comparable to previously-studied saturated kink modes or resonant magnetic perturbations that are generated by an external control coil array. Measurements of the magnetic perturbations from the probe-injected currents determine a set of current-carrying helical filaments used to model active feedback control of resistive wall modes. These experiments suggest current-injection feedback may be an effective alternative to external control coils for control of RWMs and other long-wavelength kink-like modes at the edge of tokamaks.