Resistive Wall Mode Stability Research Articles

Theory based recommendations to the resistive wall mode stability studies in tokamaks

The problem of the plasma stability against the resistive wall modes is considered from two sides, theoretical and experimental. The main subject is the dispersion relation and its verification, which is commonly understood as a comparison of the predicted and observed stability thresholds. As in the conventional magnetohydrodynamics, the growth rate γ and the angular rotation frequency ω of the mode are found from the energy balance with account of some dissipation in the plasma, additional to the resistive losses in the vacuum vessel wall. The resulting relations are integral, which allows the same γ and ω with different integrands. It is shown explicitly that only two fitting parameters are needed for getting a perfect agreement of such results with measured γ and ω. This explains why all attempts with so-called kinetic relations have been good in that. This also reveals the reason for the earlier finding [A. M. Garofalo, Fusion Sci. Technol. 48, 918 (2005)] that a number of models provided the stability regardless of the type of dissipation as long as the dissipation was sufficiently large. It is shown here that such “degeneracy” is a general property. One consequence is that a similar success with any model cannot guarantee its validity, and none of them can be recommended to ITER immediately. It is also explained that the edge harmonic oscillations can be a promising candidate for testing the dissipation channels missing in the kinetic dispersion relations.

The theory of kinetic effects on resistive wall mode stability in tokamaks

Tokamak fusion plasmas benefit from high pressures but are then susceptible to modes of instability. These magnetohydrodynamic (MHD) modes are macroscopic distortions of the plasma, but certain collective motions of individual particles can provide stabilizing effects opposing them. The presence of a resistive wall slows the mode growth, converting a kink to a resistive wall mode (RWM). A kinetic MHD model includes Maxwell's equations, ideal MHD constraints, and kinetic effects included through the pressure tensor, calculated with the perturbed drift-kinetic distribution function of the particles. The kinetic stabilizing effects on the RWM arise through resonances between the plasma rotation and particle drift motions: precession, bounce, and transit. A match between particle motions and the mode allows efficient transfer of energy that would otherwise drive the growth of the mode, thus damping the growth. The first approach to calculating RWM stability is to write a set of equations for the complex mode frequency in terms of known quantities and then to solve the system. The “energy principle” approach, which has the advantage of clarity in distinguishing the various stabilizing and destabilizing effects, is to change the force balance equation into an equation in terms of changes of kinetic and potential energies, and then to write a dispersion relation for the mode frequency in terms of those quantities. These methods have been used in various benchmarked codes to calculate kinetic effects on RWM stability. The theory has illuminated the important roles of plasma rotation, energetic particles, and collisions in RWM stability.

Mutual Induction Caused by IVCC Currents on Quench Detection Circuits of the KSTAR TF Coils

The Quench Detection System (QDS) for the Toroidal Field (TF) coils and the Poloidal Field (PF) coils made of Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn or NbTi cable-in-conduit conductors is using Wheatstone bridges to compensate induced voltages, which are generated by electrical currents of the superconducting coils and a plasma, on the quench detection circuits of the Korea Superconducting Tokamak Advanced Research (KSTAR) device. On the other hand, the KSTAR device is equipped with In-Vessel Control Coils (IVCCs), which consist of 16 segmented windings made of normal conductors, for fast plasma position control, field error correction, and resistive wall mode stabilization. Electrical currents of the middle Field Error correction Coil (FEC) in a part of the IVCCs have strong mutual induction on the quench detection circuits of the TF coils due to the paths of the FEC's conductors, and the middle FEC currents, which had unusually long and very steep ramps, raised an emergency protection sequence of the TF coils in a KSTAR plasma experiment. Quench detection circuits only using traditional Wheatstone bridges are insufficient to cancel out such a mutual induction; whereas, the mutual induction can be numerically compensated in a theoretically straightforward calculation.

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.

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.

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.

Influence of Off-Axis Neutral Beam Injection on Resistive Wall Mode Stability

Investigated are the effects of energetic particles (EPs), arising from off-axis neutral beam injection, on the resistive wall mode (RWM) instability in tokamaks. The analytic results for a cylindrical plasma show that EPs contribute the strongest kinetic damping to the RWM, as the deposition radius approaches the peak location of the mode eigenfunction. Toroidal computations are also carried out utilizing the MARS-K code, which includes EPs with anisotropic equilibrium distribution in the particle pitch angle space. These self-consistent numerical results confirm the analytic finding, that the RWM growth rate decreases as the peak of the EPs’ radial density profile approaches the maximum of the mode displacement. This study thus demonstrates the possibility of the RWM stabilization by the off-axis neutral beam injection in tokamak experiments.

Analytic investigation of combined effects of anisotropic thermal transport and energetic particles on stability of resistive plasma resistive wall mode

The combined effects of anisotropic thermal transport and trapped energetic particles (EPs) on the stability of the resistive plasma resistive wall mode (RPRWM) are investigated by an energy-principle based analytical model. The results qualitatively confirm that of a recent toroidal modeling study [Bai et al., Phys. Plasmas 27, 072502 (2020)], in which the thermal transport can stabilize the RPPWM depending on the parameters of both the plasma equilibrium and energetic particles. The analytical model predicts a complete stabilization of the RPRWM in highly resistive plasmas, at sufficiently high EPs' pressure, and finite plasma flow. The stabilizing effect of thermal transport originates from its enhancement of energy dissipations associated with both the resistive layer and the trapped energetic particles.

Model predictive control of resistive wall mode for ITER

Active feedback stabilization of the dominant resistive wall mode (RWM) for an ITER H-mode scenario at high plasma pressure using infinite-horizon model predictive control (MPC) is presented. The MPC approach is closely-related to linear-quadratic-Gaussian (LQG) control, improving the performance in the vicinity of constraints. The control-oriented model for MPC is obtained with model reduction from a high-dimensional model produced by CarMa code. Due to the limited time for on-line optimization, a suitable MPC formulation considering only input (coil voltage) constraints is chosen, and the primal fast gradient method is used for solving the associated quadratic programming problem. The performance is evaluated in simulation in comparison to LQG control. Sensitivity to noise, robustness to changes of unstable RWM dynamics, and size of the domain of attraction of the initial conditions of the unstable modes are examined.

Toroidal modeling of anisotropic thermal transport and energetic particle effects on stability of resistive plasma resistive wall mode

Effects of anisotropic thermal transport on the linear stability of the resistive plasma resistive wall mode (RPRWM) are investigated by the magnetohydrodynamic-kinetic hybrid code MARS-K [Liu et al., Phys. Plasmas 15, 112503 (2008)], including the kinetic contribution from energetic particles (EPs). It is found that thermal transport can further stabilize the RPRWM in the presence of drift kinetic contributions from EPs. This is different from the fluid model, which always predicts destabilization of the mode by thermal transport. Furthermore, the thermal transport effect is found to amplify the role played by an adiabatic term, associated with the radial distribution of EPs' birth energy, in modifying the mode stability as well as the mode eigenfunction. The shape of the equilibrium profiles of EPs, in particular that of the temperature, is also found to strongly affect the mode stabilization. This profile effect is more pronounced in the absence of thermal transport. MARS-K computations show that the stabilizing effect by thermal transport is more likely to occur at slower plasma rotation and lower EP energy.

Active Control System for Stabilization of Resistive Wall Mode in the Low-aspect-ratio RFP RELAX

Active Control System for Stabilization of Resistive Wall Mode in the Low-aspect-ratio RFP RELAX

Matrix-Based Rational Interpolation for New Coupling Scheme Between MHD and Eddy-Current Numerical Models

In this article, a matrix-based Pade rational interpolation is used to couple a 3-D eddy-current code with a linear magneto-hydrodynamic (MHD) solver. This approach is a general methodology viable for multiphysics problems involving the coupling of an electromagnetic model with another nonalgebraic physical model, which has to be solved in a certain region of space. The matrix-based Pade interpolation has been applied to a typical plasma physics problem of modeling the plasma response to external perturbation, providing an accurate and reliable mathematical model viable for the feedback stabilization of resistive wall modes (RWMs) in fusion plasmas. The choice of matrix-based Pade interpolation gives a reliable approach for the considered problem and can be viewed as a convenient formalism for the coupling strategy in this class of multi-physics problems.

Resistive wall mode physics and control challenges in JT-60SA high scenarios

The superconducting tokamak JT-60SA is being built in Naka (Japan) under the Broader Approach Satellite Tokamak Programme jointly by Europe and Japan, and under the Japanese national programme. JT-60SA has an important supporting mission for the development of fusion energy. It will help in both the exploitation of ITER and in the definition of an optimized DEMO design. The focus of this work is set on high scenarios, in which kink-like instabilities (e.g. one or more resistive wall modes) are potentially unstable and possibly lead to disruptions. As a fundamental step to ensure the safe realization of high plasmas, modeling activities are being carried out for MHD stability and control. The drift-kinetic damping model in particular will be considered in the present work, with a stability study in Scenario 5-like plasmas carried out with MARS-F/K. Resistive wall mode (RWM) stability is found with this model for low plasma rotation and precession drift resonance with thermal ions. The dependence on normalized and flow profile is discussed. The challenge of active control is also addressed, taking advantage of the set of RWM control coils that JT-60SA will install. A dynamic simulator, based on the CarMa code, has been developed for feedback control modeling. A demonstration of this tool is given for one of the aforementioned plasmas. Stabilization of the most unstable RWM is achieved within basic power limits. Potential applications, results and latest development of this tool are discussed.

Toroidal modeling of resistive wall mode stability and control in HL-2M tokamak

Effects of toroidal plasma flow, magnetic drift kinetic damping as well as feedback control, on the resistive wall mode instability in HL-2M tokamak are numerically investigated, using the linear stability codes MARS-F/K (Liu et al 2000 Phys. Plasmas 7 3681, Liu et al 2008 Phys. Plasmas 15 112503). It is found that the precession drift resonance damping due to trapped thermal particles ensures a robust passive stabilization of the n = 1 (n is the toroidal mode number) RWM in the 2 MA double-null advanced plasma scenario designed for HL-2M, provided that the toroidal flow speed is not too fast: . With two rows of magnetic control coils designed for HL-2M, the optimal poloidal location for the RWM stabilization is found to be . Toroidal modeling also shows that the plasma flow damping, drift kinetic damping and magnetic feedback can be arranged to synergistically stabilize the RWM in HL-2M, by tuning the feedback gain phase and/or including derivative actions in the control loop. The numerical results obtained by MARS-F/K are qualitatively well re-produced by an analytic single-pole model.

Feedback stabilization of ideal kink and resistive wall modes in tokamak plasmas with negative triangularity

Active control of the ideal external kink mode and the resistive wall mode (RWM) is numerically investigated using the MARS-F code (Liu et al 2000 Phys. Plasmas 7 3681), for a reactor relevant tokamak plasma shaped with negative triangularity (NTR). Magnetic coils are used as the actuators of the control system. An ideal feedback system (i.e. with no time delays), located inside the vacuum vessel, is shown to be capable of stabilizing the external kink mode and moderately increasing the ideal-wall beta limit by up to 10%. Despite the rather different plasma boundary shape as compared to the conventional D-shaped plasma, the optimal poloidal location of the active coils is still the low-field-side of the torus. The eddy currents in the wall may enhance or cancel the control field produced by active coils depending on the poloidal location of the active coils, thus improving or deteriorating the feedback performance. For a single row of active coils, the optimal poloidal width is about 50° for the RWM stabilization, for the NTR plasmas considered in this study. With two rows of coils, optimization of the feedback gain phasing helps to substantially improve the RWM control. The control performance experiences jumps as the radial location of the active coils is shifted across the poloidal sensor location, as shown in both MARS-F computations and by an analytic model.

Optimal control techniques for resistive wall mode feedback in tokamaks

DIII-D experiments show that a new, advanced algorithm enables resistive wall mode (RWM) stability control in high performance discharges using external coils. DIII-D can excite strong, locked or nearly locked external kink modes whose rotation frequencies and growth rates are on the order of the magnetic flux diffusion time of the vacuum vessel wall. Experiments have shown that modern control techniques like linear quadratic Gaussian (LQG) control require less current than the proportional controller in use at DIII-D when using control coils external to DIII-D’s vacuum vessel. Experiments were conducted to develop control of a rotating n = 1 perturbation using an LQG controller derived from VALEN and external coils. Feedback using this LQG algorithm outperformed a proportional gain only controller in these perturbation experiments over a range of frequencies. Results from high experiments also show that advanced feedback techniques using external control coils may be as effective as internal control coil feedback using classical control techniques.

Toroidal Modeling of RWM Feedback in the Presence of Control Voltage Saturation and Sensor Noise

Systematic, multiple initial value simulations are performed for a toroidal plasma using the recently updated MARS-F code in order to understand how the resistive wall mode (RWM) can be feedback controlled in the presence of control coil voltage saturation and/or sensor noise. The former renders the control nonlinear, thus generally requiring initial value computations for toroidal plasmas. This numerical study complements and confirms the key results from a previously analytic investigation of the RWM feedback with power saturation for a cylindrical plasma [Li et al., Physics of Plasmas, Vol. 19, 012502 (2012)]. Moreover, simulation results reveal a linear trend between the maximum tolerable sensor noise level and the degree of relaxing the control coil voltage saturation requirement, up to a certain level of noise, corresponding to a noise-to-signal ratio of about 25%. Beyond this level, further relaxing the control voltage saturation limit does not lead to increased sensor noise tolerance for the RWM stabilization.

Application of benchmarked kinetic resistive wall mode stability codes to ITER, including additional physics

Leading resistive wall mode (RWM) stability codes MARS-K [Liu et al., Phys. Plasmas 15, 112503 (2008)] and MISK [Hu et al., Phys. Plasmas 12, 057301 (2005)] have been previously benchmarked. The benchmarking has now been extended to include additional physics and used to project the stability of ITER in a realistic operating space. Due to ITER's relatively low plasma rotation and collisionality, collisions and non-resonance rotational effects were both found to have little impact on stability, and these non-resonance rotational effects will also not self-consistently affect the ITER RWM eigenfunction. Resonances between thermal ions and electrons and the expected level of ITER toroidal rotation were found to be important to stability, as were alpha particles, which are not in rotational resonance. MISK calculations show that without alpha particles, ITER is projected to be unstable to the RWM, but the expected level of alphas is calculated to provide a sufficient level of stability.