Resistive Wall Mode Research Articles

An extended variational method for the resistive wall mode in toroidal plasma confinement devices

The external-kink stability of a toroidal plasma surrounded by a rigid resistive wall is investigated. The well-known analysis of Haney and Freidberg is rigorously extended to allow for a wall that is sufficiently thick that the thin-shell approximation does not necessarily hold. A generalized Haney–Freidberg formula for the growth-rate of the resistive wall mode is obtained. Thick-wall effects do not change the marginal stability point of the mode but introduce an interesting asymmetry between growing and decaying modes. Growing modes have growth-rates that exceed those predicted by the original Haney–Freidberg formula. On the other hand, decaying modes have decay-rates that are less than those predicted by the original formula. The well-known Hu–Betti formula for the rotational stabilization of the resistive wall mode is also generalized to take thick-wall effects into account. Increasing wall thickness facilitates the rotational stabilization of the mode, because it decreases the critical toroidal electromagnetic torque that the wall must exert on the plasma. On the other hand, the real frequency of the mode at the marginal stability point increases with increasing wall thickness.

Loss of energetic particles due to feedback control of resistive wall mode in HL-3

Effects of three-dimensional (3D) magnetic field perturbations due to feedback control of an unstable ( is toroidal mode number) resistive wall mode (RWM) on the energetic particle (EP) losses are systematically investigated for the HL-3 tokamak. The MARS-F (Liu et al 2000 Phys. Plasmas 7 3681) code, facilitated by the test particle guiding center tracing module REORBIT, is utilized for the study. The RWM is found to generally produce no EP loss for co-current particles in HL-3. Assuming the same perturbation level at the sensor location for the close-loop system, feedback produces nearly the same loss of counter-current EPs compared to the open-loop case. Assuming however that the sensor signal is ten times smaller in the close-loop system than the open-loop counter part (reflecting the fact that the RWM is more stable with feedback), the counter-current EP loss is found significantly reduced in the former. Most of EP losses occur only for particles launched close to the plasma edge, while particles launched further away from the plasma boundary experience much less loss. The strike points of lost EPs on the HL-3 limiting surface become more scattered for particles launched closer to the plasma boundary. Taking into account the full gyro-orbit of particles while approaching the limiting surface, REORBIT finds slightly enhanced loss fraction.

Resistive wall tearing mode disruptions

Abstract This paper deals with resistive wall tearing mode (RWTM) disruptions. RWTMs are closely related to resistive wall modes. RWTMs are tearing modes whose linear and nonlinear behavior is strongly dependent on the resistive wall outside the plasma. The consequence for ITER, is that the thermal quench timescale could be much longer than previously conjectured. Active feedback stabilization is another possible way to mitigate or prevent RWTM disruptions. Simulations of RWTM disruptions are reviewed for DIII-D and MST. MST has a longer resistive wall time than ITER, and disruptions are not observed experimentally when MST is operated as a standard tokamak. Simulations indicate that the RWTM disruption time scale is longer than the experimental shot time. Edge cooling causes contraction of the current profile, which can destabilize RWTMs. The equilibria studied here have the q = 2 rational surface close to the edge of the plasma, and low current density between the q = 2 surface and the wall. A sequence of low edge current model equilibria has major disruptions only for a resistive, not ideal, wall, and edge q ⩽ 3.4 . This is consistent with regimes of tokamak disruptivity, suggesting that tokamak disruptions caused by edge cooling at low edge q could be RWTMs.

Validation study of RWM stability in DIII-D high-βN plasmas

Abstract The n = 1 (n is the toroidal mode number) resistive wall mode (RWM) stability is numerically investigated for two DIII-D high-β N discharges 176440 and 172461, utilizing the MARS-F (Liu et al 2000 Phys. Plasmas 7 3681) and MARS-K (Liu et al 2008 Phys. Plasmas 15 112503) codes. Systematic validation efforts are attempted, for the first time, for discharges with very slow or vanishing toroidal flow for a large fraction of the plasma volume. While gaining physics insights in accessing stable operation regime at β N exceeding the Troyon no-wall limit in these slow-rotation experiments, the predictive capability of fluid and non-perturbative magnetohydrodynamic-kinetic hybrid models for the RWM is further confirmed. The MARS-F fluid model, with a strong but numerically tunable viscosity mimicking ion Landau damping of parallel sound waves, finds complete stabilization of the n = 1 RWM in the considered DIII-D plasmas under the experimental flow conditions. Similarly, either full stabilization (for discharge 176440) or marginal stability (for discharge 172461) of the mode is computed by the MARS-K hybrid model, which is first-principle based without free model parameters. In particular, all drift kinetic resonances, including those of thermal and energetic particles, are found to synergistically act to marginally stabilize the RWM in discharge 172461. These MARS-F/K modeling results explain the experimentally observed stable operational regime in DIII-D, as far as the RWM stability is concerned. Extensive numerical sensitivity studies, with respect to the plasma toroidal flow speed as well as the radial location of the resistive wall, are also carried out to further support the validation study.

Plasma burn-mind the gap.

The programme to design plasma scenarios for the Spherical Tokamak for Energy Production (STEP), a reactor concept aiming at net electricity production, seeks to exploit the inherent advantages of the spherical tokamak (ST) while making conservative assumptions about plasma performance. This approach is motivated by the large gap between present-day STs and future burning plasmas based on this concept. It is concluded that plasma exhaust in such a device is most likely to be manageable in a double null (DN) configuration, and that high core performance is favoured by positive triangularity (PT) plasmas with an elevated central safety factor. Based on a full technical and physics assessment of external heating and current drive (CD) systems, it was decided that the external CD is provided most effectively by microwaves. Operation with active resistive wall mode (RWM) stabilization as well as high elongation is needed for the most compact solution. The gap between existing devices and STEP is most pronounced in the area of core transport, owing to high normalized plasma pressure in the latter which changes qualitatively the nature of the turbulence controlling transport. Plugging this gap will require dedicated experiments, particularly on high-performance STs, and the development of reduced models that faithfully represent turbulent transport at high normalized pressure. Plasma scenarios in STEP will also need to be such that edge localized modes (ELMs) either do not occur or are small enough to be compatible with material lifetime limits. The high current needed for a power plant-relevant plasma leads to the unavoidable generation of high runaway electron beam current during a disruption, where novel mitigation techniques may be needed. This article is part of the theme issue 'Delivering Fusion Energy - The Spherical Tokamak for Energy Production (STEP)'.

Plasma control for the step prototype power plant

In 2019 the UK launched the Spherical Tokamak for Energy Production (STEP) programme to design and build a prototype electricity producing nuclear fusion power plant, aiming to start operation around 2040. The plant should lay the foundation for the development of commercial nuclear fusion power plants. The design is based on the spherical tokamak principle, which opens a route to high pressure, steady state, operation. While facilitating steady state operation, the spherical design introduces some specific plasma control challenges: (i) All plasma current during the burn phase should to be generated through non-inductive means, dominated by bootstrap current. This leads to operation at high normalised plasma pressure βN with high plasma elongation, which in turn imposes effective active stabilisation of the vertical plasma position. (ii) The tight aspect ratio means very limited space for a central solenoid, imposing that even the current ramp up must be non-inductively generated. (iii) The compact design leads to extreme heat loads on plasma facing components. A double null design has been chosen to spread this load, putting strict demands on the control of the unstable vertical plasma position. (iv) The heat pulses associated with unmitigated ELMs are unlikely to be acceptable imposing ELM free operation or active ELM control. (v) To reduce and spread heat loads, core and divertor radiation and momentum loss has to be controlled, aiming to operate with simultaneously detached upper and lower divertors. (vi) High pressure operation is likely to require active resistive wall mode (RWM) stabilisation. (vii) The conductivity distribution in structures near the plasma must be carefully selected to reduce the growth rates for the vertical instability and the RWM without damping the penetration of the of magnetic fields from active control coils too much. This article describes the initial work carried out to develop a STEP plasma control system.

Resistive wall mode and fishbone mode in ITER steady state scenario: roles of fusion-born alphas and plasma flow

Drift-kinetic effects of fusion-born alpha particles on the n= 1 (n is the toroidal mode number) resistive wall mode (RWM) is numerically investigated for a recent design of the ITER 10 MA steady state plasma scenario, utilizing a magneto-hydrodynamic (MHD)-kinetic hybrid toroidal model. While the fluid theory predicts unstable RWM as the normalized plasma pressure β N exceeds the no-wall Troyon limit and with the mode growth rate monotonically increasing with β N, inclusion of the drift-kinetic contribution of trapped alphas qualitatively modifies the behavior by stabilizing the mode at high β N. In fact, a complete stabilization of the n= 1 RWM up to the ideal-wall Troyon limit is found. On the other hand, another unstable branch—the alpha-driven n = 1 fishbone mode (FB)—is identified in the high-β N regime, with the mode frequency matching that of the toroidal precession frequency of trapped alphas. Fast plasma toroidal flow however helps mitigate the FB instability. Kinetic stabilization of the RWM and flow stabilization of the (alpha-triggered) FB result in an enhancement of β N from the design value of 3.22–3.52 for the ITER scenario considered, while still maintaining stable plasma operation against the aforementioned MHD instabilities.

Plasma rotation and diamagnetic drift effects on the resistive wall modes in the negative triangularity tokamaks

It was found previously that the negative triangularity (NT) configuration is more MHD-unstable for low n modes than the positive triangularity (PT) case, although the situation is reversed for intermediate n modes and the NT configuration becomes more stable for intermediate n modes ( n=3−10 ) (Zheng et al 2021 Nucl. Fusion 61 116014). Here, n is the toroidal mode number. In this work, we extend the studies to include the rotation effects, as well as the diamagnetic drift effects, to see how the resistive wall modes (RWMs) in the NT configuration are affected as compared with the PT configuration. This is particularly motivated by noting that the wall interface with the plasma is quite different between the NT and PT configurations. It affects the plasma rotation and diamagnetic drift effects on the low n RWM. We consider the DIII-D-NT-experiment equilibrium reconstructed by the EFIT code. Based on the equilibrium g-file, the extended equilibria are constructed with the VMEC code by varying the beta values while keeping the pressure and poloidal current flux profiles basically unchanged. The bootstrap current contribution to the equilibria is taken into account with the Sauter formula. The MHD stability is then computed using the AEGIS code with the rotation and diamagnetic drift effects taken into account. We found that, although the NT configuration is less stable for n = 1 MHD modes, the rotation and diamagnetic drift stabilization effects on RWMs are more effective in the NT configuration than in the PT one. Note that even in the PT case, the stabilization of RWMs by the rotation and kinetic effects is critical. Because the low-n RWMs in the regular NT case are more unstable, the rotation and diamagnetic drift stabilization effects found in this research are important for the NT tokamak concept.

Variable-spectrum mode control of high poloidal beta discharges

DIII-D experiments demonstrate that high pressure, broad current profile equilibria can be accessed in the high poloidal beta regime by optimizing the MHD mode control poloidal spectrum. A novel, variable spectrum (VS) magnetic feedback scheme implemented using the DIII-D internal non-axisymmetric coils (I-coils) facilitated access to reduced internal inductance ℓi operation above the no-wall beta limit compared with both no feedback and fixed spectrum feedback. In addition, the VS feedback helped avoid beta collapses caused by marginally unstable resistive wall mode activity. The lower and upper I-coil rows were configured in two independent feedback loops, allowing the feedback field’s poloidal spectrum to vary and track changes in the plasma mode structure as the edge safety factor q 95 varied from 11 to 6 during the discharges. The q 95 dependence of the measured phase difference between the lower and upper I-coil rows during VS feedback is qualitatively compatible with ideal MHD simulations of the least-stable plasma kink mode and with plasma response simulations that included kinetic modifications to ideal MHD. The VS feedback approach is a straightforward way to improve resilience to variations in mode structure that occur as plasma parameters change. The demonstrated expansion of the operating space to lower ℓi is expected to improve the coupling of the plasma kink mode to external fields and beneficial wall eddy currents, and is compatible with high bootstrap fraction operation.

Role of electrostatic perturbation on kinetic resistive wall mode with application to spherical tokamak

A more complete non-perturbative magnetohydrodynamic (MHD)-kinetic hybrid formulation is developed by including the perturbed electrostatic potential δφ in the particle Lagrangian. The fluid-like counter-parts of the hybrid equations, in the Chew-Goldberger-Low high-frequency limit, are also derived and utilized to test the new toroidal implementation in the MARS-K code. Application of the updated non-perturbative hybrid model for a high-β spherical tokamak plasma in MAST finds that the perturbed electrostatic potential generally plays a minor role in the n = 1 (n is the toroidal mode number) resistive wall mode instability. The effect of δφ is largely destabilizing, with the growth rate of the instability increased by several (up to 20) percent as compared to the case without including δφ. A similar relative change is also obtained for the kinetic-induced resonant field amplification effect at high-β in the MAST plasma considered. The updated capability of the MARS-K code allows quantitative exploration of drift kinetic effects on various MHD instabilities and the antenna-driven plasma response where the electrostatic perturbation, coupled to magnetic perturbations, may play important roles.

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.

Experimental investigations on mechanisms of RMP-induced intrinsic rotations at EAST

Plasma spontaneous rotation significantly influences confinement performance and stability in tokamaks. Effectively inducing this rotation is essential for stabilizing resistive wall modes (RWMs) and ensuring the stable operation of the International Thermonuclear Experimental Reactor (ITER). Recent experiments on the Korea Superconducting Tokamak Advanced Research (KSTAR) device demonstrated that resonant magnetic perturbations (RMPs) can induce neoclassical toroidal viscosity (NTV) torque under certain conditions, successfully driving plasma rotation. Similarly, an increase in plasma rotation in the direction of the plasma current following RMP application has been observed on the Experimental Advanced Superconducting Tokamak (EAST). However, unlike the KSTAR findings, NTV torque simulations for EAST are two orders of magnitude lower than experimental measurements, suggesting additional mechanisms beyond NTV may be driving the observed plasma rotations. To investigate these mechanisms, momentum balance, causality, and statistical analyses have been performed at EAST. An increase in rotation velocity has been found to correlate with significant changes in the <i> <b>E</b> × <b>B</b> </i> flow, matching the RMP-induced torque distribution. This alignment suggests that residual stress, arising from variations in <i> <b>E</b> × <b>B</b> </i> shear, may drive the observed rotation increases. The effects of stochastic fields on multi-scale turbulence are proposed as a possible explanation for correlations between <i> <b>E</b> × <b>B</b> </i> velocity and toroidal rotation. Stochastic fields appear to enhance the inertia of large-scale turbulence while driving small-scale turbulence to maintain quasi-neutrality. The resulting turbulent Reynolds stress, generated by small-scale turbulence, may account for the observed <i> <b>E</b> × <b>B</b> </i> velocity increases during RMP application. Statistical analysis further highlights the importance of island width in understanding the threshold RMP current in ramping-up RMP experiments, supporting the conclusion that turbulence-driven <i> <b>E</b> × <b>B</b> </i> shear-related residual stress is the key mechanism driving plasma rotation following RMP application.

Model based optimal magnetic feedback control of multiple resistive wall modes with discrete coil and sensor arrays

A model-based optimal control method for multiple resistive wall mode (RWM) feedback stabilization has been developed and tested in plasma experiments at the EXTRAP T2R reversed field pinch (RFP) device. The controller is designed to target issues that arise in connection with RWM magnetic feedback stabilization systems based on discrete control coil and sensor arrays in tokamak and reversed field pinch devices. Multi-mode control capabilities in these systems is limited due to coupling of modes induced by the control system. The coupling originates from the generation of side-band control field harmonics and from aliasing of multiple harmonics in the sensor measurements. These couplings naturally leads to a multiple-input, multiple-output (MIMO) control problem. A model based state space controller has been designed based on a relatively simple physics model of the RWM plasma response. The physics model, which is applicable for the high aspect ratio RFP, is the basis for Fourier decoupling of the MIMO control problem into a set of single-input, multiple-output (SIMO) systems using the discrete Fourier transform (DFT). The linear, time-invariant physics model allows for the design of a state space model with states representing physical quantities; in this case the Fourier harmonics of the radial field at the resistive wall. Since the states cannot be directly measured, a Kalman filter is used for estimation of the states from the aliased sensor array measurements. A linear–quadratic (LQ) optimal state controller has been implemented. Design parameters, such as the LQ control cost function state weights and the Kalman filter input error covariances have been used to optimize the control operation in various ways. The controller has enhanced multi-mode control capabilities compared to earlier designs. For example it allows the prioritizing of suppression of one of the multiple magnetic field Fourier harmonics produced by a given control current DFT component. The controller has been tested in plasma experiments at EXTRAP T2R device, utilizing a newly installed extended sensor array, and the enhanced capabilities for multiple RWM feedback stabilization has been demonstrated.

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.

Interplay of plasma resistivity and rotation on β limits in free boundary diverted tokamaks

A plasma resistivity-β driving mechanism aimed at explaining the appearance of long wavelength global instabilities in free boundary high-β tokamak plasmas with a divertor is presented. These perturbations resemble very closely the resistive wall mode phenomenon. Performing a proper toroidal analysis, we show that the magnetohydrodynamic stability is worsened by the interplay of plasma β and resistivity. By modelling the effect of a magnetic separatrix through a careful positioning of the resonant surfaces, we find that in an ideal plasma wall effects are effectively screened, so that the ideal β limit becomes independent of the wall position/physics. A lower wall dependent critical β is found if plasma resistivity is allowed. We find that global stability can be improved with a toroidal flow, small enough not to induce equilibrium modification. The rotation stabilisation effectiveness depends upon the proximity of the plasma equilibrium parameters to the resistive marginal boundary.

Design and manufacturing of resistive wall mode control coil of JT-60SA

Resistive wall mode control coils (RWMCs) will be installed in the vacuum vessel of JT-60SA. Since 200 °C baking of vacuum vessel on JT-60SA is performed to remove the impurity in the plasma facing components, in-vessel components must be made with heat-resistant materials such as metal and ceramic or must be cooled with water. We looked for the heat-resistant organic insulator for JT-60SA RWMC and performed the heat resistant test for several resins. However, no resin passed the test (Sukegawa et al., 2015). We again performed the heat resistant test of several organic insulator in the circumstances without air and finally found that the some Bismaleimide–Triazine (BT) resin has enough heat resistance without air. We designed the eight-turn RWMC with the BT resin. Based on this design, the specification of RWMC and power supply requirement are decided. For the design of RWMC, the finite element (FEM) analysis of electromagnetic force during disruption and thermal stress during baking and operation were performed. Manufacturing of the RWMC has already launched.

On the use of error field correction coils in JET

This work describes the usage of Error Field Correction Coil (EFCC) system [Barlow I. et al. 2001 Fusion Eng. Des. 58–59 189], which is a set of 4 coils located external to the vessel of the JET device, with the aim of introducing non-axisymmetric n = 1 magnetic field perturbations in various targeted plasma experiments. Besides being used to characterize and correct the intrinsic error field, the EFCCs system has been exploited to i) probe plasma stability in high-βN regimes through the MHD spectroscopy technique, allowing the identification of resistive-wall mode stable operational scenarios, ii) study radiation asymmetry when testing the shattered pellet injector as the prime candidate for ITER disruption mitigation system, and iii) control edge localized modes, permitting a reduction in heat fluxes and carbon erosion of the divertor target plates.

The Hodge decomposition of shell current on the Keda Torus eXperiment device

The Hodge decomposition is a valuable tool for uniquely decomposing total currents on the composite shell into three types: inductive current, halo current, and harmonic current, each with its specific physical meaning. During plasma disruptions, halo currents appear, essential for studying the wall’s thermal load and electromagnetic force. Furthermore, understanding halo currents is crucial for improving the existing methodologies by removing their effects on equilibrium reconstructions and instability analyses based on boundary magnetic probe data. On the Keda Torus eXperiment (KTX) device, radial and tangent halo currents can be simultaneously provided to locate the contact region during a minor disruption experimentally. Additionally, experimental results demonstrate that, in addition to the occurrence of halo current during minor disruption events, halo current is already present simultaneously with the generation of inductive current when a resistive wall mode exists. For devices that lack the capability to measure the two-dimensional shell current distribution on the entire shell, we propose a method to estimate inductive and halo currents only using a set of shell currents along the toroidal direction. This technique is demonstrated on the KTX device and provides an overall good approximation of the inductive and halo current distribution.

General dispersion relations for resistive wall modes in tokamaks

The dispersion relation for the resistive wall modes (RWMs) is derived without the use of the trial function bHF proposed in S. W. Haney and J. P. Freidberg [Phys. Fluids B 1, 1637 (1989)] for the magnetic perturbation b outside the plasma. Another difference from the Haney–Freidberg (HF) approach is the incorporation of non-ideal effects in the plasma description. These enter the final result through the energy functional and affect the external solution for b through the boundary conditions only. This allows to perform the derivations in a general form without constraints on the dissipation mechanisms in the plasma. Then, the main mathematical difficulties are related to the description of the energy flow outside the plasma. This part of the task is presented with details allowing easy comparisons with the reference HF case. Being universally applicable, the resulting dispersion relation covers the existing variants, including those based on the so-called kinetic approaches. It shows that, because of its integral nature, the same predictions can be expected from various models for the plasma. Another conclusion is that, with a non-ideal contribution, just one or two free parameters would be enough to get agreement with experimental data on the plasma stability boundary. This, however, does not guarantee that the same choice of the fitting coefficients will be similarly efficient on other devices. The proposed relations provide a unified approach to the problem of plasma stability against RWMs.

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.