AAPPS Bulletin
> home > Review and Research
Origin of the Gap Between Theoretical Model and Experimental Results of the MHD Instabilities in Fus
Hyeon K. Park
File 1 : Vol30_No6_Review And Research-76~92.pdf (0 byte)

DOI: 10.22661/AAPPSBL.2020.30.6.76

Origin of the Gap Between Theoretical Model
and Experimental Results of the MHD Instabilities
in Fusion Plasma Physics

Hyeon K. Park
Ulsan National Institute of Science and Technology, Ulsan, Korea


The theory and modeling of the complex dynamics of high temperature plasma in tokamak devices must be validated against precise measurements with comprehensive visualization diagnostics so that fully validated modelling can be used for stable operation of the plasmas. A new and advanced two-dimension (2-D) electron cyclotron emission imaging (ECEi) system was developed for this need. Through comparative studies with the newly uncovered physics from the ECEi system, theoretical models either have gained high confidence or have substantially improved. For the sawtooth instability, the long discarded, full reconnection model has been vindicated and axisymmetry of the 1/1 kink mode right before the crash time is critical for and may have relevancy to the violent kink instability of magnetic filament ropes in a solar flare. For the neoclassical tearing mode (NTM) instability, the 2-D ECEi data can determine the critical parameters such as Δ' and ωc with high confidence. The observed anisotropic distribution of the turbulence and flow in the presence of the 2/1 island is validated by the modelled potential and gyro-kinetic calculation of the turbulence. In a study of the edge localized mode (ELM), validation of the ELM structure and the dynamics of the ELM-crash cycle have provided an opportunity to improve the theoretical model. The dynamics of a broadband turbulence induced by the resonant magnetic perturbation (RMP) in ELM-crash suppression experiments may shed light on the physics of coupling between the broadband turbulence and ELMs, growth/decay of the ELMs and enhanced transport at the pedestal region.


Starting from the early 1970s, the theory and modelling of magnetohydrodynamic (MHD) instabilities [1, 2] in tokamak plasmas have rapidly expanded to interpret many exciting new observations from experiments in tokamak devices. Since the early research on MHD instabilities in fusion plasma was performed with one-dimension, (1-D) conventional diagnostics, the limited and/or simple information may have prevented full understanding of disruptive behaviors. The ultimate goal of study is to achieve preemptive control of harmful MHD instabilities for steady state operation in fusion devices. In order to achieve this goal, it is imperative for the theoretical modeling to improve through a vigorous verification and validation process with other models and diagnostic information. Without such a comprehensive iterative process in verification among theories and validation with the measurement, the theory and modeling can be fragmented and then is only useful for post-interpretation for the experimental observations. The validation process requires precise information regarding a wide range of relevant plasma parameters with sufficient spatial and temporal resolution. In spite of sophisticated diagnostic systems employed in modern fusion plasma research since the early 70's, the measured plasma information is not quite sufficient for full validation of the theory and modeling due to the hostile environment in tokamaks. The MHD instability is a large-scale perturbation with symmetry on flux surfaces in the linear stage and rapidly become explosive for a short time scale. Therefore, the validation process of the MHD instabilities in the linear stage has been relatively successful in the stationary sawtooth, neoclassical tearing modes (NTMs), and edge localized mode (ELM) instabilities. However, there is no guarantee of symmetry during the explosive growth period. Here, the validation process has to introduce many assumptions on the generically symmetric MHD model. The theoretical model has to account for dynamic changes of the geometry and mode structure through measurement. As the degree of asymmetry of the MHD mode and/or flux geometry is not trivial to measure with conventional 1-D diagnostics [3], it is imperative to measure the evolution of the MHD mode in 2-D with adequate spatial and temporal resolution. The gap between theoretical models and experimental outcomes can be closed when reliable diagnostic information can guide the validation process step-by-step. Effective control of the harmful MHD instabilities that influence the stability of the plasma can be achieved with the fully validated models. Therefore, multi-dimensional measurements with adequate spatial and time resolution are critical so that the physics validation can be performed with precision and tight constraints against the model. The 2-D electron cyclotron emission imaging (ECEi) system [4] was developed for this reason in the majority of tokamaks and the newly uncovered physics information from the ECEi systems [5] has provided an opportunity to improve theoretical models for tokamak plasmas so that preemptive stability control is feasible in the future.


Fig. 1: Internal views of three large tokamak devices (TFTR, JT-60U and JET, from left to right). These devices were constructed to test a "break-even" condition. DT experiments were performed only at TFTR and JET. Pictures are from https://w3.pppl.gov/tftr/, and https://en.wikipedia.org/wiki/Joint_European_Torus

This paper is organized as follows: in section two, a brief review is given regarding progress in confinement improvement and in understanding of MHD instabilities in tokamak plasmas. In section three, shortcomings of conventional diagnostic techniques for study of harmful MHD instabilities is introduced together with the progress of a multi- dimensional diagnostic tool that could enhance the validation process. In section four, examples of new findings of the harmful MHD instabilities with the 2-D ECEi diagnostic system are compared with the present understanding of the theoretical model and a summary follows.


Following the first demonstration of high electron temperature measurement in the T3 tokamak of the former Soviet Union in the late 1960's, many tokamak devices were constructed throughout the world to harness magnetic fusion energy. Prior to the tokamak devices, the stellarator program, which was first developed in the 1950's at Princeton, USA, faced many difficulties in achieving good confinement and control of MHD instabilities. Due to the relative simplicity of the tokamak geometry as compared to that of the stellarator [6], empirical progress regarding tokamak plasma evolved significantly and rapid progress of the theoretical understanding of the cross field energy transport physics and MHD instabilities followed. In the late 1970's, confidence in theoretical modeling and experimental results from various tokamak devices inspired the construction of three large tokamaks: Tokamak Fusion Test Reactor (TFTR), USA; Joint European Torus (JET), UK; and JT-60U (Japan Torus-60 Upgrade), Japan. The goal at the time was to demonstrate a break-even condition (fusion energy gain factor: Q~1, where the Q is the ratio of output power and input power) as shown in Fig. 1. Here, TFTR was the first tokamak that performed a Deuterium/Tritium[DT] experiment with Q~0.3; JET, with Q~0.7, followed. JT-60U's result projected a DT equivalent Q of ~1.25 based on a Deuterium/Deuterium[DD] experiment. In terms of steady state tokamak operation, superconducting devices [7] such as KSTAR (Korea Superconducting Tokamak Advanced Research) and Experimental Advanced Steady State [EAST] were developed after the large tokamak era and JT-60U has been transformed into a superconducting device, JT60SA [8], and is expect to lead the fusion science of steady state operation. The successful operation of these three large devices eventually led to the construction of ITER (formerly the International Thermonuclear Experimental Reactor), a reactor that is anticipated to demonstrate fusion power of ~500 MW, which is equivalent to Q~10. While performance of tokamak plasma has made great progress, the design and construction of tokamak devices have been predominantly based on empirical scaling laws and the confinement improvement was justified with an appropriate transport physics model. Note that the improved stored energy of the tokamak plasmas from small devices to large devices is largely due to the volume dependence as shown in the empirical scaling law (ITER 98P) for the energy confinement time (𝜏E) in Eq. 1 [9]. Here, strong dependence of 𝜏E on R: major radius, κ and ε: elongation and aspect ratio factor, and IP: plasma current, is notable.


Historically, tokamak plasma operation started with a relatively low energy confinement mode (L-mode) where the edge pedestal height was low. The shape of the plasma evolved from a circular shape, where the plasma was in contact with the material surface ("limiter" plasma), to an elongated shape with a diverted plasma with an X-point at the divertor area, The divereted plasmas has a higher confinement mode (H-mode) [10] with the energy confinement time which is almost twice higher compared to that of the L-mode. Another improved confinement mode is the internal transport barrier (ITB) mode [11], which was first demonstrated at TFTR (supershot regime) with high central heating/fueling and ITB discharges are demonstrated as high Ti discharges in many other tokamaks. Here, the core confinement is significantly enhanced with the L-mode edge plasmas. The ITB mode and H-mode operations are vulnerable to internal instabilities such as the NTM instability and H-mode discharges are suffered from additional instabilities, such as ELMs.

It is well known that the essence of closed magnetic devices such as tokamaks and stellarators is the helical magnetic field line required for stable equilibrium. In tokamak plasma, the helically nested magnetic surface is generated by superposition of the applied toroidal magnetic field (BT) by external coils and the poloidal magnetic field (BP) induced by the driven toroidal plasma current (IP), as illustrated in Fig. 2. The degree of helicity proportional to (BP/BT) at fixed geometry (R, r, and κ, where R is the major radius, r is the minor radius and κ is the elongation factor of the nested flux surface) is characterized by the safety factor q(r) as shown in Eq. (2).


Most of the tokamak devices were designed and operated with a narrow range of helicity (~3<qedge<~7) where qedge is the q value at the edge of the plasma. The q dependence of the confinement time is not explicitly strong in the confinement scaling law. In practice, when the size parameters such as R and a are increased, BT and BP (or IP) also have to increase in order to maintain stability of the plasmas. This may be the reason why size dependence is dominant in scaling studies of the energy confinement in tokamaks, together with a strong IP dependence. It is notable that the scaling law exhibits a strong BT dependence for stellarators where the driven current (IP) is absent.


Fig. 2: (a) Schematic of magnetically confined plasma in a tokamak device. (b) Helically twisted magnetic field) (m=1 and n=5) is formed by both the toroidal field by external coils and poloidal field induced by the toroidal plasma current. Bv is the vertical field for positioning of the plasma.

The theory of MHD instability is largely based on Maxwell's equations and generalized Ohm's law and has been fairly well understood. The experimentally observed MHD instabilities in a linear stage (saturated linear stage) have been well matched with the simulation results from MHD models. However, the stage of sudden rapid growth of these instabilities that leads to a burst or disruption of the plasma, is often difficult to be modeled. In order to develop predictive capability in theoretical modeling for preemptive control of these harmful instabilities, fully validated theoretical models are essential. Among the MHD instabilities, the harmful ones are sawtooth instability inside the q~1 surface in the core, neoclassical tearing modes (NTM) (2/1 tearing mode) near the q~2 layer and the edge localized mode (ELM) (high m/n mode) at the pedestal of the H-mode plasma where the pressure gradient is extremely steep and the edge current profile is significantly modified by the bootstrap current.



Fig. 3: (a) Arrangement of the conventional 1-D ECE system for Te profile measurement. The system utilizes a single detector and a wideband sweeping local oscillator source for a single row of sampling volumes with a typical resolution of ~5 cm x ~5 cm. (b) Arrangement of the 2-D ECEi system with a quasi-optical 1-D vertical detector array with large optics (triplet lens system). Each detection element which consists of a Schottky diode and dipole antenna, is like a single mixer in the 1-D ECE system and a 2-D sampling volume is formed within the focal depth of the optical system. The down converted IF signal is split into 8 radial channels to form the radial profile of Te at a given vertical position.

In the course of studying the physics of MHD instabilities, various diagnostic tools [3] have been employed to measure the physical quantities that can influence stability and confinement of the tokamak plasma. To monitor current flow and pressure change in the plasma, precise measurement of the plasma current density (or safety factor profile) and pressure profile (ions and electrons) with adequate spatial and temporal resolution is critical for stability analysis of the MHD instabilities in tokamak plasmas. In general, measurement of the electron pressure profile is well established through the Thomson Scattering system [3], which is capable of measuring the electron temperature (Te) and density (ne) simultaneously. On the other hand, the ion density profile (ni) is deduced from the measured impurity profile with the measured ne and the ion temperature (Ti) profile is measured with the charge exchange spectroscopy of impurities such as "impurities such as carbon" assuming the main ions are in equilibrium with the impurity. Most importantly, local measurement of the growth and decay of the MHD modes must be achieved with high accuracy and adequate spatial and temporal resolution.

It is important to address the limits in measuring small quantities through a complex diagnostic system for the plasma current density. First, Faraday rotation [12-14] requires a double inversion process, since the measured Faraday rotation angle is a convolution of the plasma density and magnetic field along the path of the electromagnetic wave propagating through the plasma. However, intrinsic weaknesses of the polarimetry arise because the signal becomes extremely small near the magnetic axis, where the poloidal field (Bp) approaches zero, and because of uncertainty of the magnetic axis. Note that the q0 is proportional to the derivative of the measured Faraday rotation angle profile across the axis. Second, the nature of the motional Stark effect (MSE) [15-21] is a local measurement but the measured emission occurs along the chord of the optics and requires careful subtraction of the background signal along the chord. Here, the polarization of the emission is sensitive to the local electric field induced by the local magnetic field's direction and the velocity of the beam ions. Similar to the polarimetry case, the MSE measurement faces the same sensitivity issue near the magnetic axis, since the polarization angle of the 𝜋 component emission is proportional to the field line pitch angle which is zero on the axis. Systematic reduction of errors from the analysis is nontrivial near the axis.

Among the emission-based measurements, the electron cyclotron emission (ECE), which depends solely on the local Te, has been used to measure the electron temperature profile and its fluctuation [22-29]. An ECE measurement can provide fast temporal evolution of the local Te as long as the plasma is optically thick [30]. In that case, the emission intensity, I(ω), approaches to that of black body radiation and is proportional to Te as given by Eq. (3),


where ω is the radiation frequency, c is the speed of light and Te is the electron temperature. Here, the ECE frequency has a spatial dependence due to the radial dependence of the toroidal magnetic field, BT ∝ 1/R, where BT and R are the toroidal field and major radius of the tokamak plasma, respectively.


Fig. 4: (a) Arrangement of the KSTAR quasi 3-D ECEi system. Two toroidally separated (~23 degrees) ECEI systems are combined with an MIR system at KSTAR. ECEI-I, which is equipped with two views for simultaneous measurement at two poloidal planes (e.g. core/edge or high field side/low field side), is shown in the red box. The blue ECEi-II system (b) is added at the toroidal plane separated by 22.90 (b). Two sample images of the same ELM structure with different zoom factors at two toroidal locations (ECEi-I and ECEi-II) are shown. Here, the pitch angle, velocity and mode numbers can easily be calculated. Figures from Ref. 5.

Among the different techniques of ECE measurement, the heterodyne system yields the highest sensitivity with absolute calibration. A schematic of the typical arrangement of instruments required for a 1-D heterodyne ECE radiometer is shown in Fig. 3a. Here, emissions from the plasma on the mid-plane are collected by a single detector through optics. The detected emissions are split with adequate radial spacings and then they are down converted with local oscillator (LO) sources to measure the local Te.

Using the proven and robust ECE technique, it is feasible to develop a 2-D ECE imaging (ECEi) system for 2-D images of the fluctuation of Te with high spatial (e.g. ~1.0 cm × ~1.0 cm) and temporal (~ a few μs) resolution using a highly sensitive miniaturized detection system with advances in sub-millimeter technology [31]. The single detection element is replaced with a 1-D array detector where each detection element is vertically stacked as shown in Fig. 3b. As shown in this figure, the vertically extended large optical elements are employed to have a one-to-one mapping of the vertically resolved beam lines of the emissions from the plasma within the focal depth to each detection element in the vertical array through a mini-lens to collect the emissions effectively and simultaneously. Details regarding the first ECEi system is described in References [4]. Note that absolute calibration is feasible but in practice there are difficulties in calibrating all channels due to the variation in the local oscillator power at various frequencies. The processed image is therefore based on a relatively calibrated value (δTe = Te / <Te>) for each channel, where <Te> is the time-averaged value for a certain time zone. Following the first successful ECEi system [4], the ECEi system has become a standard advanced diagnostic system on tokamaks as well as stellarators [32-38]. At KSTAR, two ECEi systems were employed, as shown in Fig. 4a. The first ECEi system (ECEi-II) with two poloidal views and 24 vertical array detectors was commissioned in 2008. The second system (ECEi-II) with a single view, toroidally separated by 22.90, was added to form a semi three-dimensional (3-D) system along with the first system. The nominal view window is ~40 cm (vertical) x ~12 cm (radial) with a radial resolution of ~1.5 cm and a vertical zoom factor of ~3 (total of 192 channels). Time resolution can be adjusted by the digitizing speed, and the nominal operating time resolution is ~2 μsec. Two simultaneously measured images of an ELM from two edge toroidal views are illustrated in Fig. 4b. Important information such as the magnetic pitch angle, velocities, and self-consistent mode numbers can be comprehensively obtained, as illustrated in this figure.


Sawtooth Instability

Sawtooth instability is an internal disruption process of the m/n = 1/1 kink mode that occurs in the core (inside the q~1 surface) of the tokamak plasma with the characteristic slow rise of the core plasma pressure followed by a sudden crash. Despite being studied for a relatively long time, the basic physics of the sawtooth crash process has been disputed. Following the first observation of this instability [39], the full (or complete) reconnection model [40] based on the Sweet-Parker reconnection model [41] was proposed. In this model, the excess core current density and plasma pressure responsible for the 1/1 kink mode are fully removed within the characteristic time scale, 𝜏c = , where 𝜏r is the resistive time and 𝜏A is the Alfvén time.


Fig. 5: (a) Accumulated measurements of q0 for the last three decades. Measurements were mainly from polarimeters, MSEs, probes, etc. (b) The measured electron temperature and q0 by the MSE system at KSTAR are shown. The measured average <q0> value is ~1.0 and variation of the q0q) before and after the crash is ~0.06 with an error range of ±0.03. The figure is from Y. B. Nam, et al., Nucl. Fusion 58, 066009, 2018.

It is not surprising to find that the model was rejected, since the observed time scale of the sawtooth crash in tokamak plasmas was an order of magnitude faster than the proposed 𝜏c [42]. During the last four decades, numerous theoretical models were developed to explain the fast crash time: an earlier theory is the quasi-interchange mode model [43-45], which assumes that the q profile is flat at 1.0 inside the q~1 surface. The latest theory is the plasmoid model, [46] which has been popular in explaining the fast reconnection process in astrophysical plasmas and solar flares, and which has been introduced to explain the fast reconnection process in the sawtooth crash. A direct comparison between the measured partial 2-D images of the 1/1 kink mode/cold island and simulated images from various proposed models is possible [47-49]. The results demonstrated that the measured 2-D images are consistent with those from the full reconnection model and inconsistent with those from the quasi-interchange mode and plasmoid models, which may be feasible but are rare events. It is important to focus on the physics of the dominant event and to modify our understanding of the physics by allowing deviations from the dominant event.


Fig. 6: Excited resonant mode is shown when the current blip (dip in the q profile) is scanned from the center of the plasma to the edge of the q~1 using ECCD. In zone 1 (r/a<0.15), a hot spot in the core is observed. In zone 2 (0.1 < r/a < 0.22), the 2/2 mode is excited. In zone 3 (0.2 < r/a < 0.27), the 3/3 mode is observed. Near the q=1 region, a higher order mode is excited. The figure is from Y. B. Nam, et al., Nucl. Fusion 58, 066009, 2018.

The first q0 measurements [by Faraday rotation at TEXTOR (Tokamak Experiment for Technology Oriented Research), Germany, and MSE measurements at TFTR] of the sawtooth instability was well below ~1.0 (q0~0.8) before and after the crash. This result contradicted with the full reconnection model and was the trigger to develop a theory of the stable 1/1 kink mode with q0<1.0. As the measurements have accumulated, the value of q0 have spread from ~0.6 to ~1.1 as shown in Fig. 5b. The peak-peak variation of δq~0.05 is common for all measurements. Note that measurement of the relative change is more accurate than the absolute value. This small variation is consistent with the expected small current diffusion after the crash. The latest measurement of the q0 with the MSE system at KSTAR [50] was~1.0±0.03, as shown in Fig. 5b. Even if the measurement (<q0>~1.0) is correct, it is still difficult to validate the model, since the required absolute error of the diagnostics is too stringent to address that q0 is above ~1.0 right after the crash.


Fig. 7: Illustration of 2-D images of the fast crash process at the high (a) and low (b) field side of q~1 surface (black line) of the TEXTOR plasma where the center of the plasma is ~177 cm. The time trace is from (z=0) near the q~1 surface from both sides. A ballooning type of bulge with a clear "finger" is shown at both sides. Severe distortion (or harmonic generation) of the 1/1 kink mode prior the crash at both sides is shown. Figures are from H.K. Park, et al., Phys. Rev. Lett. 96, 195004, 2006.


Fig. 8: (a) The 2-D images of the "post-cursor" case at high field side are shown with the time trace of Te to demonstrate that the reconnection time scale is an order of magnitude longer compared to the fast reconnection events (TEXTOR data). Prior to the crash, the 1/1 kink mode is nearly symmetric (frame 1) and partial heat is transported to the mixing zone after the first crash (frame 2). The reconnected field lines of the remnant 1/1 kink mode are clearly illustrated in the frames 3 and 4. (b) The contour plot of Te illustrates that the 1/1 kink mode is connected to the q~1 surface with the reconnected field lines. (c) The measured reconnected field lines of the 1/1 kink mode at the high field side and cold island at the low field side are overlaid on the reconstructed crash model. Figures are from Ref. 5.

A controlled supplementary experiment [51], supported by earlier simulation [52] employing higher order tearing modes that is extremely sensitive to the background q0, successfully confirmed that q0>1.0 after the crash, as shown in Fig. 6. A test of the double tearing mode inside the q~1 surface, which is similar to the off-axis sawtooth crash of the double tearing mode near the q~2 surface [53], was designed. The observed tearing modes right after each crash event are well matched with the modes (2/2 and 3/3), with the highest growth rate from modeling for the q0 = 1.04 case, as illustrated in Fig.6. When q0 = 0.98, growth rate of the 1/1 kink mode is dominant. These experimental results confirm that the q0 after the crash is likely above 1.0 and this is consistent with the time evolution of the m=3 mode to m=1 mode before the crash [5]. Since the "full reconnection model" was developed based on symmetric cylindrical geometry, estimation of the crash time scale (𝜏c) is based on the helically symmetric 1/1 kink mode and the reconnection zone along the toroidal plane (i.e., 2-D nature). As shown in 2-D images of the crash process from both high and low field sides in Fig. 7, neither the observed 1/1 kink mode near the crash time nor the reconnection zone is axisymmetric. Distortion of the 1/1 kink mode and localization in the toroidal plane, which resembles the ballooning mode case [49, 54, 55], can be interpreted as higher harmonic Fourier components of the 1/1 kink mode; numerous 2-D measurements in other devices also supported this observation [56-58]. The time history of the 2-D images during the crash process suggests that non-axisymmetry of the 1/1 kink mode is an important characteristic of the dominant cases with a fast crash time. "Post-cursor oscillation" is a rare event of sawtooth oscillations [55, 59], as shown in Fig. 8a. After the first reconnection event, the 1/1 kink mode in a reconnected state is slowly decaying in the post-cursor oscillation. In a toroidally rotating system, the slowly decaying 1/1 kink mode in a reconnected state (post-cursor) appears as an oscillatory motion and one period represents one full toroidal rotation of the plasma. The measured 2-D image of the post-cursor oscillation shows new information that is not available from conventional diagnostics, as shown in Fig. 8. Here, a clearly symmetric 1/1 kink mode remains in a reconnected state for a long time after the first crash, as shown in Fig. 8a. The decaying oscillatory motion in 2-D shows that the reconnection zone is helically symmetric on the toroidal plane and the reconnection time scale is significantly slower than that of the dominant fast reconnection cases that we have studied. In Fig. 8b, a clear 2-D image shows the flow of the heat from the remaining 1/1 kink mode to outside of the q~1 layer along the field line through a wide reconnection zone (~7 cm). A reconstructed image of the reconnection process with the reconnected 1/1 kink mode at the high field side and cold island formation at the low field side is illustrated in Fig. 8c. Extensive analysis of the post-cursor oscillation with the 2-D images shows that the post-cursor case is consistent with the axisymmetric reconnection model used in the full reconnection model.


Fig. 9: (a) A crash event with a fast reconnection time is dominant in sawtooth crashes. They exhibit a highly distorted 1/1 kink mode (higher harmonics in poloidal and toroidal planes) and initial reconnection is likely on the tip of the "finger" as shown in the image from KSTAR (examples in Fig. 7a, 7b) (i.e., 3-D nature). (b) The crash time of the "post-cursor" case shown in Fig. 8a, is an order of magnitude slower as compared to that of the fast crash cases. The reconnection zone is much wider at the poloidal plane and it is toroidally axisymmetic (i.e., 2-D nature). The slow reconnection time case resembles the Sweet-Parker model and the fast reconnection time case fits to the Petschek model. Figures are from Ref. 5.

Two distinctively different reconnection patterns are compared in Fig. 9. As shown here, the reconnection zone of the axisymmetric case is long (~7 cm) (Fig. 9b) along the poloidal direction as compared to that of the "ballooning" non-axisymmetric case (<2 cm) (Fig. 9a), where the reconnection is likely induced at the tip of the "finger" as shown in this figure. The slow crash time scale observed in the "post-cursor" case (~8 ms) is consistent with 𝜏c of the full reconnection model, whereas the crash time of the dominant fast crash case is ~100μs. The common feature of the cases with a slow crash time is their 2-D nature (helically axisymmetric system) while that of the cases with a fast crash time is their 3-D nature (helically non-axisymmetric system). The two distinctive cases can be compared with the two well-known reconnection models: the Sweet-Parker and Petscheck models [41]. Physically the current sheet of the Sweet- Parker model much longer than that of the Petscheck model as shown in the middle of these figures. Note that the Petscheck model was introduced to explain the fast reconnection time which cannot be explained with the Sweet-Parker model.

Neo Classical Tearing (NTM) Instability

The next class of instabilities that occur near rational surfaces are the neoclassical tearing mode (NTM) instabilities with low m/n mode numbers (m/n=2/1, 3/1, 3/2, 4/1, 4/2, 4/3, …, where m and n are poloidal and toroidal mode numbers, respectively). NTM instabilities were first discovered at TFTR [60]. A schematic illustration of the positions and shapes of these NTMs for KSTAR is depicted in Fig. 10. In this figure, the rational surfaces (q = 2,3,4) are passing X-points and the middle of islands (O-points) of each NTM. This instability is excited due to the lack of the helical bootstrap current inside the island (O-point), where the pressure profile is flattened near the resonant rational surfaces (i.e. q = 2,3,4, ...). As the plasma β is further increased, the m/n=2/1 mode can be excited at the q~2 surface, where the β is the ratio of the plasma energy to the magnetic energy [61, 62]. Onset of this instability imposes a significant limit to the growth of the core plasma energy due to altered cross-field transport in the presence of the island. Rapid growth of the island above the critical size often leads to the slowing of mode rotation in the plasma, eventually locking to the conducting vessel, causing a disruption.


Fig. 10: A single null equilibrium is constructed with respect to the KSTAR vessel (left). Schematics of the position and shape of NTMs (m/n=2/1, 3/1 and 4/1) on the KSTAR equilibrium geometry. The dotted lines are rational surfaces with q=2, 3 and 4. Two figures of NTMs shown at different phases represent the O-point (left) and X-point (right) on the mid-plane, respectively.

Therefore, control mechanisms to maintain the island size below a critical size is essential for high β tokamak operation. The NTMs can be linearly stable and nonlinearly unstable and can be controlled with injection of a current inside the island to compensate for the loss of the helical current inside the flattened island. While control of the 2/1 mode has been empirically successful with the injection of a current in the island using an Electron Cyclotron Current Drive [ECCD] system [63, 64], the stability physics of the 2/1 mode has complex dependence on various plasma parameters and the cross-field transport has not been comprehensively validated yet. Comprehensive validation of the stability criteria of the 2/1 instability as well as the modified turbulence critical for the cross-field transport across the q~2 surface in the presence of the 2/1 island, has been attempted in the course of modeling studies. However, it is a non-trivial problem to solve this problem due to the lack of accurate diagnostics that can measure the dynamics of the 2/1 mode, the modified turbulence distribution and the flow shear with adequate spatial and temporal resolutions.

The change of the island size in time is expressed in terms of the classical linear stability index (Δ'), which can be positive or negative, and the destabilizing term from loss of the helical bootstrap current inside the island [65]. The dynamics of the stability of the 2/1 mode is well described by the modified Rutherford equation (MRE), as given in Eq. (4)


where ω is the island half width, a1 and a2 are flux geometry related coefficients, rs is the minor radius, 𝜏r is the current diffusion time, 𝜏s is the resistive time, ε is the inverse aspect ratio, βθ is the plasma poloidal beta and Lq and Lq are scale lengths of the safety factor and pressure profile, respectively. It is critical to determine the sign of Δ' and ωc with high confidence in this equation, since the first term containing Δ' is closely related to the equilibrium current profile and the second term is the destabilizing contribution stemming from the lack of the bootstrap current inside the island due to the flattened island. ωc is half of the width of the island and is relatively easy to determine experimentally. When the second term is significant (high poloidal beta and large island), the mode is referred to as a neoclassical tearing mode (NTM) and control of the NTM is critical for high performance plasmas. Since precise determination of the critical parameters like Δ' and ωc is key, many experiments have been performed previously with conventional 1-D diagnostics such as ECE and Thomson scattering systems but the results were not conclusive due to lack of spatial and time resolutions using conventional 1-D data. For the validation of theoretical models and smart control of the 2/1 mode, clear and speedy identification of key parameters such as the stability parameter (Δ') and the critical island width (ωc) of the 2/1 mode is essential. Therefore, it is important to test if the confidence level can be improved in determining these parameters with 2-D data and the first such attempt was made in a study of the 2/1 mode with 2-D ECEi data at KSTAR; the detailed analysis can be found in Ref. [63]. The analysis of Δ' is relatively straightforward and is deduced from the calculated magnetic flux function based on magnetic field diffusion.

Empirical understanding of the role of macroscopic MHD islands on limiting the core energy confinement as well as how they lead to disruption has to be supported by the comprehensive physical process of cross-field transport physics based on modified micro-turbulence in presence of the 2/1 island. In recent years, high frequency turbulence spectral measurement of Te, employing a correlation technique, has been routinely performed using 2-D ECEi data at KSTAR. Together with the measured macroscopic MHD fluctuation (i.e. 2/1 island) induced by the resonant magnetic perturbation (RMP), the measurement of small-scale turbulences and the 2/1 island has provided an opportunity to study multiscale interaction between macro-fluctuation and micro-turbulence [66]. The simultaneously measured macroscopic fluctuation of the 2/1 island and dynamics of micro-turbulences in the proximity of the island in a discharge with R0=180cm, a0=50cm, and q95~4.6 are illustrated in Fig. 11 [66].


Fig. 11: (a) The measured 2-D image of the 2/1 island induced by RMP is shown with the flattened Te profile inside the island. Separatrix with X and O points is shown in purple dotted lines and flattened Te profile is supported by the measured Te profile with 1-D ECE. (b) Examples of cross coherence of the Te fluctuation obtained using pairs of vertically adjacent ECEI channels inside the island, inner side and outer side of the 2/1 island are shown together with the summed coherence 2-D image. The fluctuation level is higher at X-point than at O-point. (c) The cross phase between two vertically adjacent ECEi channels with measured inner and outer regions of the 2/1 island is shown. The 2-D pattern velocity is measured using the coherent cross phase. The observed flow is stronger near the O-point than that of the X-point. Figures are from Choi, M.J., et al., Nucl. Fusion 57, 126058, 2017.


Fig. 12: a) The perturbed equilibrium potential calculated from XGC1 code in the presence of the 2/1 island, (b) the contours of micro-instabilities (TEM and ITG) around the magnetic island in the outer mid-plane, and (c) comparison of the ExB shearing rates at the O- and X-point of the magnetic island and the growth rates of the micro-instabilities. These results are consistent with the experimental results. Figures are from Kwon, J-M, Phys. of Plasma, 25, 052506, 2018.

The 2-D image of the modified Te profile in the presence of the 2/1 island shows a clear flattened 2/1 island in which the flat profile is supported by the measured Te profile with 1-D ECE and steepened gradient near the O-point on the inner side of the island and no change in gradient near the X-point are shown in Fig. 11a. The cross coherence of the Te fluctuation between two ECEI channels is calculated to estimate the coherent fraction of the Te fluctuation; examples are illustrated in Fig. 11b. The sum of the cross coherence is plotted in 2-D in this figure. The measured micro-turbulence of Te is highly inhomogeneous around the 2/1 island (i.e., both the inner and outer sides) as shown in this figure. Inside the island, the level of turbulence is almost non-measurable. In the inner side of the island, the turbulence has a broad spectrum and the level of micro-turbulence is stronger near the X-point and weaker near the O-point, despite the steepened gradient at the O-point side as shown in this figure. This observation suggests that there are other mechanisms for this strong asymmetry in this turbulence level, since the turbulence level should be higher at the steepened gradient region. On the outer side, the observed spectrum is narrow and the level of turbulence is higher near the X-point. On the other hand, the measured flow speed of the micro-turbulence is striking, as shown in Fig. 11c. Here, the cross phase of two adjacent ECEI channels is calculated to measure 2-D flow velocity in the laboratory frame as shown in this figure. The observed poloidal flow of the higher frequency spectrum is in the electron diamagnetic direction on the inner side and that of the lower frequency spectrum is in the ion diamagnetic direction on outer side of the island, as shown in cross phase analysis. More importantly, the level of poloidal flow shear, which mostly results from the E x B flow shear, increases toward the O-point. This is the opposite trend as compared to that of the fluctuation level, (i.e., the fluctuation level is strongest near the X-point rather than the O-point). The strong flow shear near the O-point may be responsible for the insignificant fluctuation level at the X-point. Over the critical values of vortex flow and fluctuation level, the 2/1 island becomes a transport channel of the electrons and can lead eventually to a disruption.

Global gyrokinetic simulations were carried out to understand the underlying physics of the measured anisotropy of the micro-turbulence and strong flow shear in presence of the stationary 2/1 island [67]. The global equilibrium E x B flow perturbed by the 2/1 island was calculated using X-point Gyrokinetic Code 1 [XGC1] code [68] as shown in Fig. 12a. Here, the E x B flow is significantly enhanced in the presence of the O- and X-points of the 2/1 island. It was found that the flow shear is maximum and minimum near the O- and X-point of the island, respectively. From global micro-instability analyses using the Gyro-Kinetic Plasma Simulation Program[gKPSP] code [69], it was found that the collisionless trapped electron mode (CTEM) and the ion temperature gradient (ITG) mode could be excited around the island as shown in Fig. 12b. This is quite consistent with the measured high frequency (CTEM) and low frequency spectrum (ITG) with opposite rotation direction. However, due to the strong shear of the E x B flow, a significant portion of the CTEM is suppressed in the region near the O-point, as shown in Fig. 12c. On the other hand, the flow shear around the X-point is not strong enough to stabilize ambient instabilities.

Edge Localized Mode (ELM) Instability

The "edge localized mode (ELM)" instability is a periodic bursting event observed routinely in a high pedestal pressure gradient region of the H-mode plasmas [70] and the underlying physics of the "ELM" is known as a crash event of a rapidly growing ideal MHD mode with intermediate to high toroidal mode number (n) with a coupled poloidal mode spectrum (m) at the pedestal region of the plasma where the pressure gradient is steepest and/or strong bootstrap current is abundant. For the ELM instability, a "peeling and ballooning" mode model, [71, 72] based on two driving energy sources for this instability has been developed, using the pressure gradient and current density at the edge. Validation of this model has been attempted with the ballooning and peeling boundary determined by experimental data and modeled mode numbers with various assumptions [71, 72]. Note that many critical parameters, such as the bootstrap current and pressure gradient, are non-trivial to be measured and there are limited validated dynamics of the internal MHD modes. While the measurement of pedestal pressure is well established, bootstrap current information is lacking due to difficulties in measurement at the edge and thus bootstrap current information has relied on model calculation. The most critical information comes from the dynamics of the ELM mode numbers. As the crash of the ELM mode was discovered by the Dα lights from the divertor region, the research on the ELM was dominated by Dα lights. The advent of the fast camera system captured a filamentary structure that is generally aligned along the helical magnetic field line that was used to address the mode numbers. Note that the camera image was also based on Dα lights from the interaction between the radially moving filaments and neutrals at the scrape-off layer (SOL) region (outside of the separatrix) at Mega Ampere Spherical Tokamak [MAST] as shown in Fig. 13. The measured filamentary structures in the inter-"ELM" period and L-mode and "ELM" phase with the intensity increasing as the mode number is lowered from the inter-"ELM" period, L-mode to the "ELM" phase are shown in this figure [73]. The dynamics of the filamentary structure with well-defined mode numbers provide a better physical quantity than Dα lights from the divertor region to build the physics basis of this instability. The 2-D ECEi system is capable to measure the dynamics of the ELM near the pedestal region; the term ELM represents the mode itself and "ELM-crash" will be used in the remainder of the paper to mean "ELM" in order to avoid confusion.


Fig. 13: The filamentary structures captured by a fast camera with high toroidal mode numbers at MAST. The fast camera image is the image of the Dα light, from interaction between a radially moving filament structure and neutrals outside of the separatrix. The filamentary structure exists in the (a) inter-ELM-crash period, (b) L-mode phase, and (c) ELM-crash phase. The intensity of the mode is plotted on the toroidal plane and the mode number moves from high to low as the intensity of the filament is increased. The figure is from Ayed, N. B. et al., Plasma Phys. control. Fusion, 51, 035016, 2009.

KSTAR plasma is ideal for studying ELM dynamics and the role of resonant magnetic perturbations (RMPs) in suppression/mitigation of the ELM-crash, since KSTAR is equipped with three unique features and capabilities [74]; 1) a higher degree of symmetry of the tokamak plasma compared to other devices due to small intrinsic error field (approximately an order of magnitude lower error field compared to other tokamaks) and low magnetic ripple [75], 2) three rows of IVCC coils with n=1 and n=2 toroidal mode numbers to use for the application of magnetic perturbations [76], and 3) an advanced 2-D ECEi system to study the response of the magnetic perturbation [37].


Fig. 14: (a) The position of the ECEi window (black box) and sight of the Dα light (green line) are depicted on the calculated equilibrium flux surface. The separatrix (or last closed flux line) is the red line. (b) The captured image of the ELM with n=8 is shown with the separatrix (red line). (c, d) Dα spikes shown together with the spectrogram of one of the ECEi channels. The arrow sign at (d) indicates the time when the image was taken. Figure is from Kim, M. Nucl. Fusion 54, 093004, 2014.


Fig. 15: Identification of the measured ELM with a synthetic image of the simulated edge localized eigenmode by (BOUT++). (a) Calculated eigenmode with n=8 for the plasma equilibrium is shown, (b) A synthetic ECEi image is shown with the mirror image of down shifted spectra, (c) Background noise of the ECEi system is added, (d) The measured image of the ELM to be compared with (c). Figure is from Kim, M. Nucl. Fusion 54, 093004, 2014.

In KSTAR experiments with the ECEi system located near the edge of the plasma, a coherent mode structure near the pedestal region was detected with self-consistently determined toroidal mode numbers during the inter-ELM-crash period, as shown in Fig. 14 [77]. The eigenmode structure of the n=8 toroidal mode number is simulated with the resistive MHD code BOUndary Turbulence (BOUT++) using a reconstructed plasma equilibrium at the time when the mode was measured, as shown in Fig. 15a [78]. In order to understand the striking difference from the observed ELM, a simulation result of the eigenmode structure accounting for the intrinsic spatial resolution of each pixel is shown in Fig. 15b. Here, even the down shifted images of the mode are shown in the far-right corner of this figure. Then, the background noise of the detection system is added, as shown in Fig. 15c. The final synthetic image in Fig. 15c is directly compared with the measured one in Fig. 15d. The discrepancy is attributed to the instrumental broadening of the present KSTAR ECEi system.


Fig. 16: (a) Simultaneous emergence and growth of multiple ELM filaments (shot no. 4431) in a rotating system in counterclockwise direction (white arrows). The arrows follow the same filament illustrating the counterclockwise rotation. Multiple bursts of the same filament in a large ELM crash event are indicated in the time trace of ECEi. (b) First in the series of four bursts. The bottom left sketch depicts the flux surface with filamentary perturbations and the burst zone entering the ECEi view (yellow). The white box arrow indicates the flow velocity of the filaments. (c) The third burst of the same filament, 150 μs later. The sketch above is the corresponding model. In each example, the bursting filament develops a narrow fingerlike structure bulging outward. Figures are from Yun, G., Phys. Rev. Lett., 107, 045004 (2011).

Based on confidence of the validated ELM, the time evolution of the ELM cycle from growth to the crash has been studied and an example is illustrated in Fig. 16 [77]. As shown in this figure, multiple modes are growing at the initial stage and the dominant mode is immediately saturated before the crash as it is rotating in the counterclockwise direction, as depicted in Fig. 16a. At the time of the crash, the images of multiple bursting processes of the filament are shown in Fig. 16b and 16c. It is also common to observe the ELM-crash with a toroidal mode number in the range n=4~20 at KSTAR. In general, the toroidal mode number of the ELM filament changes from high to low (e.g. n=11 to n=4) as the amplitude of the Dα spike is increased. Qualitatively, the observed mode structure is consistent with the filamentary structure from the fast camera illustrated in Fig. 13.

While the majority of experiments were performed at the low field side of the plasma, two imaging stations were simultaneously deployed to both high and low field sides at the edge of the plasma to study the ELM dynamics on the same flux surface as illustrated in Fig. 17. The simultaneously observed 2-D images of the ELM on the high and low field side during inter ELM-crash period are depicted in this figure and the timing of this measurement is ~0.5 ms before the crash.


Fig. 17: Observation of the ELM at both high and low field sides of the plasma. The position of the windows is depicted on the KSTAR geometry. The intensity of the ELM at both sides is similar and this is inconsistent with the ballooning mode model. The mode number is not consistent with the global ELM structure (the white line is the same mode structure at high and low field sides). The rotation direction is opposite from each other with different speed. Figures are from Ref. 5.

While the simulation results from MHD codes such as the BOUT++ code and M3D-C1 showed dominance of the mode activity at the low field side, a recent numerical simulation from the kinetic code, XGC, produced a comparable ELM mode strength at both the high and low field sides [79]. Further studies are needed to clarify the different results between the MHD and kinetic simulation codes. The observed poloidal wavenumber of the ELM at the high field side is almost two times lower than the expected poloidal wavenumber on the same flux surface corresponding to that of the low field side, as shown in the white lines in this figure. So far, the physics basis of the ELM is still at a preliminary stage and the dynamics and global behaviors of the observed eigenmode in the ELM cycle will provide an opportunity to establish an improved physics basis of the ELM.


Fig. 18: (a) The time trace of the fast RMP current ramp up, plotted with Dα light together with the time traces of the slowly decreasing integrated spectral powers of the ELM (blue; 5-30 kHz) and slowly increasing turbulence level (red; 30-70 kHz) along with the RMP coil current (gold) are shown. (b) 2-D images of the ELM before, middle and after the RMP current ramp up during the ELM-crash suppression experiment. After suppression, the toroidal mode number is shifted from n~15 to n~20 and the ELM become marginally stable. Figures are from Lee, J. et al Phys. Rev. Lett. 117, 075001 2016.

Among many methods of mitigation or suppression, resonant magnetic perturbation (RMP) [80-82] has been very effective [83]. However, details of the RMP configuration for optimum penetration and the nature of the stochastic magnetic islands in the presence of the plasma are not yet clearly understood. In general, when the ELM-crash is mitigated by the RMP, an edge density pump-out follows and the pump-out is less from the mitigation to the suppression phase. At this stage, it is important to clarify the role of the perturbed magnetic field in the growth/decay of the ELM amplitude and enhanced transport of the edge density so that an appropriate transport physics model can be applied to minimize the loss of edge pressure due to the density pump out while the suppression period is sustained. If the observed turbulence is in response to the RMP in the presence of plasmas, a non-linear interaction between the ELM and turbulence can slow down growth of the ELM below the threshold level. At the same time, turbulence can enhance the radial transport of plasma density [84]. However, identification of the observed turbulence is challenging, since the characteristics of the measured turbulence of ne, and Te and magnetic turbulence is quite similar to each other in the wavelength and frequency space.

In an early experiment on ELM-crash suppression using RMPs at KSTAR [85], the toroidal mode number (from n~15 to n~20) was notable, with a marginally stable phase, as shown in the last image of Fig. 18a. The time history of the sum of the broadband turbulence (~30-70 kHz) and the coexisting eigenmode (ELM) (~5-30 kHz) are plotted together with the RMP current ramp up as shown in Fig. 18b. It is interesting to note that the RMP is ramped up with a fast ramp up time scale (~0.2 s) but the sum of the broadband turbulence in response to the RMP slowly increases while the ELM (not ELM-crash) amplitude decreases on a similar time scale, as illustrated in this figure. This observation may suggest that penetration of the magnetic perturbation from the applied RMP is slower than the particle transport time scale. If the slowly increasing turbulence level drains the energy of the ELM eigenmode through cross interaction between the turbulence induced by RMP and the ELM, the time scale of the decreasing Dα spike amplitude should occur in a similar time scale but the suppression occurs as the fast ramp up is completed. The fact that the toroidal mode number of the inter-ELM period is changed from n~15 to n~20, implies that the ELM has been marginally unstable. The growth of the ELM may have been slightly above the threshold level and a small increase of the turbulence could drain the energy of the ELM and suppress the ELM-crash.


Fig. 19: An ELM-crash suppression experiment with a slow RMP current ramp up and down time scale (green) comparable to the magnetic diffusion time scale (~2s) for the KSTAR edge plasma parameters. (a) The intensity of Dα spikes are linearly reduced as the amplitude of the broadband turbulence linearly increases with the RMP current ramp up, while the perpendicular flow speed of the turbulence suddenly dropped to a minimum at about the same time when the ELM-crash was suppressed. The decay of the turbulence level is significantly delayed as the RMP ramp down is started and Dα spikes returned when the amplitude of turbulence dropped to the level where the suppression began and the perpendicular rotation is increased suddenly. (b) The coherence spectra for the poloidal direction grows as the RMP is ramped up. Radial spread of the turbulence occurs when the turbulence level is fully saturated poloidally. Figures are from Ref. 5.

In a recent experiment for further studies on the role of the turbulence as a suppression mechanism of the ELM-crash, the RMP current is ramped up and down slowly in a time scale comparable to the magnetic diffusion time scale (𝜏md ~ 2s) for the edge plasma parameters as shown in Fig. 19a. The amplitude of the sum of the turbulence spectra from the inter-ELM-crash period increased almost linearly with the RMP current, while the amplitude of Dα light spikes (i.e. ELM-crash) decreased linearly until the suppression time as shown in this figure. The perpendicular electron flow speed suddenly dropped when the ELM-crash was suppressed. The sudden bifurcation of the perpendicular electron flow is consistent with the previous observation in Ref. [86], where magnetic signals were used to address the electron flow. Note that direct measurement of turbulence was used to address these issues at KSTAR for the first time. Since the poloidal flow speed is likely dominated by the Er x B term, it is logical to conclude that the sudden change of the perpendicular flow speed is related to the change of Er. It is important to separate this effect from the Er x B physics of the H-mode near the pedestal region, which is extremely narrow [87]. As the RMP current is ramped down, amplitude of the turbulence has a long-time delay before it starts decreasing. At about the same amplitude of the turbulence when the ELM-crash was suppressed, the ELM-crash (i.e. Dα light) and perpendicular flow speed return with a much higher intensity of Dα light. Does this implicate recovery of Er x B? If the sudden bifurcation of the electron flow speed is associated with the Er change [87], it is reasonable to conclude that the time history of the turbulence is not correlated with that of Er. As shown in Fig. 19b, the time evolution of the observed turbulence on a poloidal plane shows that the level is increasing with broad spectra as it approaches the flat top of the RMP current ramp up phase. On the other hand, the radial spread of the turbulence is only shown as the poloidal turbulence is saturated. This observation suggests that the turbulence induced by the RMP is radially very narrow (~5 cm) and the spread only occurs when the penetration of the magnetic perturbation is fully saturated. More experiments should be conducted to clarify these issues, and to clarify issues such as the coupling efficiency of the magnetic perturbation, the role of the turbulence in enhanced transport of the electron density and nonlinear interaction with the ELMs.


The long development of fusion research now has allowed us to build ITER for realization of fusion energy development. The success of the ITER project may warrant a design of an advanced fusion reactor and modelling with predictive capability is essential. New insights and multi-dimensional boundary constraints are critical in validating the theoretical models for preemptive control of the critical MHD instabilities. Studies of these instabilities with the 2-D ECEi system revealed new findings and identified the gap between the theory/modeling and experimental observations. In sawtooth instability, it was found that the crash process of the dominant fast crash case is different from that of the slow crash case through the 2-D ECEi measurement. Here, the axisymmetry of the 1/1 kink mode prior to the crash time is the key for the two different crash time scales. A combination of the measured q0~1.0 and a supplemental tearing mode experiment that is sensitive to the background q0 proved that the q0 went back to q0>1.0 after the crash. The full reconnection model is correct after all. In NTM instability, it was demonstrated that 2-D imaging data is effective in determining the critical stability parameters of the 2/1 mode (i.e. Δ' and ωc). A study of the coupling between the simultaneously measured mesoscale MHDs (i.e. 2/1 island) and anisotropic micro-turbulence with its flow shear in the presence of a 2/1 island was performed. Here, the anisotropy of micro-turbulence and strong flow shear arise from competition between growth rates of the TEM and ITG and E x B shearing rates near the X and O-points of the 2/1 island. The 2-D imaging data of the ELMs and ELM-crashes have provided unprecedented new physics information. New information has been acquired from the 2-D dynamics of ELMs, such as temporal evolution to the crash and asymmetry of mode behaviors. In the ELM-crash suppression experiment, the simultaneously measured ELMs and turbulence induced by the RMP provided an opportunity to understand fundamentals of the ELM-crash suppression physics. The slow growth of the turbulence on the magnetic diffusion time scale in response to the slow RMP current ramp up suggests the nature of the turbulence may be magnetic rather than electrostatic. Also, bifurcation of the perpendicular electron flow was observed through direct measurement of the turbulence. No correlation between the growth of the turbulence and flow speed raises an important issue on the contribution of Er x B to the perpendicular flow speed and enhanced transport at the pedestal region. The inter-coupling of the growth and decay of the turbulence, the time scales of the ELM-crash amplitude (Dα spikes) into and from the suppression period and perpendicular rotation are extremely important for the suppression mechanism of the ELM-crashes.

Acknowledgements: This work is supported by the National Research Foundation of Korea (grant No. NRF- 2014 M1A 7A1A03029865).


[1] Bateman, G. MHD instabilities, Cambridge, Mass., MIT Press, 1978.
[2] Wesson, J.A., Tokamaks, Oxford University press, Oct., 2011.
[3] Hutchinson, I. H. Principles of Plasma Diagnostics, 2nd Edition (Cambridge University Press, New York, 2002.
[4] Park, H., Mazzucato, E., Munsat, T., et al Rev. Sci. Instrum., 75, 3787, 2004.
[5] Park, H., Advances in Physics-X, 4, 1633956, 2019.
[6] Helander, P. et al Plasma Phys. Control. Fusion 54, 124009, 2012.
[7] Kamada, Y. et al AAPPS Bulletin, 23(1): 5-8, 2013.
[8] Ide S. JT-60SA: AAPPS Bulletin, 23(1):19-23, 2013.
[9] ITER Physics Expert Groups et al, Nucl. Fusion 39, 2137, 1999.
[10] Wagner, F. et al Phys. Rev. Lett., 53 1453, 1984.
[11] Ida K. and Fujita T., Phys. Control. Fusion 60, 033001, 2018.
[12] Soltwisch, Rev. Sci. Instrum., 59, 1599, 1988.
[13] O'Rourke, J.et al Phys. Plasma Cont. Fusion, 33, 289, 1991.
[14] Rice, et al., Rev. Sci. Instrum., 63, 5002, 1992.
[15] Wroblewski D. et al Phys. Rev. Lett. 61, 1724, 1988.
[16] Levinton F.M. et al Rev. Sci. Instrum. 63, 5157, 1992.
[17] Wroblewski D. et al Phys. Rev. Lett. 71, 859, 1993.
[18] Rice B.W. et al Rev. Sci. Instrum. 70, 815, 1999e97) 1.
[19] Chung J. et al, Rev. Sci. Instrum. 85, 11D827, 2014.
[20] Wolf, R.C. et al, JINST 10, p10008, 2015.
[21] West, W.P. Thomas, D.M. deGrassie J.S. et al, Phys. Rev. Lett. 58, 2758, 1987.
[22] Costley, A. E., Hastie, R.J., Paul, J.W.M., et al Phys. Rev. Lett., 33, 758, 1974.
[23] Efthimion, P.C., Arunasalam, V., Bitzer, R., et al Rev. Sci. Instrum., 50, 949, 1979.
[24] Cavallo, A. and Cutler, R., Rev. Sci. Instrum. 56, 931, 1985.
[25] Buratti, P., and Zerbini, M., Rev. Sci. Instrum., 66, 4208, 1995.
[26] Chang, Z., Park, W., Frederickson, E., et al Phys. Rev. Lett., 77, 3553, 1996.
[27] Fredrickson, E.D., Austin, M.E., Groebner, R., et al Phys. Plasmas, 7, 5051, 2000.
[28] Nagayama, Y., Kawahata, K., Inagaki, S., et al Phys. Rev. Lett., 90, 205001, 2003.
[29] Udintsev, V.S., Ottaviani, et al Plasma Phys. Control. Fusion, 47, 1111, 2005.
[30] Bornatici, R., et al Nucl. Fusion 23, 1153, 1983.
[31] Park, H.K., Chang, C.C., Deng, B.H., et al Rev. Sci. Instrum., 74, 4239, 2003.
[32] Classen, I.G.J., Boom, J. E., Suttrop, W. et al Rev. Sci. Instrum. 81, 10D929, 2010.
[33] Tobias, B. Domier, C.W. et al Rev. Sci. Instrum. 81, 10D928, 2010.
[34] Zhu Y. L., et al Rev. Sci. Instrum. 87, 11D901, 2016.
[35] Jiang M., et al Rev Sci Instrum. 84, 113501, 2013.
[36] Kuwahara D., et al Rev. Sci. Instrum. 81, 10D919, 2010.
[37] Yun G.S., et al Rev. Sci. Instrum. 85, 11D820, 2014.
[38] Nam, Y.B., Park, H.K., Lee W., et al Rev. Sci. Instrum. 87, 11E135, 2016.
[39] Von Goeler, S. et al Phys. Rev. Lett., 33, 1201, 1973.
[40] Kadomtsev B.B., Sov. J. Plasma Phys. 1, 389, 1975.
[41] Kulsrud, R.M., Earth Planets Space, 53, 417-422, 2001.
[42] Campbell, D.J., et al Nucl. Fusion 26, 1085, 1986.
[43] Wesson, J. A., Plasma Phys. Controlled Fusion 28, 243, 1986.
[44] Granetz, R.S., et al Nucl. Fusion, 28, 457, 1988.
[45] Janicki, C., et al Nucl. Fusion, 30, 950, 1990.
[46] Gunter, S., et al Plasma Phys. Cont. Fusion, 57, 014017, 2015.
[47] Park H.K., et al Phys. Rev. Lett. 96, 195003, 2006.
[48] Munsat, T., Park, H.K., Classen, I.G.J., et al Nucl. Fusion 47, L31-L35, 2007.
[49] Park, H.K., et al Phys. Rev. Lett. 96, 195004, 2006.
[50] Ko, J., Rev. Sci. Instrum. 87, 11E541, 2016.
[51] Nam, Y.B., et al Nucl. Fusion 58, 066009, 2018.
[52] Bierwage, A., et al Phys. Plasmas 12, 082504, 2005.
[53] Chang, Z., et al Phys. Rev Lett., 77, 3553, 1996.
[54] Westerhof, E., Smeulders P., Lopes Cardozo, N., Nucl. Fusion 29, 6, 1056, 1989.
[55] Fredrickson, E. D. et al Physics of Plasmas 3, 2620, 1996.
[56] Tobias, B., et al Rev. Sci. Instrum., 81, 10D928, 2010??
[57] Gao, B.X., et al JINST 13, P02009, 2018.
[58] Igochine, V., et al Phys. of Plasma, 17, 122506, 2010.
[59] Aydemir, A.Y., Wiley, J.C. and Ross, D.W., Plasma Physics 1, 774, 1989.
[60] Chang, Z., et al Phys. Rev. Lett. 74, 4663, 1995.
[61] Buttery, R.J., et al Plasma Phys. Control. Fusion 42, B61-B73, 2000.
[62] Kasparek, W., et al Nucl. Fusion 56, 126001, 2016.
[63] Choi, M.J, et al Nucl. Fusion 54, 083010, 2014.
[64] Classen, I.G.J. et al Phys. Rev. Lett., 98, 035001, 2007.
[65] Ren, C., Callen, J.D., et al Phys. Plasmas 5, 450, 1998.
[66] Choi, M.J., et al Nucl. Fusion 57, 126058, 2017.
[67] Kwon, J-M. et al Phys. of Plasma, 25, 052506, 2018.
[68] Ku, S. et al Phys. Plasmas 25, 056107, 2018.
[69] Kwon, J.-M. et al Comput. Phys. Commun. 215, 81 2017.
[70] Zohm, H., Plasma Phys. Control. Fusion 38, 1213-1223, 1996.
[71] Hegna, C., Connor, J.W., Hastie, R.J. and Wilson, H.R., Phys. of Plasmas 3, 584, 1996.
[72] Snyder, P.B., et al Nucl. Fusion 44, 320, 2004.
[73] Kirk, A., et al Phys. Rev. Lett. 92, 245002, 2004.
[74] Park, H.K. et al 59, 112020, Nucl. Fusion, 2019.
[75] In, Y., et al Nucl. Fusion, 55, 043004, 2015.
[76] Park, J.K. et al https://doi.org/10.1038/s41567-018-0268-8, Nature Physics, 2018.
[77] Yun, G.S., Lee, W., et al Phys. Rev. Lett, 107, 045004, 2011.
[78] Kim, M. et al Nucl. Fusion 54, 093004, 2014.
[79] C.S., Chang, private communication.
[80] Evans, T.E., Fenstermacher, M.E., et al Nucl. Fusion 48, 024002, 2008.
[81] Lang, P.T, et al, Nucl. Fusion 53, 043004, 2013.
[82] Evans, T.E., J. Nucl. Matter, 438, 511, 2013.
[83] Evans, T., et al Phys. Rev. Lett. 92, 235003, 2004.
[84] McKee, G.R. et al Nucl. Fusion 53, 113011, 2013.
[85] Lee, J., et al Phys. Rev. Lett. 117, 075001, 2016.
[86] Nazikian, R., et al, Phys. Rev. Lett. 114, 105002, 2015.
[87] Lee, J., et al Nucl. Fusion 59, 066033, 2018.


Hyeon K. Park is a professor at the School of Natural Science, Ulsan National Institute of Science and Technology (UNIST). After receiving his PhD from the University of California, Los Angeles (UCLA), USA, he worked at Princeton Plasma Physics Laboratory (PPPL), Princeton University, for 25 years and pioneered many diagnostics including the first innovative 2-D microwave imaging system (ECEi/MIR) for fusion plasma physics. He continued developing a 2D/3D ECEi/MIR system for KSTAR (Korea Superconducting Tokamak Advanced Research), after returning to Korea to work at Pohang University of Science and Technology (POSTECH). He has been instrumental in accelerating the fusion science program at KSTAR. He serves in several international fusion organizations, including International Fusion Researsch Council [IFRC], ITER Science and Technology Advisery Committee [STAC]. He specializes in experimental fusion science through innovative diagnostic development for confinement and magnetohydrodynamic (MHD) stability physics.

AAPPS Bulletin        ISSN: 2309-4710
Copyright © 2018 Association of Asia Pacific Physical Societies. All Rights Reserved.
Hogil Kim Memorial Building #501 POSTECH, 67 Cheongam-ro, Nam-gu, Pohang-si, Gyeongsangbuk-do, 37673, Korea
Tel: +82-54-279-8663 Fax: +82-54-279-8679 e-mail: aapps@apctp.org