Multi-device study of characteristics of disruptive magnetohydrodynamic modes in Tokamaks

Fusion plasmas confined in tokamaks by magnetic fields often experience disruptions, i.e. sudden losses of the plasma confinement, consisting of a fast thermal quench followed by a plasma current quench, accompanied by the destabilization of the vertical position of the plasma column. Disruptions are a serious threat to the device components in terms of large heat and particle loads on the plasmafacing components and the forces applied on the various components of the device. Disruption avoidance, prediction and, in case of an unavoidable disruption, mitigation, is a prerequisite for safe, efficient operation of large tokamaks (e.g. ITER, currently under construction). Disruption onset is known to be linked with the development of magnetohydrodynamic (MHD) modes. In particular, the crossing of a critical value of the mode amplitude has been identified as a main disruption trigger in the past (de Vries, 2011). This thesis addresses multiple aspects of MHD mode development prior to a disruption. The main diagnostic instruments serving for the mode amplitude monitoring were magnetic sensors, particularly saddle and Mirnov coils. The main tool in the work is an extensive (> 1100 entries) database of discharges terminated by a disruption. The database consists of measurements from devices of various plasma size (COMPASS, ASDEX Upgrade, DIII-D, JET), but similar aspect ratios. Identical data selection criteria were applied across all devices for compiling the database. All database entries were manually classified according to the main cause leading to onset of the MHD mode. Earlier works reported that in large devices, most of the modes were static in the laboratory frame (’locked’) (de Vries, 2016). However, in general modes are often observed to rotate prior to becoming locked, as also seen in the database compiled in this work. This thesis addresses important characteristics of both rotating and locked modes in the context of the disruption initiation. The mode amplitude development is followed throughout the mode braking, the stationary phase of the mode and the disruption onset. The observations reported in this work may contribute to a set of design criteria for future disruption forecasting schemes. The work explores both existing physical models for describing mode dynamics, as well as a phenomenological description of mode behavior on the basis of the multi-machine database. A first part of the work aims to validate a model for mode locking on the basis of a reduced database of ASDEX Upgrade discharges. Not discriminating between plasma configurations, the model allows to estimate the duration of the deceleration phase, as well as the critical mode width for locking. Both quantities are important for the design of algorithms that aim to avoid disruptions by means of external actuators. The reduced ASDEX Upgrade database consists of discharges covering a broad range of plasma parameters and discharge scenarios. It was found that the model successfully describes locking of large modes in those cases where the mode deceleration started in a quasi-stationary phase of the discharge (i.e. with low variability of the global plasma angular momentum prior to mode seeding) and where deceleration took place over temporal intervals that are long in comparison with the momentum confinement time. Theoretical braking curves and locking durations predicted with the model were in good quantitative agreement with the experimental data. On the other hand, the model failed to reproduce the braking curves of modes appearing towards the end of a transient phase, e.g. during an impurity influx or when approaching the disruptive density limit. A modified mode equation of motion is proposed, which accounts for transient variation of the plasma density, e.g. during the development of a MARFE and its poloidal destabilization from its stable location at the plasma X-point. The experimental and theoretical mode braking curves were in closer accordance when the modified model was applied. The second part of the work focuses on the analysis of the duration of (quasi-) stationary modes, as well as the pre-disruptive growth of the measured mode amplitude. In addition, regression analysis is conducted of the locked phase duration and a previously derived scaling for the disruptive mode amplitude is validated (de Vries, 2016). The study was performed using the full database of disruptive discharges covering a broad range of plasma parameters, including a considerable range of plasma dimensions. The measured mode durations span several orders of magnitude in all devices, but nevertheless the median duration is seen to increase with plasma size. Several factors are discussed that could influence the locked mode duration, such as the plasma control system response to exceptional situations (e.g. switching on or off external heating modules, initiation of a fast plasma current ramp-down, plasma shape modification etc.), the specific location of the discharge within the typical device parametric space (often reflected in the disruption root cause) and the occurrence of minor disruptive events (accompanied by a partial loss of the plasma confinement). The scaling formula for the disruptive mode amplitude is reported to systematically overestimate the experimental amplitudes in case of modes detected with magnetic sensors located at the torus high-field-side. A proposal for modifying the scaling, adjusting for this case, is presented. The modified scaling equation allowed more accurate predictions of the critical mode amplitude threshold. Linear extrapolation with plasma size of both experimental and predicted times-to-disruptions and the associated fraction of disruptions suggests that, in devices with large plasma minor radius, the locked modes will grow on time scales that are long enough to allow for disruption mitigation by means of fast massive gas injection or pellet injection. A regression analysis aimed at establishing a scaling relation for the locked mode phase duration with plasma parameters. A physically plausible scaling relation could be established, which however explains only part of the variability of the data. Possible origins of the remaining scatter are discussed, such as the onset of minor disruptions in the presence of the mode, mode re-rotation under a constant external torque input etc. Application of the scaling to the ITER Baseline scenario suggests that the locked phase duration will be of the order of hundreds of milliseconds or seconds in ITER, depending on the particular disruption root cause. Such time scales are in favour of a timely disruption mitigation in ITER

Multi-device study of characteristics of disruptive magnetohydrodynamic modes in tokamaks

Fusion plasmas confined in tokamaks by magnetic fields often experience disruptions, i.e. sudden losses of the plasma confinement, consisting of a fast thermal quench followed by a plasma current quench, accompanied by the destabilization of the vertical position of the plasma column. Disruptions are a serious threat to the device components in terms of large heat and particle loads on the plasmafacing components and the forces applied on the various components of the device. Disruption avoidance, prediction and, in case of an unavoidable disruption, mitigation, is a prerequisite for safe, efficient operation of large tokamaks (e.g. ITER, currently under construction). Disruption onset is known to be linked with the development of magnetohydrodynamic (MHD) modes. In particular, the crossing of a critical value of the mode amplitude has been identified as a main disruption trigger in the past (de Vries, 2011). This thesis addresses multiple aspects of MHD mode development prior to a disruption. The main diagnostic instruments serving for the mode amplitude monitoring were magnetic sensors, particularly saddle and Mirnov coils. The main tool in the work is an extensive (> 1100 entries) database of discharges terminated by a disruption. The database consists of measurements from devices of various plasma size (COMPASS, ASDEX Upgrade, DIII-D, JET), but similar aspect ratios. Identical data selection criteria were applied across all devices for compiling the database. All database entries were manually classified according to the main cause leading to onset of the MHD mode. Earlier works reported that in large devices, most of the modes were static in the laboratory frame (’locked’) (de Vries, 2016). However, in general modes are often observed to rotate prior to becoming locked, as also seen in the database compiled in this work. This thesis addresses important characteristics of both rotating and locked modes in the context of the disruption initiation. The mode amplitude development is followed throughout the mode braking, the stationary phase of the mode and the disruption onset. The observations reported in this work may contribute to a set of design criteria for future disruption forecasting schemes. The work explores both existing physical models for describing mode dynamics, as well as a phenomenological description of mode behavior on the basis of the multi-machine database. A first part of the work aims to validate a model for mode locking on the basis of a reduced database of ASDEX Upgrade discharges. Not discriminating between plasma configurations, the model allows to estimate the duration of the deceleration phase, as well as the critical mode width for locking. Both quantities are important for the design of algorithms that aim to avoid disruptions by means of external actuators. The reduced ASDEX Upgrade database consists of discharges covering a broad range of plasma parameters and discharge scenarios. It was found that the model successfully describes locking of large modes in those cases where the mode deceleration started in a quasi-stationary phase of the discharge (i.e. with low variability of the global plasma angular momentum prior to mode seeding) and where deceleration took place over temporal intervals that are long in comparison with the momentum confinement time. Theoretical braking curves and locking durations predicted with the model were in good quantitative agreement with the experimental data. On the other hand, the model failed to reproduce the braking curves of modes appearing towards the end of a transient phase, e.g. during an impurity influx or when approaching the disruptive density limit. A modified mode equation of motion is proposed, which accounts for transient variation of the plasma density, e.g. during the development of a MARFE and its poloidal destabilization from its stable location at the plasma X-point. The experimental and theoretical mode braking curves were in closer accordance when the modified model was applied. The second part of the work focuses on the analysis of the duration of (quasi-) stationary modes, as well as the pre-disruptive growth of the measured mode amplitude. In addition, regression analysis is conducted of the locked phase duration and a previously derived scaling for the disruptive mode amplitude is validated (de Vries, 2016). The study was performed using the full database of disruptive discharges covering a broad range of plasma parameters, including a considerable range of plasma dimensions. The measured mode durations span several orders of magnitude in all devices, but nevertheless the median duration is seen to increase with plasma size. Several factors are discussed that could influence the locked mode duration, such as the plasma control system response to exceptional situations (e.g. switching on or off external heating modules, initiation of a fast plasma current ramp-down, plasma shape modification etc.), the specific location of the discharge within the typical device parametric space (often reflected in the disruption root cause) and the occurrence of minor disruptive events (accompanied by a partial loss of the plasma confinement). The scaling formula for the disruptive mode amplitude is reported to systematically overestimate the experimental amplitudes in case of modes detected with magnetic sensors located at the torus high-field-side. A proposal for modifying the scaling, adjusting for this case, is presented. The modified scaling equation allowed more accurate predictions of the critical mode amplitude threshold. Linear extrapolation with plasma size of both experimental and predicted times-to-disruptions and the associated fraction of disruptions suggests that, in devices with large plasma minor radius, the locked modes will grow on time scales that are long enough to allow for disruption mitigation by means of fast massive gas injection or pellet injection. A regression analysis aimed at establishing a scaling relation for the locked mode phase duration with plasma parameters. A physically plausible scaling relation could be established, which however explains only part of the variability of the data. Possible origins of the remaining scatter are discussed, such as the onset of minor disruptions in the presence of the mode, mode re-rotation under a constant external torque input etc. Application of the scaling to the ITER Baseline scenario suggests that the locked phase duration will be of the order of hundreds of milliseconds or seconds in ITER, depending on the particular disruption root cause. Such time scales are in favour of a timely disruption mitigation in ITER

Diamagnetic Stabilization of Double-tearing Modes in MHD Simulations

Double-tearing modes have been proposed as a driver of ‘off-axis sawtooth’ crashes in reverse magnetic shear tokamak configurations. The DTM consists of two nearby rational surfaces of equal safety factor that couple to produce a reconnecting mode weakly dependent on resistivity and capable of nonlinearly disrupting the annular current. In this dissertation we examine the linear and nonlinear growth of the DTM using the extended magnetohydrodynamic simulation code MRC-3d. We consider the efficacy of equilibrium diamagnetic drifts, which emerge in the presence of a pressure gradient when ion inertial physics is included, as a means of stabilizing DTM activity. In linear slab simulations we find that a differential diamagnetic drift at the two resonant surfaces is able to both interfere with the inter-surface coupling and suppress the reconnection process internal to the tearing layers. Applying these results to a m=2, n=1 DTM in cylindrical geometry, we find that asymmetries between the resonant layers and the presence of an ideal MHD mode result in stabilization being highly dependent on the location of the pressure gradient. We achieve a significant reduction in the linear DTM growth rate by locating a strong diamagnetic drift at the outer resonant surface. In nonlinear simulations we show that growth of the magnetic islands may enhance the pressure gradient near the DTM current sheets and significantly delay disruption. Only by locating a strong drift near the outer, dominant resonant surface are we able to saturate the mode and preserve the annular current ring, suggesting that the appearance of DTM activity in advanced tokamaks may depend on the details of the plasma pressure profile

Newly uncovered physics of MHD instabilities using 2-D electron cyclotron emission imaging system in toroidal plasmas

Validation of physics models using the newly uncovered physics with a 2-D electron cyclotron emission imaging (ECEi) system for magnetic fusion plasmas has either enhanced the confidence or substantially improved the modeling capability. The discarded "full reconnection model" in sawtooth instability is vindicated and established that symmetry and magnetic shear of the 1/1 kink mode are critical parameters in sawtooth instability. For the 2/1 instability, it is demonstrated that the 2-D data can determine critical physics parameters with a high confidence and the measured anisotropic distribution of the turbulence and its flow in presence of the 2/1 island is validated by the modelled potential and gyro-kinetic calculation. The validation process of the measured reversed-shear Alfveneigenmode (RSAE) structures has improved deficiencies of prior models. The 2-D images of internal structure of the ELMs and turbulence induced by the resonant magnetic perturbation (RMP) have provided an opportunity to establish firm physics basis of the ELM instability and role of RMPs. The importance of symmetry in determining the reconnection time scale and role of magnetic shear of the 1/1 kink mode in sawtooth instability may be relevant to the underlying physics of the violent kink instability of the filament ropes in a solar flare

On the mechanism of RMP-driven pedestal transport and ELM suppression in KSTAR

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 에너지시스템공학부, 2020. 8. 나용수.A tokamak is a torus device that uses a helical magnetic field to confine a hot plasma. It has been developed to produce controlled thermonuclear fusion power. For the ignition of fusion, high-performance plasma must be sustained for sufficient time. Plasma instability can cause a strong perturbation in the plasma and worsen the plasma confinement. Therefore, it is essential to understand and control the plasma instability. Edge Localized Modes (ELM) are rapid Magneto-hydrodynamics (MHD) events occurring at the edge region of tokamak plasmas, which can result in damages to the divertor plates. Various methods were developed to control ELM, and among them, the ELM suppression by resonant magnetic perturbation (RMP) showed promising results. Therefore, to fully suppress ELMs via RMP is of great interest to reach and sustain high-performance H-mode discharges. It was found that certain conditions must be met for the RMP-driven ELM crash suppression, so understanding its mechanism is crucial for reliable ELM control using RMP. This thesis addresses the effect of RMP on pedestal transport and the mechanism of RMP-driven ELM suppression. They are investigated with nonlinear reduced MHD simulations on KSTAR plasmas. First, I developed a numerical method to reconstruct accurate plasma equilibrium, which is an essential component for these state-of-the-art simulations. I employed theoretical models and numerical schemes to solve obstacles in kinetic equilibrium reconstruction. Second, the effect of RMP on pedestal transport is investigated. The numerical simulation shows that RMP forms the kink-peeling structure, the stochastic layer, and neoclassical toroidal viscosity (NTV). The convective and conductive radial fluxes from these responses increase the radial transport and result in the degradation of the pedestal. Finally, I successfully reproduce ELM suppression by RMP in agreement with experiments. One of the main conclusion of this work is that the ELM crash suppression is attributable not only to the degraded pedestal but also to direct a coupling between ELM and RMP-driven plasma response. The coupling effect 1) enhances the size of magnetic islands at the pedestal, reducing the instability source by further pedestal degradation, and 2) increases the spectral transfer between edge harmonics preventing catastrophic growth and crash of the most unstable modes. Due to these effects, ELMs are non-linearly saturated, and the peeling-ballooning mode activity persists during the suppression phase without a sharp mode crash. I discuss a condition to reinforce this coupling effect for ELM suppression. In summary, this thesis reveals the importance of plasma response and mode coupling to explain the RMP-driven pedestal transport and ELM suppression. In particular, it improves the previous understanding of the mechanism by discovering the contribution of nonlinear mode interaction on the ELM suppression mechanism. Based on this study, new insight and approach for ELM control are expected to be developed.플라즈마 경계 불안정성 (ELM) 은 토카막 플라즈마의 경계 페데스탈 영역에서 발생하는 급격한 MHD 불안정성으로, 토카막 내벽과 다이버터에 치명적인 손상을 입힐 수 있다. 따라서, 고성능 플라즈마 운전을 유지하고 핵융합 반응을 일으키기 위해서는 ELM을 억제하는 것이 필수적이다. 과거 실험 연구로부터 공명 자장 섭동 (RMP) 을 통해 ELM 억제가 가능하다는 것이 밝혀졌다. 그러나, RMP를 활용해 ELM을 제어하기 위해서는 특정 조건들이 반드시 충족되어야 하고, 이는 매우 좁은 작동 영역을 갖는다. 그러므로, 안정적인 ELM 제어를 위해서는 RMP-ELM 제어 메커니즘을 이해하는 것이 중요하다. 이 논문은 RMP 인가에 따른 페데스탈 영역의 플라즈마 수송 변화와 ELM 억제 메커니즘에 대한 MHD 기반 수치 연구를 다룬다. 첫째로, KSTAR 플라즈마 대상으로 비선형 MHD 시뮬레이션을 수행하는 데 필요한 고성능 플라즈마 구축 방법론을 개발하였다. 해당 평형 계산의 어려움을 해결하기 위해 이론적 모델과 여러 수치 기법들이 사용되며, 비선형 MHD 연구에 적합한 완성도 높은 플라즈마 평형이 도출되었다. 둘째로, RMP인가에 따른 MHD 기반의 페데스탈 수송 현상을 분석하였다. RMP에 의해 구동되는 뒤틀림-껍질 응답 (KPM) 및 확률적 수송 층이 발생한다. 해당 요소들로 인해 페데스탈 영역에서 대류, 전도성 및 신고전 (NTV) 플라즈마 수송을 증가하며 온도와 밀도 페데스탈의 기울기가 줄어드는 것을 설명하였다. KSTAR 실험에서 관측된 결과와의 비교를 통해 본 MHD 기반의 수송 연구 결과의 타당성을 일부분 확보하였으나, 실험 결과를 완전히 설명하기 위해서는 난류 수송과 같은 추가적인 물리 기작이 필요하다는 것이 확인되었다. 마지막으로, KSTAR 실험과 유사한 조건의 RMP 인가에 따른 ELM 억제 현상을 시뮬레이션 상에서 성공적으로 재현하였다. 이로부터 ELM 억제는 RMP에 의한 페데스탈 기울기의 감소뿐만 아니라 ELM과 RMP 간의 직접적인 상호작용에 기인하는 것을 밝혀냈다. 이때 상호작용의 효과는 1) 페데스탈 영역의 자장 섬 크기를 증가시켜 추가적인 페데스탈 기울기와 불안정성 발생 요소를 줄이고 2) ELM의 급격한 증가와 붕괴를 방지하는 불안정성 간의 에너지 이동을 증가시키는 것으로 확인되었다. 이와 같은 효과로 인해 ELM은 비선형적으로 포화 상태에 도달하게 되고 지속해서 억제될 수 있다. 추가로 본 연구는 ELM 억제를 위해 해당 RMP-ELM 간의 상호작용을 강화하는 플라즈마 조건을 논의하였다.1 Introduction 1 1.1 Tokamak 2 1.2 Edge localized mode 4 1.3 RMP-driven ELM suppression 7 1.4 Objectives and outline of this dissertation 9 2 Development of advanced equilibrium tool in KSTAR 11 2.1 Obstacles in KSTAR EFIT reconstruction 13 2.2 Improvement of EFIT constraints 14 2.2.1 Numerical compensation 14 2.2.2 Theoretical compensation 16 2.3 Kinetic EFIT reconstruction in KSTAR 20 2.3.1 GEFIT toolkit 20 2.3.2 Reference equilibrium 21 3 RMP-driven Plasma response 25 3.1 Numerical analysis tools 26 3.1.1 JOREK 26 3.1.2 ERGOS 30 3.1.3 Numerical modeling of RMP 31 3.2 Plasma response 33 3.2.1 Kink response 33 3.2.2 Tearing response 36 3.3 Increased pedestal transport 39 3.3.1 Kink-tearing response driven transport 41 3.3.2 NTV-driven transport 42 3.3.3 Limitation of applied modeling 48 4 RMP-driven ELM crash suppression 51 4.1 Numerical setup for analysis 52 4.1.1 Natural ELM simulation 52 4.1.2 Numerical modeling of RMP and PBM 56 4.2 ELM crash suppression 58 4.2.1 PBM suppression 58 4.2.2 Change in divertor heat flux 60 4.3 RMP and PBM coupling 62 4.3.1 Effect on the pedestal transport 62 4.3.2 Effect on the spectral transfer 66 4.4 RMP-driven PBM locking 75 4.4.1 Enhanced mode coupling by PBM locking 77 5 Conclusions and future work 82 초록 91Docto

1997 international Sherwood fusion theory conference

Papers presented during the conference are indexed separately