Active Control of Magneto-hydrodynamic Instabilities in Hot Plasmas (eBook)

Preface 6
Acknowledgments 7
Contents 8
Main Definitions, Notations and Abbreviations 9
Contributors 13
1 Introduction to Tokamak Operational Scenarios 14
Abstract 14
1.1…Plasma Conditions Needed for Nuclear Fusion 14
1.2…Optimisation of Tokamak Operational Scenarios 15
1.2.1 Tokamak Operational Limits 15
1.2.2 Conventional Tokamak Scenarios 18
1.2.3 Advanced Tokamak Scenarios 18
1.3…Summary 20
2 Magneto-Hydrodynamics and Operational Limits 21
Abstract 21
2.1…Introduction to the Main Concepts of Magnetic Confinement 21
2.1.1 Tokamak 26
2.1.2 Stellarator 28
2.1.3 Reversed Field Pinch 28
2.2…Fluid Description of the Plasma 29
2.3…Plasma Equilibrium 31
2.4…Plasma Stability 36
2.5…Basic Classifications of MHD Instabilities 40
2.6…Hugill Diagram 44
2.6.1 Current Limit 45
2.6.2 Greenwald Limit 47
2.7…Restriction Due to Plasma Shaping 51
2.8…Beta Limit 53
2.9…Different Plasma Scenarios and their Limits 58
2.10…Further Reading 61
References 63
3 Identification of MHD Instabilities in Experiments 64
Abstract 64
3.1…Mode Numbers, Frequency and Mode Coupling 65
3.1.1 Mode Numbers in an Axisymmetric Tokamak 65
3.1.2 Mode Rotation 66
3.2…Signal Analysis 69
3.2.1 Fourier Transform 69
3.2.1.1 Harmonics 70
3.2.1.2 Periodicity Limit 71
3.2.1.3 Discrete Data 71
3.2.1.4 Aliasing and Analog Filtering 71
3.2.2 Spectral Analysis for Non-stationary Signals 72
3.2.2.1 Spectrogram 72
3.2.2.2 Wavelet Transform 73
3.2.3 Multi-signal Analysis 74
3.2.3.1 Singular Value Decomposition 74
3.2.3.2 Cross Correlation 75
3.3…Diagnostics for MHD Mode Observation 76
3.3.1 Basic Requirements 76
3.3.2 Diagnostic Geometry 77
3.3.3 Magnetic Pick-Up Coils 78
3.3.4 Soft X-Ray Measurements 79
3.3.5 Electron Cyclotron Emission Spectroscopy 81
3.4…Toroidal Mode Number Determination 82
3.4.1 Phase Fitting 82
3.4.2 Spatial Aliasing 82
3.5…Poloidal Mode Number Determination 84
3.5.1 Flux Coordinates 85
3.5.2 Toroidal Mode Coupling 85
3.5.3 m from Local Phase 86
3.5.3.1 Magnetic Pick-Up Coils 86
3.5.3.2 SXR 87
3.5.3.3 ECE 89
3.5.4 m from Line Integrated Signals 90
3.5.4.1 SXR Camera and Mode Profile 90
3.5.4.2 Phase Jumps and Amplitude Minima 90
3.5.4.3 Toroidal Mode Number 93
3.6…Radial Mode Structure 93
3.6.1 Radial Displacement of Ideal Modes 93
3.6.2 Mode Localization and Radial Structure 95
3.6.2.1 Local Data 95
3.6.2.2 SXR 96
3.6.3 Structure of Magnetic Islands 96
3.6.4 Determination of Resonant Surface for Magnetic Islands 97
3.6.5 Determination of Island Width W 98
3.6.5.1 W from Magnetic Data 98
3.6.5.2 W from Flat Temperature Region in the O-Point Phase 98
3.6.5.3 W from Temperature Amplitude Maxima 99
3.6.6 Effects of Incomplete Flattening and Local Extrema in the Island 100
3.7…Evolution of Modes and Growth Rate 101
3.8…Local Quantities from Line Integrated SXR Data 102
3.8.1 1D Deconvolution 102
3.8.2 Deviation from Flux Surface Constants 103
3.8.3 Plain Tomography 104
3.8.4 Rotational Tomography 104
3.9…Locked Modes 105
3.9.1 Detection of Locked Modes 105
3.9.2 Detecting Amplitude and Phase of Locked Modes 107
3.10…Localization of q = 1 109
3.10.1 Localization of the (1,1) Mode 109
3.10.2 Sawtooth Inversion 110
3.11…Further Remarks on Observation Quantities and Diagnostics 112
References 114
4 Sawtooth Instability 116
Abstract 116
4.1…Introduction 116
4.2…The Physics of Sawtooth Stability 120
4.2.1 Effect of Energetic Particles 121
4.2.1.1 Trapped Energetic Ions 122
4.2.1.2 Passing Energetic Ions 124
4.2.2 Effect of Toroidal Rotation 125
4.2.2.1 Equilibrium Mass Flow of the Order of the Sound Speed 125
4.2.2.2 Flows of the Order of the Diamagnetic Velocity 126
4.2.3 Sawtooth Crash Trigger Modelling 126
4.2.4 Sawtooth Control Actuators 127
4.3…Current Drive Schemes 129
4.4…Neutral Beam Injection 134
4.5…Ion Cyclotron Resonance Heating 138
4.6…Discussion and Implications for ITER 143
4.7…Summary 144
Chap4 145
References 149
5 Edge Localized Mode (ELM) 154
Abstract 154
5.1…Introduction 154
5.2…Physics of Edge Localized Mode in Tokamaks 156
5.2.1 ELM Types 156
5.2.2 Understanding Edge Localized Modes 158
5.2.2.1 Localized Peeling Modes 158
5.2.2.2 Edge Ballooning Modes 159
5.2.2.3 Coupled Peeling-Ballooning Modes 160
5.2.3 ELM Stability Diagram 161
5.3…ELM Control Methods 163
5.3.1 Radiating Dispersion 163
5.3.1.1 Type-I ELM Mitigation with Radiative Divertor 164
5.3.1.2 Open Questions 164
5.3.2 Vertical Kicks 165
5.3.2.1 ELM Control Using Vertical Kicks 165
5.3.2.2 Physics and Open Questions 167
5.3.3 Pellet Pace-Making 167
5.3.3.1 ELM Control Using Frozen Pellet Injection 168
5.3.3.2 Physics of Pellet Pace-Making 170
5.3.3.3 Open Questions 170
5.3.4 Resonant Magnetic Perturbation Fields 172
5.3.4.1 Type-I ELM Suppression with RMPs 173
5.3.4.2 Type-I ELM Mitigation with RMPs 174
5.3.4.3 RMP Effects on the Pedestal Profiles and Stability 178
5.3.4.4 Non-resonant Magnetic Braking 180
5.3.4.5 Strike Point Splitting 181
5.3.4.6 Multiple Resonances Effects 182
5.3.4.7 3D Plasma Displacement 183
5.3.4.8 Open Questions 183
5.3.4.9 Future RMP ELM Control/Suppression Experiments 184
5.4…New Control Schemes 185
5.4.1 SMBI ELM Mitigation 185
5.4.2 ELM Mitigation with Lower Hybrid Waves 186
5.5…Combination of Different Methods 186
5.6…Summary 188
References 188
6 Resistive Wall Mode (RWM) 193
Abstract 193
6.1…Introduction 194
6.2…Stability Boundary of the Resistive Wall Mode 195
6.3…Simple Dispersion Relation for the Resistive Wall Mode 197
6.4…Structure of the Resistive Wall Mode 198
6.5…Physics and Control of Resistive Wall Modes 200
6.5.1 RWM Interaction with External Magnetic Fields 201
6.5.1.1 Main Idea of RWM Stabilization with External Coils 203
6.5.1.2 Algorithms for RWM Stabilization 204
6.5.1.3 Cylindrical Model of RWM and Feedback Control 211
6.5.1.4 3D Effects for RWM Stability and Control 215
6.5.2 RWM Interaction with Plasma 216
6.5.3 Experimental Evidence of Kinetic Effects on RWM Stability 223
6.6…RWM Stability in ITER 223
6.6.1 Influence of the Plasma Rotation on the RWM Stability 224
6.6.2 Influence of the Alpha Particles on RWM Stability 224
6.7…Resonant Field Amplification 227
6.8…Triggering of RWM at Low Plasma Rotation 229
6.9…Achievement of high /beta_{N} plasmas in tokamaks 230
6.10…Conclusions and Discussion 231
References 234
7 Disruptions 237
Abstract 237
7.1…Introduction 237
7.2…Causes of Disruptions 239
7.2.1 Performance Stability Limits 240
7.2.2 VDEs 242
7.3…Consequences of Disruptions 242
7.3.1 Heat Loads 242
7.3.2 Eddy Currents, Halo Currents and Forces 243
7.3.3 Runaway Electrons 246
7.4…Detection of Disruptions 247
7.4.1 Artificial Neural Networks 247
7.4.2 Other Methods 252
7.4.3 Remaining Issues 254
7.5…Disruption Avoidance and Control 255
7.6…Disruption Mitigation 256
7.7…Conclusions 263
References 263
8 Neoclassical Tearing Mode (NTM) 268
Abstract 268
8.1…Introduction 268
8.2…Description of the Tearing Mode 269
8.2.1 Current Driven Instabilities 270
8.2.2 Tearing Mode Equation 270
8.2.3 Stability of the Tearing Mode---Rutherford Equation 271
8.2.3.1 Linear Solution for Small Perturbations 271
8.2.3.2 Non-linear Solution for Large Islands 273
8.3…Description of the NTM Physics and Their Suppression or Avoidance 273
8.3.1 Generalized Rutherford Equation Describing NTMs 273
8.3.1.1 Destabilizing Neoclassical Bootstrap Drive 274
8.3.1.2 Stabilizing Finite Parallel Heat Conductivity ( /upchi_{ /bot } //upchi_{{/parallel }} -Correction) 275
8.3.1.3 Stabilizing Glasser Effect 276
8.3.1.4 Stabilizing Polarization Currents 276
8.3.2 Natural Development of an NTM 277
8.3.2.1 Frequently Interrupted Regime (FIR) 278
8.3.3 Distinction Between Current and Neoclassically Driven Tearing Modes 278
8.3.4 Stabilization of Excited NTMs 279
8.3.5 Avoidance of the Excitation of NTMs 281
8.4…Relevant Systems for Controlling and Detecting NTMs 282
8.4.1 Electron Cyclotron Resonance Heating and Current Drive (ECRH/ECCD) 282
8.4.1.1 Control of the ECCD Deposition on a Resonant Surface 283
8.4.1.2 Control of the ECCD Phase in O-Point of the NTM 284
8.4.2 Ion Cyclotron Resonance Heating (ICRH) 285
8.4.3 Lower Hybrid Current Drive (LHCD) 286
8.4.4 External Coils for Repositioning of Locked Modes 287
8.4.5 Relevant Measurements for Detecting NTMs 287
8.5…Stabilization of Excited NTMs 289
8.5.1 Removal of Rotating (3,2) and (2,1) NTMs 289
8.5.2 Experiments Steering the ECCD Phase in the Islands O-Point 291
8.5.3 Locked (2,1) NTMs Before Disruptions---Disruption Avoidance 294
8.6…Avoidance of the Excitation of NTMs 296
8.6.1 Preemptive ECCD at Resonant Surface(S) 296
8.6.2 Profile Tailoring with Wave Heating 297
8.6.3 Current Profile Control with LHCD with Excited NTM 301
8.6.4 Avoidance of NTM Triggering MHD 301
8.7…Effect and Mitigation of Unavoidable NTMs 303
8.7.1 Triggering the FIR Regime 303
8.7.2 Beneficial Effect of NTMs in Improved H-Mode/Hybrid Scenario 304
8.8…Combining the Sensors and Actuators into a Control Scheme 305
8.9…Implication and Outlook for ITER 306
8.10…Summary 309
References 309
9 Energetic Particle Driven Modes 314
Abstract 314
9.1…Introduction 314
9.2…Fast Ions in Tokamaks 317
9.2.1 Sources of Fast Ions 317
9.2.2 Orbit Topology 318
9.3…AlfvÕn Eigenmodes 320
9.3.1 Discrete Spectrum of AlfvÕn Eigenmodes in Toroidal Plasmas and Wave-Particle Resonance Condition 320
9.3.2 Damping Mechanisms of AlfvÕn Eigenmodes 322
9.3.2.1 Continuum Damping 322
9.3.2.2 Ion Landau Damping 322
9.3.2.3 Radiative Damping of TAE 323
9.3.3 Diagnostic Potential 323
9.4…AlfvÕn Eigenmode Stability Measurements 324
9.5…Nonlinear Evolution of Weakly Damped AEs 327
9.6…Conclusions 329
Acknowledgment 329
References 330
10 Perspectives for Integrated Control 331
Abstract 331
10.1…Control Integration to Merge Performance and Reliability 331
10.2…A Brief Summary of Present Control Tools 335
10.2.1 Sawtooth 335
10.2.2 Neoclassical Tearing Modes 336
10.2.3 Edge Localized Modes 337
10.2.4 Resistive Wall Modes 338
10.2.5 Disruptions 340
10.2.6 Fast Particle Driven Instabilities 341
10.3…The Challenge of Integrated Control 342
10.4…Control Integration 345
10.5…Conclusions 349
References 349