Hartmut Zohm is Director of the Tokamak Scenario Development Division at the Max-Planck-Institute for Plasma Physics located in Garching, Germany. His main fields of interest are the magnetohydrodynamic (MHD) stability of fusion plasmas and their heating by Electron Cyclotron Resonance Heating (ECRH). By combining these two fields, he pioneered the active stabilisation of neoclassical magnetic islands, which set a major performance limit to the tokamak, by ECRH. His present field is the study of tokamak physics on the ASDEX Upgrade tokamak which is operated by his department.Professor Zohm has published a total of more than 200 papers. He is member of several international committees such as the ITPA coordinating committee, the IEA Implementing Agreement on Collaboration of Tokamak Programmes, the Programme Advisory Committees of MAST, KSTAR, DIII-D and the scientific advisory board of IPP.CR and the EU Fusion STAC. He is also a member of the board of editors of the 'Nuclear Fusion' journal and a member of the advisory boards of the 'Annalen der Physik' journal.

“The book is an excellent introduction and composition of modern results that may help not only the newcomers but also the specialists { congratulations to the author.”  (Zentralblatt MATH, 1 September 2015)

• Preface IX1 The MHD Equations 11.1 Derivation of the MHD Equations 11.2 Consequences of the MHD Equations 82 MHD Equilibria in Fusion Plasmas 152.1 Linear Configurations 152.2 Toroidal Configurations 223 Linear Ideal MHD Stability Analysis 433.1 Linear MHD Stability as an Initial Value Problem 443.2 The Energy Principle of Ideal MHD 473.3 Forms of δW 483.4 The Ideal MHD Energy Principle for the Tokamak 514 Current Driven Ideal MHD Modes in a Tokamak 55 4.1 Expression for δW in Tokamak Ordering 554.2 External Kinks in a Tokamak with β= 0 564.3 Internal Kink Modes 614.4 n = 0 Modes: The Vertical Displacement Event (VDE) 635 Pressure Driven Modes in a Tokamak 69 5.1 Localized Interchange Modes in the Screw Pinch 695.2 Localized Pressure Driven Modes in the Tokamak 726 Combined Pressure and Current Driven Modes: Edge Localized Modes 836.1 ELM Phenomenology 846.2 Linear Stability of the Pedestal 866.3 Non-linear Evolution 906.4 ELM Control 947 Combined Pressure and Current Driven Modes: The Ideal β-Limit 1037.1 Tokamak Operational Scenarios 1037.2 External Kink Modes in a Tokamak with Finite β 1057.3 The Effect of a Conducting Wall on External Kink Modes 1077.4 The Resistive Wall Mode (RWM) 1127.5 The Troyon Limit 1188 Resistive MHD Stability 123 8.1 Stability of Current Sheets 1248.2 Reconnection in the Presence of a Guide Field 1278.3 Magnetic Islands in Tokamaks 1348.4 The Rutherford Equation 1379 Current Driven ('classical') Tearing Modes in Tokamaks 141 9.1 Effect of Tearing Modes on Kinetic Profiles 1419.2 Nonlinear Saturation 1449.3 Tearing Mode Rotation and Locking 14610 Disruptions 159 10.1 Phenomenology of Disruptions 15910.2 Consequences of Disruptions 16510.3 Disruption Avoidance and Mitigation 17111 M=1 Modes beyond Ideal MHD: Sawteeth and Fishbones 17511.1 The Sawtooth Instability 1711.2 The Fishbone Instability 18412 Tearing Modes in Finite β-Tokamaks 189 12.1 The Modified Rutherford Equation 18912.2 The Neoclassical Tearing Mode (NTM) 19012.3 Onset Criteria for NTMs 19412.4 Frequently Interrupted Regime (FIR) NTMs 19713 Control of Resistive MHD Instabilities by External Current Drive 20113.1 Basic Properties of Localized Electron Cyclotron Current Drive (ECCD) 20213.2 Criteria for Control of Resistive Instabilities 20313.3 Sawtooth Control 20813.4 Tearing Mode Control 211References 215Index 221

Hartmut Zohm is Director of the Tokamak Scenario Development Division at the Max-Planck-Institute for Plasma Physics located in Garching, Germany. His main fields of interest are the magnetohydrodynamic (MHD) stability of fusion plasmas and their heating by Electron Cyclotron Resonance Heating (ECRH). By combining these two fields, he pioneered the active stabilisation of neoclassical magnetic islands, which set a major performance limit to the tokamak, by ECRH. His present field is the study of tokamak physics on the ASDEX Upgrade tokamak which is operated by his department.Professor Zohm has published a total of more than 200 papers. He is member of several international committees such as the ITPA coordinating committee, the IEA Implementing Agreement on Collaboration of Tokamak Programmes, the Programme Advisory Committees of MAST, KSTAR, DIII-D and the scientific advisory board of IPP.CR and the EU Fusion STAC. He is also a member of the board of editors of the 'Nuclear Fusion' journal and a member of the advisory boards of the 'Annalen der Physik' journal.

“The book is an excellent introduction and composition of modern results that may help not only the newcomers but also the specialists { congratulations to the author.”  (Zentralblatt MATH, 1 September 2015)

• Preface IX1 The MHD Equations 11.1 Derivation of the MHD Equations 11.2 Consequences of the MHD Equations 82 MHD Equilibria in Fusion Plasmas 152.1 Linear Configurations 152.2 Toroidal Configurations 223 Linear Ideal MHD Stability Analysis 433.1 Linear MHD Stability as an Initial Value Problem 443.2 The Energy Principle of Ideal MHD 473.3 Forms of δW 483.4 The Ideal MHD Energy Principle for the Tokamak 514 Current Driven Ideal MHD Modes in a Tokamak 55 4.1 Expression for δW in Tokamak Ordering 554.2 External Kinks in a Tokamak with β= 0 564.3 Internal Kink Modes 614.4 n = 0 Modes: The Vertical Displacement Event (VDE) 635 Pressure Driven Modes in a Tokamak 69 5.1 Localized Interchange Modes in the Screw Pinch 695.2 Localized Pressure Driven Modes in the Tokamak 726 Combined Pressure and Current Driven Modes: Edge Localized Modes 836.1 ELM Phenomenology 846.2 Linear Stability of the Pedestal 866.3 Non-linear Evolution 906.4 ELM Control 947 Combined Pressure and Current Driven Modes: The Ideal β-Limit 1037.1 Tokamak Operational Scenarios 1037.2 External Kink Modes in a Tokamak with Finite β 1057.3 The Effect of a Conducting Wall on External Kink Modes 1077.4 The Resistive Wall Mode (RWM) 1127.5 The Troyon Limit 1188 Resistive MHD Stability 123 8.1 Stability of Current Sheets 1248.2 Reconnection in the Presence of a Guide Field 1278.3 Magnetic Islands in Tokamaks 1348.4 The Rutherford Equation 1379 Current Driven ('classical') Tearing Modes in Tokamaks 141 9.1 Effect of Tearing Modes on Kinetic Profiles 1419.2 Nonlinear Saturation 1449.3 Tearing Mode Rotation and Locking 14610 Disruptions 159 10.1 Phenomenology of Disruptions 15910.2 Consequences of Disruptions 16510.3 Disruption Avoidance and Mitigation 17111 M=1 Modes beyond Ideal MHD: Sawteeth and Fishbones 17511.1 The Sawtooth Instability 1711.2 The Fishbone Instability 18412 Tearing Modes in Finite β-Tokamaks 189 12.1 The Modified Rutherford Equation 18912.2 The Neoclassical Tearing Mode (NTM) 19012.3 Onset Criteria for NTMs 19412.4 Frequently Interrupted Regime (FIR) NTMs 19713 Control of Resistive MHD Instabilities by External Current Drive 20113.1 Basic Properties of Localized Electron Cyclotron Current Drive (ECCD) 20213.2 Criteria for Control of Resistive Instabilities 20313.3 Sawtooth Control 20813.4 Tearing Mode Control 211References 215Index 221

Hartmut Zohm is Director of the Tokamak Scenario Development Division at the Max-Planck-Institute for Plasma Physics located in Garching, Germany. His main fields of interest are the magnetohydrodynamic (MHD) stability of fusion plasmas and their heating by Electron Cyclotron Resonance Heating (ECRH). By combining these two fields, he pioneered the active stabilisation of neoclassical magnetic islands, which set a major performance limit to the tokamak, by ECRH. His present field is the study of tokamak physics on the ASDEX Upgrade tokamak which is operated by his department.Professor Zohm has published a total of more than 200 papers. He is member of several international committees such as the ITPA coordinating committee, the IEA Implementing Agreement on Collaboration of Tokamak Programmes, the Programme Advisory Committees of MAST, KSTAR, DIII-D and the scientific advisory board of IPP.CR and the EU Fusion STAC. He is also a member of the board of editors of the 'Nuclear Fusion' journal and a member of the advisory boards of the 'Annalen der Physik' journal.

“The book is an excellent introduction and composition of modern results that may help not only the newcomers but also the specialists { congratulations to the author.”  (Zentralblatt MATH, 1 September 2015)

• Preface IX1 The MHD Equations 11.1 Derivation of the MHD Equations 11.2 Consequences of the MHD Equations 82 MHD Equilibria in Fusion Plasmas 152.1 Linear Configurations 152.2 Toroidal Configurations 223 Linear Ideal MHD Stability Analysis 433.1 Linear MHD Stability as an Initial Value Problem 443.2 The Energy Principle of Ideal MHD 473.3 Forms of δW 483.4 The Ideal MHD Energy Principle for the Tokamak 514 Current Driven Ideal MHD Modes in a Tokamak 55 4.1 Expression for δW in Tokamak Ordering 554.2 External Kinks in a Tokamak with β= 0 564.3 Internal Kink Modes 614.4 n = 0 Modes: The Vertical Displacement Event (VDE) 635 Pressure Driven Modes in a Tokamak 69 5.1 Localized Interchange Modes in the Screw Pinch 695.2 Localized Pressure Driven Modes in the Tokamak 726 Combined Pressure and Current Driven Modes: Edge Localized Modes 836.1 ELM Phenomenology 846.2 Linear Stability of the Pedestal 866.3 Non-linear Evolution 906.4 ELM Control 947 Combined Pressure and Current Driven Modes: The Ideal β-Limit 1037.1 Tokamak Operational Scenarios 1037.2 External Kink Modes in a Tokamak with Finite β 1057.3 The Effect of a Conducting Wall on External Kink Modes 1077.4 The Resistive Wall Mode (RWM) 1127.5 The Troyon Limit 1188 Resistive MHD Stability 123 8.1 Stability of Current Sheets 1248.2 Reconnection in the Presence of a Guide Field 1278.3 Magnetic Islands in Tokamaks 1348.4 The Rutherford Equation 1379 Current Driven ('classical') Tearing Modes in Tokamaks 141 9.1 Effect of Tearing Modes on Kinetic Profiles 1419.2 Nonlinear Saturation 1449.3 Tearing Mode Rotation and Locking 14610 Disruptions 159 10.1 Phenomenology of Disruptions 15910.2 Consequences of Disruptions 16510.3 Disruption Avoidance and Mitigation 17111 M=1 Modes beyond Ideal MHD: Sawteeth and Fishbones 17511.1 The Sawtooth Instability 1711.2 The Fishbone Instability 18412 Tearing Modes in Finite β-Tokamaks 189 12.1 The Modified Rutherford Equation 18912.2 The Neoclassical Tearing Mode (NTM) 19012.3 Onset Criteria for NTMs 19412.4 Frequently Interrupted Regime (FIR) NTMs 19713 Control of Resistive MHD Instabilities by External Current Drive 20113.1 Basic Properties of Localized Electron Cyclotron Current Drive (ECCD) 20213.2 Criteria for Control of Resistive Instabilities 20313.3 Sawtooth Control 20813.4 Tearing Mode Control 211References 215Index 221