Magnetohydrodynamic Stability of Tokamaks.

By: Zohm, HartmutPublisher: Weinheim : John Wiley & Sons, Incorporated, 2015Copyright date: ©2015Edition: 1st edDescription: 1 online resource (256 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9783527677368Subject(s): Tokamaks.;Magnetohydrodynamic generatorsGenre/Form: Electronic books. Additional physical formats: Print version:: Magnetohydrodynamic Stability of TokamaksDDC classification: 538.6 LOC classification: TK9204 -- .Z64 2015ebOnline resources: Click to View
Contents:
Intro -- Magnetohydrodynamic Stability of Tokamaks -- Contents -- Preface -- Chapter 1 The MHD Equations -- 1.1 Derivation of the MHD Equations -- 1.1.1 Multispecies MHD Equations -- 1.1.2 One-Fluid Model of Magnetohydrodynamics -- 1.1.3 Validity of the One-Fluid Model of Magnetohydrodynamics -- 1.2 Consequences of the MHD Equations -- 1.2.1 Magnetic Flux Conservation -- 1.2.2 MHD Equilibrium -- 1.2.3 Magnetohydrodynamic Waves -- 1.2.3.1 Compressional Alfvén Waves -- 1.2.3.2 Shear Alfvén Waves -- Chapter 2 MHD Equilibria in Fusion Plasmas -- 2.1 Linear Configurations -- 2.1.1 The z-Pinch -- 2.1.2 The Screw Pinch -- 2.2 Toroidal Configurations -- 2.2.1 The Tokamak -- 2.2.1.1 The Grad-Shafranov Equation -- 2.2.1.2 Circular Cross Section -- 2.2.1.3 Arbitrary Cross Section -- 2.2.1.4 The Straight Field Line Angle -- 2.2.2 The Stellarator -- Chapter 3 Linear Ideal MHD Stability Analysis -- 3.1 Linear MHD Stability as an Initial Value Problem -- 3.2 The Energy Principle of Ideal MHD -- 3.3 Forms of δW -- 3.4 The Ideal MHD Energy Principle for the Tokamak -- Chapter 4 Current Driven Ideal MHD Modes in a Tokamak -- 4.1 Expression for δW in Tokamak Ordering -- 4.2 External Kinks in a Tokamak with β = 0 -- 4.2.1 Modes with m=1 -- 4.2.2 Modes with m ≥ 2 -- 4.3 Internal Kink Modes -- 4.4 n=0 Modes: The Vertical Displacement Event (VDE) -- Chapter 5 Pressure Driven Modes in a Tokamak -- 5.1 Localized Interchange Modes in the Screw Pinch -- 5.2 Localized Pressure Driven Modes in the Tokamak -- 5.2.1 Interchange Modes in a Tokamak -- 5.2.2 Ballooning Modes -- Chapter 6 Combined Pressure and Current Driven Modes: Edge Localized Modes -- 6.1 ELM Phenomenology -- 6.2 Linear Stability of the Pedestal -- 6.3 Non-linear Evolution -- 6.3.1 Non-linear Cycles -- 6.3.2 Magnitude of the ELM Crash -- 6.3.3 Timescale of the ELM Crash -- 6.4 ELM Control.
6.4.1 Small ELM Regimes -- 6.4.2 Active ELM Control -- Chapter 7 Combined Pressure and Current Driven Modes: The Ideal β-Limit -- 7.1 Tokamak Operational Scenarios -- 7.2 External Kink Modes in a Tokamak with Finite β -- 7.3 The Effect of a Conducting Wall on External Kink Modes -- 7.3.1 Ideally Conducting Wall -- 7.3.2 Resistive Wall -- 7.4 The Resistive Wall Mode (RWM) -- 7.5 The Troyon Limit -- Chapter 8 Resistive MHD Stability -- 8.1 Stability of Current Sheets -- 8.2 Reconnection in the Presence of a Guide Field -- 8.3 Magnetic Islands in Tokamaks -- 8.4 The Rutherford Equation -- Chapter 9 Current Driven (`classical') Tearing Modes in Tokamaks -- 9.1 Effect of Tearing Modes on Kinetic Profiles -- 9.2 Nonlinear Saturation -- 9.3 Tearing Mode Rotation and Locking -- 9.3.1 Rotation of Tearing Modes in Tokamaks -- 9.3.2 Locking of Pre-existing Magnetic Islands -- 9.3.3 Ab-initio Locked Modes -- Chapter 10 Disruptions -- 10.1 Phenomenology of Disruptions -- 10.1.1 The Density Limit -- 10.2 Consequences of Disruptions -- 10.2.1 Thermal Loads -- 10.2.2 Mechanical Loads -- 10.2.3 Runaway Generation -- 10.3 Disruption Avoidance and Mitigation -- Chapter 11 M=1 Modes beyond Ideal MHD: Sawteeth and Fishbones -- 11.1 The Sawtooth Instability -- 11.1.1 Phenomenology -- 11.1.2 Sawtooth Period and Onset Criterion -- 11.1.3 Models for the Sawtooth Crash -- 11.2 The Fishbone Instability -- Chapter 12 Tearing Modes in Finite β-Tokamaks -- 12.1 The Modified Rutherford Equation -- 12.2 The Neoclassical Tearing Mode (NTM) -- 12.3 Onset Criteria for NTMs -- 12.4 Frequently Interrupted Regime (FIR) NTMs -- Chapter 13 Control of Resistive MHD Instabilities by External Current Drive -- 13.1 Basic Properties of Localized Electron Cyclotron Current Drive (ECCD) -- 13.2 Criteria for Control of Resistive Instabilities.
13.2.1 Control by Changing the Equilibrium Current Density -- 13.2.2 Control by Generating Helical Currents -- 13.3 Sawtooth Control -- 13.4 Tearing Mode Control -- References -- Color Plates -- Index -- EULA.
Summary: This book bridges the gap between general plasma physics lectures and the real world problems in MHD stability. In order to support the understanding of concepts and their implication, it refers to real world problems such as toroidal mode coupling or nonlinear evolution in a conceptual and phenomenological approach. Detailed mathematical treatment will involve classical linear stability analysis and an outline of more recent concepts such as the ballooning formalism. The book is based on lectures that the author has given to Master and PhD students in Fusion Plasma Physics. Due its strong link to experimental results in MHD instabilities, the book is also of use to senior researchers in the field, i.e. experimental physicists and engineers in fusion reactor science. The volume is organized in three parts. It starts with an introduction to the MHD equations, a section on toroidal equilibrium (tokamak and stellarator), and on linear stability analysis. Starting from there, the ideal MHD stability of the tokamak configuration will be treated in the second part which is subdivided into current driven and pressure driven MHD. This includes many examples with reference to experimental results for important MHD instabilities such as kinks and their transformation to RWMs, infernal modes, peeling modes, ballooning modes and their relation to ELMs. Finally the coverage is completed by a chapter on resistive stability explaining reconnection and island formation. Again, examples from recent tokamak MHD such as sawteeth, CTMs, NTMs and their relation to disruptions are extensively discussed.
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Intro -- Magnetohydrodynamic Stability of Tokamaks -- Contents -- Preface -- Chapter 1 The MHD Equations -- 1.1 Derivation of the MHD Equations -- 1.1.1 Multispecies MHD Equations -- 1.1.2 One-Fluid Model of Magnetohydrodynamics -- 1.1.3 Validity of the One-Fluid Model of Magnetohydrodynamics -- 1.2 Consequences of the MHD Equations -- 1.2.1 Magnetic Flux Conservation -- 1.2.2 MHD Equilibrium -- 1.2.3 Magnetohydrodynamic Waves -- 1.2.3.1 Compressional Alfvén Waves -- 1.2.3.2 Shear Alfvén Waves -- Chapter 2 MHD Equilibria in Fusion Plasmas -- 2.1 Linear Configurations -- 2.1.1 The z-Pinch -- 2.1.2 The Screw Pinch -- 2.2 Toroidal Configurations -- 2.2.1 The Tokamak -- 2.2.1.1 The Grad-Shafranov Equation -- 2.2.1.2 Circular Cross Section -- 2.2.1.3 Arbitrary Cross Section -- 2.2.1.4 The Straight Field Line Angle -- 2.2.2 The Stellarator -- Chapter 3 Linear Ideal MHD Stability Analysis -- 3.1 Linear MHD Stability as an Initial Value Problem -- 3.2 The Energy Principle of Ideal MHD -- 3.3 Forms of δW -- 3.4 The Ideal MHD Energy Principle for the Tokamak -- Chapter 4 Current Driven Ideal MHD Modes in a Tokamak -- 4.1 Expression for δW in Tokamak Ordering -- 4.2 External Kinks in a Tokamak with β = 0 -- 4.2.1 Modes with m=1 -- 4.2.2 Modes with m ≥ 2 -- 4.3 Internal Kink Modes -- 4.4 n=0 Modes: The Vertical Displacement Event (VDE) -- Chapter 5 Pressure Driven Modes in a Tokamak -- 5.1 Localized Interchange Modes in the Screw Pinch -- 5.2 Localized Pressure Driven Modes in the Tokamak -- 5.2.1 Interchange Modes in a Tokamak -- 5.2.2 Ballooning Modes -- Chapter 6 Combined Pressure and Current Driven Modes: Edge Localized Modes -- 6.1 ELM Phenomenology -- 6.2 Linear Stability of the Pedestal -- 6.3 Non-linear Evolution -- 6.3.1 Non-linear Cycles -- 6.3.2 Magnitude of the ELM Crash -- 6.3.3 Timescale of the ELM Crash -- 6.4 ELM Control.

6.4.1 Small ELM Regimes -- 6.4.2 Active ELM Control -- Chapter 7 Combined Pressure and Current Driven Modes: The Ideal β-Limit -- 7.1 Tokamak Operational Scenarios -- 7.2 External Kink Modes in a Tokamak with Finite β -- 7.3 The Effect of a Conducting Wall on External Kink Modes -- 7.3.1 Ideally Conducting Wall -- 7.3.2 Resistive Wall -- 7.4 The Resistive Wall Mode (RWM) -- 7.5 The Troyon Limit -- Chapter 8 Resistive MHD Stability -- 8.1 Stability of Current Sheets -- 8.2 Reconnection in the Presence of a Guide Field -- 8.3 Magnetic Islands in Tokamaks -- 8.4 The Rutherford Equation -- Chapter 9 Current Driven (`classical') Tearing Modes in Tokamaks -- 9.1 Effect of Tearing Modes on Kinetic Profiles -- 9.2 Nonlinear Saturation -- 9.3 Tearing Mode Rotation and Locking -- 9.3.1 Rotation of Tearing Modes in Tokamaks -- 9.3.2 Locking of Pre-existing Magnetic Islands -- 9.3.3 Ab-initio Locked Modes -- Chapter 10 Disruptions -- 10.1 Phenomenology of Disruptions -- 10.1.1 The Density Limit -- 10.2 Consequences of Disruptions -- 10.2.1 Thermal Loads -- 10.2.2 Mechanical Loads -- 10.2.3 Runaway Generation -- 10.3 Disruption Avoidance and Mitigation -- Chapter 11 M=1 Modes beyond Ideal MHD: Sawteeth and Fishbones -- 11.1 The Sawtooth Instability -- 11.1.1 Phenomenology -- 11.1.2 Sawtooth Period and Onset Criterion -- 11.1.3 Models for the Sawtooth Crash -- 11.2 The Fishbone Instability -- Chapter 12 Tearing Modes in Finite β-Tokamaks -- 12.1 The Modified Rutherford Equation -- 12.2 The Neoclassical Tearing Mode (NTM) -- 12.3 Onset Criteria for NTMs -- 12.4 Frequently Interrupted Regime (FIR) NTMs -- Chapter 13 Control of Resistive MHD Instabilities by External Current Drive -- 13.1 Basic Properties of Localized Electron Cyclotron Current Drive (ECCD) -- 13.2 Criteria for Control of Resistive Instabilities.

13.2.1 Control by Changing the Equilibrium Current Density -- 13.2.2 Control by Generating Helical Currents -- 13.3 Sawtooth Control -- 13.4 Tearing Mode Control -- References -- Color Plates -- Index -- EULA.

This book bridges the gap between general plasma physics lectures and the real world problems in MHD stability. In order to support the understanding of concepts and their implication, it refers to real world problems such as toroidal mode coupling or nonlinear evolution in a conceptual and phenomenological approach. Detailed mathematical treatment will involve classical linear stability analysis and an outline of more recent concepts such as the ballooning formalism. The book is based on lectures that the author has given to Master and PhD students in Fusion Plasma Physics. Due its strong link to experimental results in MHD instabilities, the book is also of use to senior researchers in the field, i.e. experimental physicists and engineers in fusion reactor science. The volume is organized in three parts. It starts with an introduction to the MHD equations, a section on toroidal equilibrium (tokamak and stellarator), and on linear stability analysis. Starting from there, the ideal MHD stability of the tokamak configuration will be treated in the second part which is subdivided into current driven and pressure driven MHD. This includes many examples with reference to experimental results for important MHD instabilities such as kinks and their transformation to RWMs, infernal modes, peeling modes, ballooning modes and their relation to ELMs. Finally the coverage is completed by a chapter on resistive stability explaining reconnection and island formation. Again, examples from recent tokamak MHD such as sawteeth, CTMs, NTMs and their relation to disruptions are extensively discussed.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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