Magnetically confined fusion plasma physics : ideal MHD theory
Plasma confinement Plasma (Ionized gases) Nuclear fusion
IOP Publishing
2019
EISBN 9781643271385
1. Fusion energy : concepts and prospects.
1.1. Nuclear fusion and Lawson's criterion.
1.2. Magnetic confinement.
1.3. Inertial confinement
2. Ideal magnetohydrodynamic (MHD) equations and multi-parallel-fluid MHD theory.
2.1. Moments of the kinetic equation.
2.2. Ideal MHD equations.
2.3. Multi-parallel-fluid MHD theory
3. Magnetohydrodynamic (MHD) equilibrium.
3.1. Flux coordinates for symmetric system.
3.2. Grad-Shafranov equation.
3.3. Green function and free boundary equilibrium.
3.4. Solovév solution and modification.
3.5. Local equilibrium near the X-point.
3.6. Numerical solution of Grad-Shafranov equation : ATEQ code.
3.7. Mirror equilibrium
4. Ideal magnetohydrodynamic (MHD) energy principle.
4.1. Linear ideal MHD energy principle.
4.2. Energy minimization for localized interchange modes.
4.3. Energy minimization for high-n modes.
4.4. Energy principle for tokamak geometry.
4.5. Energy principle in cylinder model
5. Magnetohydrodynamic (MHD) mode spectrum in tokamaks.
5.1. Singular differential equation in the MHD system.
5.2. Alfvén continuum theory in the real space.
5.3. Continuum theory in the complex space : quasi-modes.
5.4. Initial value problem : phase mixing.
5.5. Inhomogeneous boundary value problem : plasma heating.
5.6. Tokamak global MHD spectrum
6. Magnetohydrodynamic (MHD) stability theory in tokamaks.
6.1. Radially localized modes : Mercier criterion.
6.2. External radially localized modes : peeling modes.
6.3. Ballooning modes.
6.4. Toroidal Alfvén eigenmodes (TAEs).
6.5. Internal kink type of modes
7. Global magnetohydrodynamic (MHD) stability computation : internal and external modes.
7.1. Internal modes.
7.2. External kink modes.
7.3. Resistive wall modes.
7.3..1 Rotation stabilization.
7.4. Error-field amplification.
7.5. Alfvén modes
8. Concluding remarks.
Appendix A. Derivation of some basic MHD formula.
Appendix B. Acronym list.
This book describes the ideal magnetohydrodynamic theory for magnetically confined fusion plasmas. Advanced topics are presented in attempting to fill the gap between the up-to-date research developments and plasma physics textbooks. Nevertheless, they are self-contained and trackable with the mathematical treatments detailed and underlying physics explained. Both analytical theories and numerical schemes are given. Besides the current research developments in this field, the future prospects are also discussed.
1.1. Nuclear fusion and Lawson's criterion.
1.2. Magnetic confinement.
1.3. Inertial confinement
2. Ideal magnetohydrodynamic (MHD) equations and multi-parallel-fluid MHD theory.
2.1. Moments of the kinetic equation.
2.2. Ideal MHD equations.
2.3. Multi-parallel-fluid MHD theory
3. Magnetohydrodynamic (MHD) equilibrium.
3.1. Flux coordinates for symmetric system.
3.2. Grad-Shafranov equation.
3.3. Green function and free boundary equilibrium.
3.4. Solovév solution and modification.
3.5. Local equilibrium near the X-point.
3.6. Numerical solution of Grad-Shafranov equation : ATEQ code.
3.7. Mirror equilibrium
4. Ideal magnetohydrodynamic (MHD) energy principle.
4.1. Linear ideal MHD energy principle.
4.2. Energy minimization for localized interchange modes.
4.3. Energy minimization for high-n modes.
4.4. Energy principle for tokamak geometry.
4.5. Energy principle in cylinder model
5. Magnetohydrodynamic (MHD) mode spectrum in tokamaks.
5.1. Singular differential equation in the MHD system.
5.2. Alfvén continuum theory in the real space.
5.3. Continuum theory in the complex space : quasi-modes.
5.4. Initial value problem : phase mixing.
5.5. Inhomogeneous boundary value problem : plasma heating.
5.6. Tokamak global MHD spectrum
6. Magnetohydrodynamic (MHD) stability theory in tokamaks.
6.1. Radially localized modes : Mercier criterion.
6.2. External radially localized modes : peeling modes.
6.3. Ballooning modes.
6.4. Toroidal Alfvén eigenmodes (TAEs).
6.5. Internal kink type of modes
7. Global magnetohydrodynamic (MHD) stability computation : internal and external modes.
7.1. Internal modes.
7.2. External kink modes.
7.3. Resistive wall modes.
7.3..1 Rotation stabilization.
7.4. Error-field amplification.
7.5. Alfvén modes
8. Concluding remarks.
Appendix A. Derivation of some basic MHD formula.
Appendix B. Acronym list.
This book describes the ideal magnetohydrodynamic theory for magnetically confined fusion plasmas. Advanced topics are presented in attempting to fill the gap between the up-to-date research developments and plasma physics textbooks. Nevertheless, they are self-contained and trackable with the mathematical treatments detailed and underlying physics explained. Both analytical theories and numerical schemes are given. Besides the current research developments in this field, the future prospects are also discussed.
