This book describes the ideal magnetohydrodynamic theory for magnetically conned 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.
Nowadays, it is believed that, if the ideal MHD theory predicts major instabilities, none of the magnetic confinements of fusion plasmas can survive. The author has also written the book Advanced Tokamak Stability Theory. In view of its importance, the MHD theory is further systematically elaborated in this book. The conventional ideal MHD framework is reviewed together with the newly developed multi-parallel-fluid MHD theory. The MHD equilibrium theory and code are described with the non-letter-'X' separatrix feature pointed out. The continuum modes, quasi-modes, phase mixing, and Alfven resonance heating are analysed. The analytical theories for MHD stability in tokamak configurations are systematically presented, such as the interchange, peeling, ballooning, toroidal Alfven modes, and kink type of modes. The global stability computations are also addressed, including resistive wall modes, error-field amplifications, and Alfven modes, etc.
Author(s): Linjin Zheng
Series: IOP Concise Physics
Publisher: IOP Publishing
Year: 2019
Language: English
Pages: 154
City: Bristol
PRELIMS.pdf
Preface
Acknowledgements
Author biography
Linjin Zheng
CH001.pdf
Chapter 1 Fusion energy: concepts and prospects
1.1 Nuclear fusion and Lawson’s criterion
1.2 Magnetic confinement
1.2.1 Tokamaks
1.2.2 Stellarators
1.2.3 Rotating theta-pinched mirrors
1.3 Inertial confinement
References
CH002.pdf
Chapter 2 Ideal magnetohydrodynamic (MHD) equations and multi-parallel-fluid MHD theory
2.1 Moments of the kinetic equation
2.1.1 Continuity equation
2.1.2 Momentum equation
2.1.3 Energy equation
2.1.4 Entropy equation and adiabatic assumption
2.2 Ideal MHD equations
2.3 Multi-parallel-fluid MHD theory
References
CH003.pdf
Chapter 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
References
CH004.pdf
Chapter 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
4.4.1 Plasma energy
4.4.2 Vacuum energy
4.5 Energy principle in cylinder model
References
CH005.pdf
Chapter 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
References
CH006.pdf
Chapter 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
6.3.1 Ballooning mode representation and equations
6.3.2 Asymptotic behavior
6.3.3 Steep-pressure-gradient equilibrium model
6.4 Toroidal Alfvén eigenmodes
6.4.1 TAE theory in the configuration space
6.4.2 TAE theory in the ballooning representation space
6.5 Internal kink type of modes
6.5.1 Configuration space description
6.5.2 Ballooning representation space description
References
CH007.pdf
Chapter 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
References
CH008.pdf
Chapter 8 Concluding remarks
References
APP1.pdf
Chapter
Reference
APP2.pdf
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