**Description:**

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.

**Contents:**

**Preface **

**Acknowledgements **

**Author biography **

**Chapter 1: Fusion energy: concepts and prospects** •
Nuclear fusion and Lawson’s criterion • Magnetic confinement • Tokamaks •
Stellarators • Rotating theta-pinched mirrors • Inertial confinement •
References

**Chapter 2: Ideal magnetohydrodynamic (MHD) equations and
multi-parallel-fluid MHD theory** • Moments of the kinetic
equation • Continuity equation • Momentum equation • Energy equation • Entropy
equation and adiabatic assumption • Ideal MHD equations • Multi-parallel-fluid
MHD theory • References

**Chapter 3: Magnetohydrodynamic (MHD) equilibrium** •
Flux coordinates for symmetric system • Grad–Shafranov equation • Green
function and free boundary equilibrium • Solovév solution and modification •
Local equilibrium near the X-point • Numerical solution of Grad–Shafranov
equation: ATEQ code • Mirror equilibrium • References

**Chapter 4: Ideal magnetohydrodynamic (MHD) energy
principle** • Linear ideal MHD energy principle • Energy
minimization for localized interchange modes • Energy minimization for high-n
modes • Energy principle for tokamak geometry • Plasma energy • Vacuum energy •
Energy principle in cylinder model • References

**Chapter 5: Magnetohydrodynamic (MHD) mode spectrum in
tokamaks** • Singular differential equation in the MHD system •
Alfvén continuum theory in the real space • Continuum theory in the complex
space: quasi-modes • Initial value problem: phase mixing • Inhomogeneous
boundary value problem: plasma heating • Tokamak global MHD spectrum •
References

**Chapter 6: Magnetohydrodynamic (MHD) stability theory in
tokamaks** • Radially localized modes: Mercier criterion • External
radially localized modes: peeling modes • Ballooning modes • Ballooning mode
representation and equations • Asymptotic behavior • Steep-pressure-gradient
equilibrium model • Toroidal Alfvén eigenmodes (TAEs) • TAE theory in the
configuration space • TAE theory in the ballooning representation space •
Internal kink type of modes • Configuration space description • Ballooning
representation space description • References

**Chapter 7: Global magnetohydrodynamic (MHD) stability
computation: internal and external modes** • Internal modes • External
kink modes • Resistive wall modes • Rotation stabilization • Error-field
amplification • Alfvén modes • References

**Chapter 8: Concluding remarks** • References

**Appendix A: Derivation of some basic MHD formula** •
Reference

**Appendix B: Acronym list **

**About the Author:**

**Linjin Zheng, University of Texas at Austin**

Dr.
Linjin Zheng is a theoretical physicist for controlled thermonuclear fusion
plasmas. He received his PhD from Institute of Physics at the Chinese Academy
of Sciences in Beijing. He is currently working at The University of Texas at
Austin, Institute for Fusion Studies. His major contributions with his
colleagues include the reformulation of gyrokinetic theory, development of the
theoretical interpretation for the so-called edge localized modes, invention of
the free boundary ballooning representation, discoveries of second toroidal
Alfven egenmodes and current interchange tearing modes.

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**Target Audience:**

This
book is intended for students and academicians of Physics.