Freidberg J.P. Ideal MHD

Cambridge University Press, 2014. — 740 pp. — ISBN: 9781107006256.Comprehensive, self-contained, and clearly written, this successor to Ideal Magnetohydrodynamics (1987) describes the macroscopic equilibrium and stability of high temperature plasmas - the basic fuel for the development of fusion power. Now fully updated, this book discusses the underlying physical assumptions for three basic MHD models: ideal, kinetic, and double-adiabatic MHD. Included are detailed analyses of MHD equilibrium and stability, with a particular focus on three key configurations at the cutting-edge of fusion research: the tokamak, stellarator, and reversed field pinch. Other new topics include continuum damping, MHD stability comparison theorems, neoclassical transport in stellarators, and how quasi-omnigeneity, quasi-symmetry, and quasi-isodynamic constraints impact the design of optimized stellarators. Including full derivations of almost every important result, in-depth physical explanations throughout, and a large number of problem sets to help master the material, this is an exceptional resource for graduate students and researchers in plasma and fusion physics.Includes extensive discussion of the stellerator, including MHD equilibrium and stability, neoclassical transport, and the ways in which omigeneity, quasi-symmetry, and the quasi-isodynamic properly impact optimal stellerator design.
Addresses numerous practical issues relating to fusion configuration stability, such as the calculation of relevant eigenfrequencies and eigenfunctions, stability testing via the Energy Principle procedure, and specific instabilities such as sawtooth oscillations, major disruptions, ELMs, and resistive wall models.
Presents tropics in enough depth for readers not to have to refer to large amounts of source material to truly master the physics.Table of ContentsThe ideal MHD model
General properties of ideal MHD
Equilibrium: one-dimensional configurations
Equilibrium: two-dimensional configurations
Equilibrium: three-dimensional configurations
Stability: general considerations
Alternate MHD models
MHD stability comparison theorems
Stability: one-dimensional configurations
Stability: multi-dimensional configurations
Appendix A. Heuristic derivation of the kinetic equation
Appendix B. The Braginskii transport coefficients
Appendix C. Time derivatives in moving plasmas
Appendix D. The curvature vector
Appendix E. Overlap limit of the high b and Greene–Johnson stellarator models
Appendix F. General form for q(y)
Appendix G. Natural boundary conditions
Appendix H. Upper and lower bounds on dQKIN.