2 The linearized ideal MHO equations. . . . . . . . . . . . 204 3 Spectral problems corresponding to evolutionary problems . . 211 4 Stability of equilibrium configurations and the Energy Principle 215 5 Alternative forms of the plasma potential energy 220 6 Minimization of the potential energy with respect to a parallel displacement . . . . . . . . . . . . . 222 7 Classification of ideal MHO instabilities . 224 8 The linearized non-ideal MHO equations . 226 Chapter 6. Homogeneous and discretely structured plasma oscillations 229 I Introduction . . . . . . . . . . . . . . . 229 2 Alfven waves in an incompressible ideal plasma 230 3 Cold ideal plasma oscillations. . . . 233 4 Compressible hot plasma oscillations 236 5 Finite resistivity effects . . . . . . . 239 6 Propagation of waves generated by a local source 240 7 Stratified plasma oscillations . . . . . . . . . 247 8 Oscillations of a plasma slab . . . . . . . . . 254 9 Instabilities of an ideal stratified gravitating plasma 256 10 Instabilities of a resistive stratified gravitating plasma. 262 Chapter 7. MHO oscillations of a gravitating plasma slab 265 I Introduction . . . . . . . . . . . . . . . 265 2 Gravitating slab equilibrium . . . . . . . . 266 3 Oscillations of a hot compressible plasma slab 267 4 Investigation of the slab stability via the Energy Principle 270 5 On the discrete spectrum of the operator Kk . . . . . . 274 6 On the essential spectrum of the operator Kk . . . . . . 279 7 On the discrete spectrum embedded in the essential spectrum 282 8 The eigenfunction expansion formula . . . . . . . . . . 285 9 Excitation of plasma oscillations by an external power source . 288 10 The linearized equations governing resistive gravitating plasma slab oscillations . . . . . . . . . . . . . . . . . . . . . 290 II Heuristic investigation of resistive instabilities. . . . . . . . . .

An introduction to magnetohydrodynamics combining theory with advanced topics including the applications of plasma physics to thermonuclear fusion and plasma astrophysics.

This textbook provides a modern and accessible introduction to magnetohydrodynamics (MHD). It describes the two main applications of plasma physics, laboratory research on thermo-nuclear fusion energy and plasma astrophysics of the solar system, stars and accretion disks, from the single viewpoint of MHD. This approach provides effective methods and insights for the interpretation of plasma phenomena on virtually all scales, from the laboratory to the universe. It equips the reader with the necessary tools to understand the complexities of plasma dynamics in extended magnetic structures. The classical MHD model is developed in detail without omitting steps in the derivations and problems are included at the end of each chapter. This text is ideal for senior-level undergraduate and graduate courses in plasma physics and astrophysics.

Following on from the companion volume Principles of Magnetohydrodynamics, this textbook analyzes the applications of plasma physics to thermonuclear fusion and plasma astrophysics from the single viewpoint of MHD. This approach turns out to be ever more powerful when applied to streaming plasmas (the vast majority of visible matter in the Universe), toroidal plasmas (the most promising approach to fusion energy), and nonlinear dynamics (where it all comes together with modern computational techniques and extreme transonic and relativistic plasma flows). The textbook interweaves theory and explicit calculations of waves and instabilities of streaming plasmas in complex magnetic geometries. It is ideally suited to advanced undergraduate and graduate courses in plasma physics and astrophysics.

Magnetohydrodynamic Processes in The Solar Plasma provides comprehensive and up-to-date theory and practice of the fundamentals of heliospheric research and the Sun's basic plasma processes, covering the dynamics of the solar interior to its exterior in the framework of magnetohydrodynamics. The book covers novel aspects of solar and heliospheric physics, astrophysics and space science, and fundamentals of the fluids and plasmas. Topics covered include key phenomena in the solar interior such as magnetism, dynamo physics, and helioseismology; dynamics and plasma processes in its exterior including fluid processes such as waves, shocks, instabilities, reconnection, and dynamics in the partially ionized plasma; and physics and science related to coronal heating, solar wind, and eruptive phenomena. The content has been developed to specifically cover fundamental physics-related descriptions and up-to-date developments of the scientific research related to these significant topics. The book therefore provides the entire fundamental and front-line research aspects of solar and heliospheric plasma processes, mainly in the context of solar plasma, however, the content also has larger implications for the astrophysical plasma, and laboratory plasma, fluid dynamics, and associated basic theories. It also includes additional supplementary content such as key instruments and experimental techniques in the form of appendices, boxed-off key information highlighting the most fundamental and key aspects, and worked examples with additional question sets.Magnetohydrodynamic Processes in The Solar Plasma covers both the fundamentals of the topics included as well as up-to-date and future developments in this research field, forming an essential, foundational reference for researchers, academics, and advanced students, in the field of solar physics and astrophysics, as well as neighboring disciplines. - Applies fundamental solar science and research in magnetohydrodynamic processes to practice, and uses in teaching and research - Covers the latest developments in solar plasma processes in terms of both theoretical and fundamental aspects. - Includes the large cohort of plasma processes (e.g., waves, shocks, instabilities, reconnection, heating, magnetism, seismology) significant for the diverse scales of the plasmas and fluids. - Provides detailed physical and mathematical descriptions of the theories in each chapter, along with scientific details, which will enhance understanding of basic phenomena and aid in applying the practical content to current research

This book presents an introduction to, and modern account of, magnetohydrodynamic (MHD) turbulence, an active field both in general turbulence theory and in various areas of astrophysics. The book starts by introducing the MHD equations, certain useful approximations and the transition to turbulence. The second part of the book covers incompressible MHD turbulence, the macroscopic aspects connected with the different self-organization processes, the phenomenology of the turbulence spectra, two-point closure theory, and intermittency. The third considers two-dimensional turbulence and compressible (in particular, supersonic) turbulence. Because of the similarities in the theoretical approach, these chapters start with a brief account of the corresponding methods developed in hydrodynamic turbulence. The final part of the book is devoted to astrophysical applications: turbulence in the solar wind, in accretion disks, and in the interstellar medium. This book is suitable for graduate students and researchers working in turbulence theory, plasma physics and astrophysics.

This book presents new concepts in operator theory and covers classes of operators (in particular, non-selfadjoint operators) which exhibit various interesting phenomena. Special attention is paid to applications in many areas of mathematical physics, including quantum mechanics, fluid mechanics, and magnetohydrodynamics.The author also discusses an operator theoretic approach to spectral problems for linear operators admitting a certain block structure. The results apply to bounded or finite-dimensional operators like block matrices as well to unbounded operators describing systems of differential equations. New concepts of numerical range are developed.