| Document Type
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BL
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| Record Number
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772905
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b592899
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| Main Entry
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by Alexander E. Lifschitz.
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| Title & Author
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Magnetohydrodynamics and Spectral Theory\ by Alexander E. Lifschitz.
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| Publication Statement
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Dordrecht : Springer Netherlands, 1989
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| Series Statement
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Developments in electromagnetic theory and applications, 4.
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| Page. NO
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(XII, 446 pages).
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| ISBN
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9400925611
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: 9789400925618
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| Contents
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1. Historical background and outline of the contents --; 1 Introduction --; 2 Historical background --; 3 Outline of Chapter 2 --; 4 Outline of Chapter 3 --; 5 Outline of Chapter 4 --; 6 Outline of Chapter 5 --; 7 Outline of Chapter 6 --; 8 Outline of Chapter 7 --; 9 Outline of Chapter 8 --; 10 Outline of Chapter 9 --; 2. Preliminaries from the spectral theory of operators --; 1 Introduction --; 2 Distribution theory --; 3 Hilbert spaces --; 4 Linear functionals and linear operators --; 5 Linear bounded functionals and linear bounded operators --; 6 Linear unbounded operators --; 7 Self-adjoint extensions of symmetric operators --; 8 Spectral theorem for self-adjoint operators --; 9 Rigged Hilbert spaces and expansions in terms of generalized eigenvectors of self-adjoint operators --; 10 The stability investigation via the Energy Principle --; 11 Preliminaries from the calculus of variations --; 12 The eigenvalue problem for a system of two first-order ordinary differential equations on a finite segment --; 3. Basic equations and their main properties --; 1 Introduction --; 2 Collisional Maxwell-Boltzmann equations --; 3 Macroscopic variables describing a plasma --; 4 The properties of the collisional integral --; 5 Two-fluid equations --; 6 Asymptotic simplification of two-fluid equations --; 7 Single-fluid MHD equations --; 8 Derivation of MHD equations for conducting fluid --; 9 Dimensionless parameters --; 10 Conservative form of the ideal MHD equations and local conservation laws --; 11 Boundary and initial conditions for MHD equations --; 12 Global conservation laws and virial theorem --; 13 Lagrangian form of the ideal MHD equations --; 4. Magnetohydrodynamical equilibrium --; 1 Introduction --; 2 Basic equations --; 3 On equilibrium of a toroidal plasma with a surface current --; 4 Toroidal equilibrium configurations with nested magnetic surfaces --; 5 Natural coordinates --; 6 Hamada coordinates --; 7 Equilibrium configurations with closed lines of force --; 8 Force-free equilibria --; 9 Structure of the general three-dimensional magnetic field --; 10 Equilibrium configurations with continuous symmetry --; 11 Homogeneous and piecewise inhomogeneous equilibria --; 12 One-dimensional inhomogeneous equilibrium plasma slabs --; 13 Radially inhomogeneous equilibrium plasma pinches --; 14 General properties of two-dimensional equilibrium configurations --; 15 Translationally symmetric equilibrium configurations --; 16 Axisymmetric equilibrium configurations. The Grad-Shafranov equation --; 17 Helically symmetrie equilibrium configurations --; 18 Straight plasma column of elliptic cross-section with homogeneous current --; 19 Toroidal equilibrium configuration of circular cross-section with quasi-homogeneous current --; 20 Asymptotic approach to the axisymmetric equilibrium problem --; 21 The standard tokamak --; 22 The high-ß tokamak --; 23 The three-dimensional analogue of the Grad--Shafranov equation --; 24 Stationary solutions of the resistive MHD equations --; 5. The linearized MHD equations and their general properties --; 1 Introduction --; 2 The linearized ideal MHD equations --; 3 Spectral problems corresponding to evolutionary problems --; 4 Stability of equilibrium configurations and the Energy Principle --; 5 Alternative forms of the plasma potential energy --; 6 Minimization of the potential energy with respect to a parallel displacement --; 7 Classification of ideal MHD instabilities --; 8 The linearized non-ideal MHD equations --; 6. Homogeneous and discretely structured plasma oscillations --; 1 Introduction --; 2 Alfvén waves in an incompressible ideal plasma --; 3 Cold ideal plasma oscillations --; 4 Compressible hot plasma oscillations --; 5 Finite resistivity effects --; 6 Propagation of waves generated by a local source --; 7 Stratified plasma oscillations --; 8 Oscillations of a plasma slab --; 9 Instabilities of an ideal stratified gravitating plasma --; 10 Instabilities of a resistive stratified gravitating plasma --; 7. MHD oscillations of a gravitating plasma slab --; 1 Introduction --; 2 Gravitating slab equilibrium --; 3 Oscillations of a hot compressible plasma slab --; 4 Investigation of the slab stability via the Energy Principle --; 5 On the discrete spectrum of the operator Kk --; 6 On the essential spectrum of the operator Kk --; 7 On the discrete spectrum embedded in the essential spectrum --; 8 The eigenfunction expansion formula --; 9 Excitation of plasma oscillations by an external power source --; 10 The linearized equations governing resistive gravitating plasma slab oscillations --; 11 Heuristic investigation of resistive instabilities --; 12 Analytic evaluation of increments of resistive instabilities --; 13 Investigation of the slab stability via the Resistive Energy Principle --; 14 Global resistive interchange quasi-modes --; 15 On stable resistive modes eigenfrequencies --; 8. Oscillations of a plasma pinch --; 1 Introduction --; 2 General cylindrical equilibrium configuration --; 3 Cylindrical force operator --; 4 The Energy Principle for the pinch stability --; 5 Criterion of the general screw-pinch stability --; 6 Spectral properties of the cylindrical force operator --; 7 Secondary heating of a pinch by an external antenna --; 8 Stability of the straight tokamak --; 9 Resistive equations governing general screw-pinch oscillations --; 10 Resonant resistive instabilities of the general screw-pinch --; 11 Resistive instabilities of the straight tokamak --; 12 The stable resistive spectrum structure --; 9. MHD oscillations of two- and three-dimensional configurations --; 1 Introduction --; 2 Two- and three-dimensional equilibrium configurations --; 3 Basic equations --; 4 The Mercier criterion --; 5 The ballooning stability criterion --; 6 Axisymmetric (n = 0) instabilities of the free-boundary plasma --; 7 Spectral properties of the force operators KIn and KIIn --; 8 On the essential spectrum of the force operator K --; 9 Natural oscillations of three-dimensional configurations --; 10 Natural oscillations of three-dimensional configurations with closed magnetic lines --; 11 Resonant resistive instabilities of axisymmetric toroidal configurations --; References.
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| Abstract
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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. ... ...
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| Subject
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Magnetohydrodynamics.
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| Subject
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Nuclear physics.
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| Subject
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Physics.
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| LC Classification
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QC718.5.M36B935 1989
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| Added Entry
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Alexander E Lifschitz
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| Parallel Title
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Developments in Electromagnetic Theory and Applications, vol. 4
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