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140122 ||| eng |
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|a 9789400925618
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| 100 |
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|a Lifshits, Alexander E.
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| 245 |
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|a Magnetohydrodynamics and Spectral Theory
|h Elektronische Ressource
|c by Alexander E. Lifshits
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| 250 |
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|a 1st ed. 1989
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| 260 |
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|a Dordrecht
|b Springer Netherlands
|c 1989, 1989
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| 300 |
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|a XII, 446 p
|b online resource
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|a 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 --
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|a 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 resistivityeffects -- 6 Propagation of waves generated by a local source -- 7 Stratified plasma oscillations -- 8 Oscillations of a plasma slab --
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| 505 |
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|a 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 --
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|a 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 --
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|a 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 --
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|a 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 --
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|a 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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| 653 |
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|a Nuclear physics
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| 653 |
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|a Nuclear Physics
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| 041 |
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7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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| 490 |
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|a Developments in Electromagnetic Theory and Applications
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| 028 |
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|a 10.1007/978-94-009-2561-8
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| 856 |
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|u https://doi.org/10.1007/978-94-009-2561-8?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
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|a 539.7
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| 520 |
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|a 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 . . . . . . . . . . . . . . . . . . . . . 290II Heuristic investigation of resistive instabilities. . . . . . . . .
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