Magnetohydrodynamics and Spectral Theory [EBook] / by Alexander E. Lifschitz.
Magnetohydrodynamics and Spectral Theory [EBook] / by Alexander E. Lifschitz.
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...
Personal Name(s):  Lifschitz, Alexander E., (author) 

Imprint: 
Dordrecht :
Springer,
1989

Physical Description: 
XII, 446 p. online resource. 
Note: 
englisch 
ISBN: 
9789400925618 
DOI: 
10.1007/9789400925618 
Series Title: 
Developments in Electromagnetic Theory and Applications ;
4 
Subject (LOC):  
Full Text 
Table of Contents:
 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 Selfadjoint extensions of symmetric operators
 8 Spectral theorem for selfadjoint operators
 9 Rigged Hilbert spaces and expansions in terms of generalized eigenvectors of selfadjoint 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 firstorder ordinary differential equations on a finite segment
 3. Basic equations and their main properties
 1 Introduction
 2 Collisional MaxwellBoltzmann equations
 3 Macroscopic variables describing a plasma
 4 The properties of the collisional integral
 5 Twofluid equations
 6 Asymptotic simplification of twofluid equations
 7 Singlefluid 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 Forcefree equilibria
 9 Structure of the general threedimensional magnetic field
 10 Equilibrium configurations with continuous symmetry
 11 Homogeneous and piecewise inhomogeneous equilibria
 12 Onedimensional inhomogeneous equilibrium plasma slabs
 13 Radially inhomogeneous equilibrium plasma pinches
 14 General properties of twodimensional equilibrium configurations
 15 Translationally symmetric equilibrium configurations
 16 Axisymmetric equilibrium configurations. The GradShafranov equation
 17 Helically symmetrie equilibrium configurations
 18 Straight plasma column of elliptic crosssection with homogeneous current
 19 Toroidal equilibrium configuration of circular crosssection with quasihomogeneous current
 20 Asymptotic approach to the axisymmetric equilibrium problem
 21 The standard tokamak
 22 The highß tokamak
 23 The threedimensional 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 nonideal 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 quasimodes
 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 screwpinch 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 screwpinch oscillations
 10 Resonant resistive instabilities of the general screwpinch
 11 Resistive instabilities of the straight tokamak
 12 The stable resistive spectrum structure
 9. MHD oscillations of two and threedimensional configurations
 1 Introduction
 2 Two and threedimensional equilibrium configurations
 3 Basic equations
 4 The Mercier criterion
 5 The ballooning stability criterion
 6 Axisymmetric (n = 0) instabilities of the freeboundary 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 threedimensional configurations
 10 Natural oscillations of threedimensional configurations with closed magnetic lines
 11 Resonant resistive instabilities of axisymmetric toroidal configurations
 References.