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In the interest of speed and economy the notation of the original text has been retained so that the cross product of two vectors A and B is denoted by [AB], the dot product by (AB) , the Laplacian operator by . 6 etc. It might also be worth pointing out that the temperature is frequently expressed in energy units in the Soviet literature so that the Boltzmann constant will be missing in various familiar expressions. In matters of terminology, whenever possible several forms are used when a term is first introduced, e. g. , magnetoacoustic and magnetosonic waves, probkotron and mirror machine, etc. It is hoped in this way to help the reader to relate the terms used here with those in exist ing translations and with the conventional nomenclature. In general, in the bibliographies, when a translated version of a given citation is available, only the English translation is cited, unless reference is made to a specific portion of the Russian version. Except for the correction of some obvious misprints the text is that of the original. We wish to express our gratitude to Academician Leontovich for kindly providing the latest corrections and additions to the Russian text, and especially for some new material, which appears for the first time in the American edition. v CONTENTS Chapter 1 PLASMA CONFINEMENT IN CLOSED MAGNETIC SYSTEMS L. S. Solov'ev and V. D. Shafranov . . . . . . . . . . . . . . . . . . 1 1. Introduction. . . * . . . . . . . . . . . . . . . . . . . . . . * . . . . . . . 1 2. General Properties of Toroidal Configurations. . . . . . . . . . . .

Full Product Details

Author:   M. A. Leontovich
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   Softcover reprint of the original 1st ed. 1995
ISBN:  

9781461577959

ISBN 10:   1461577950
Publication Date:   14 January 1997
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1 Plasma Confinement in Closed Magnetic Systems.- 1. Introduction.- 2. General Properties of Toroidal Configurations.- 1. Generalized Curvilinear Coordinate System.- 2. Coordinates in Which the Lines of Force are Straight.- 3. Magnetic Differential Equation.- 4. Relation between the Integral ?dl /B and the Derivative of the Volume with Respect to the Flux V'(?).- 5. Requirements for Current Closure on Magnetic Surfaces.- 6. Natural Coordinates.- 3. Orthogonal Coordinate System with Spatial Axis.- 1. Metric.- 2. Differential Operators.- 4. Magnetic Field near a Given Line of Force.- 5. Structure of Magnetic Surfaces in the Vicinity of a Closed Line of Force.- 6. Magnetic Surfaces Close to a Magnetic Axis.- 1. Second Approximation in ?.- 2. Third Approximation in ?.- 3. Fourth and Higher Approximations in ?.- 4. Helical Symmetry.- 7. Shape of Toroidal Magnetic Surfaces.- 8. Perturbation of Magnetic Surfaces by a First-Harmonic Field.- 1. Displacement of the Magnetic Axis by a Transverse Field.- 2. Uniform Configurations.- 3. Change in the Cross-Sectional Shape of Magnetic Surfaces Due to a Transverse Magnetic Field.- 9. Solution of the Equations for the Parameters of the Magnetic Surface.- 10. Perturbation of Toroidal Magnetic Surfaces.- 1. Perturbation Method for Finding Magnetic Surfaces.- 2. Effect of an Individual Harmonic of the Perturbing Field.- 3. Perturbations of the Second and Higher Approximations.- 4. Resonance Effects in the Vicinity of a Magnetic Axis.- 5. Examples of Splitting of Magnetic Surfaces.- 11. Plasma Equilibrium in a Toroidal System.- 1. General Equations.- 2. Current Density.- 3. Perturbations of the Magnetic Field.- 4. Magnetic Surfaces in the Presence of Plasma.- 5. Plasma Equilibrium in an l = 2 Stellarator.- 6. Plasma Equilibrium in a Trap with a Spatial Magnetic Axis.- 7. Plasma Equilibrium in the Presence of a Longitudinal Current.- 12. Effect of Curvature on Classical Diffusion and Thermal Conductivity.- 13. Integral Characteristics of Toroidal Magnetic Configurations.- 1. Specific Volume V'(?).- 2. Specific Volume of Magnetic Configurations with a Straight Magnetic Axis.- 3. Mean Rotational Transform of the Lines of Force ? = 2???(?).- 4. Specific Volume of a Configuration with Cross Section That Is Approximately Circular V'(?).- 5. Estimate of the Specific Volume V'(?) on the Separatrix.- 14. Examples of Actual Systems.- 1. Configuration with a Straight Magnetic Axis.- 2. Configurations with a Helical Magnetic Axis.- 3. Closed Uniform Configurations.- 4. Uniform Configurations with a Circular Magnetic Axis.- 5. Uniform Configuration with Spatial Magnetic Axis.- 15. Helical Magnetic Configurations.- 1. Specific Volume of a Helical Magnetic Tube.- 2. Mean Rotational Transform for the Lines of Force ? = 2???(?).- 3. Exact Expressions for the Specific Volume V'(?) and the Rotational Transform ? = 2???(?).- 4. Ratio of the Specific Volumes at the Magnetic Axis and the Separatrix.- 5. Results of Numerical Calculations.- 16. Containment of Charged Particles in Closed Toroidal Configurations.- 1. Motion of Single Charges in Vacuum.- 2. Motion of Charges in a Collisionless Plasma.- Appendix I. Magnetic Surfaces Near Elliptic, and Hyperbolic Magnetic Axes.- 1. Coordinate System.- 2. Magnetic Surfaces in the Vicinity of a Closed Line of Force.- 3. Representation of Magnetic Surfaces in the Form of Series in Powers of the Departure from the Magnetic Axis.- 4. Perturbation of a Magnetic Configuration by Transverse Fields.- Appendix II. Calculation of the Surface Functions ? and ?* by the Method of Averaging.- 1. Approximate Integral for the Equations of the Magnetic Lines of Force.- 2. Stability of Magnetic Surfaces.- 3. Approximate Integrals of the Drift Equations.- Appendix III. Number of Loops for Two Closed Curves.- Appendix IV. Certain Integrals that Appear in Calculations of the Specific Volume V'(?) and the Rotational Transform ?=2? ?(?).- References.- 2 Turbulence in Toroidal Systems.- 1. Equilibrium.- 1. Equilibrium of an Ideal Plasma. Coordinate System.- 2. Drift Flows in an Equilibrium Plasma.- 3. Particle Drift Trajectories.- 4. Equilibrium of a Rarefied Plasma.- 2. Hydromagnetic Instability.- 1. Flute Instability.- 2. Screw Instability.- 3. Drift and Dissipative Instabilities.- 1. Choice of Parameters and Localization Width for the Perturbations.- 2. Equations for the Dissipative Hydromagnetic Instabilities.- 3. Current-Convective Instability.- 4. Drift-Dissipative Instability.- 5. Gravitational Dissipative Instability.- 6. Temperature Drift Instability.- 7. Collisionless Instabilities Excited by Electrons.- 8. Nonelectrostatic Instabilities.- 9. Instability in a Dense Plasma.- 4. Trapped-Particle Instability.- 1. Collision-Free Instability.- 2. Dissipative Instabilities Due to Trapped Particles.- 3. Instability Associated with Finite Orbits.- 5. High-Frequency Instabilities.- 1. Drift Cyclotron Instabilities.- 2. Ion-Acoustic Instability.- 6. Helical Magnetic Cells.- 7. Thermal Convection of a Current-Carrying Plasma.- 1. Basic Equations.- 2. Convection in an Individual Cell.- 3. Heat Flux in the Presence of Convection.- 8. Transport of Particles and Heat by the Temperature Drift Instability.- 1. Turbulent Thermal Conductivity.- 2. 0} \right) $$).- c. Excitation of Cyclotron Waves with Anomalous Dispersion ($$ \left( {\omega \frac{{\partial \operatorname{Re} \varepsilon }}{{\partial \omega }} \leqslant 0} \right) $$).- d. Waves with Frequency ? ? ?i.- 2. Basic Equation.- 3. Stability of a Plasma with an Anisotropic Maxwellian Ion Distribution.- a. Ion-Acoustic Waves (? < 1).- b. Dissipative Instability (? ? 1, ? ? 1).- c. Electron-Plasma (Electron-Acoustic) Waves (? ? 1).- d. Hydrodynamic Instabilities (? ? 1, ? ? 1).- 4. Stability of a Plasma with a ?-Function Ion Velocity Distribution.- a. Cyclotron Oscillations of a Plasma with Cold Electrons (Hydrodynamic Instability).- b. Oscillations at Frequencies ? ? ?i.- c. Cyclotron Oscillations in a Plasma with Hot Electrons (Dissipative Instability).- d. Transverse Wave Instability k? ? k?.- 5. Stability of an Anisotropic Plasma with Cold Ions.- 6. Stability of a Plasma with a Nonequilibrium Electron Velocity Distribution.- a. Anisotropie Maxwellian Distribution.- b. Velocity Distribution in the Form of a ? Function.- 7. Conclusion. Basic Results.- References.- 4 Magnetohydrodynamic Theory of the Pinch Effect in a Dense High-Temperature Plasma (Dense Plasma Focus).- 1. Magnetohydrodynamic Equations for the Pinch Effect with Dissipative Processes Taken into Account.- a. Physical Assumptions. Equations in General Vector Form.- b. One-Dimensional Equations for Cylindrical Symmetry.- c. Dissipation Coefficients for a Fully Ionized Plasma.- d. Dimensionless Form of the Equations and Defining Parameters.- e. Boundary Conditions and Initial Conditions in the General Problem.- 2. Limiting Case of Infinitely High Electrical Conductivity in a Plasma and a Constant Electric Current.- a. Transition to the Limiting Case of a One-Parameter Problem.- b. Discussion of the Solution of the One-Parameter Problem.- c. Effect of Ion Thermal Conductivity.- d. Stagnation Increase in Temperature.- e. Thermonuclear Neutron Yield and Spatial Distribution of the Soft X Radiation.- 3. Finite Electrical Conductivity and ac Electric Current. Comparisons with Experiment.- a. Effect of Finite Conductivity for dc Current.- b. General Case of ac Electrical Current with Finite Electrical Conductivity.- c. Comparison with Experimental Results.- Conclusion.- References.- 5 Energy Balance and the Feasibility of a Self-Sustaining Thermonuclear Reaction in a Mirror Device.- References.

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