Reviews of Plasma Physics

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.