Vitalii D Shafranov

Reviews of Plasma Physics - Reviews of Plasma Physics Vitalii D Shafranov 1st Ed. Softcover of Orig. Ed. 2008 edition

Jacket Description/Back: Reviews of Plasma Physics Volume 24, edited by V. D. Shafranov, presents two reviews from the cutting-edge of Russian plasma physics research. The first review by V. A. Rozhansky devoted to the mechanisms of transverse conductivity and generation of self-consistent electric fields in strongly ionized magnetized plasma. The second review by O. G. Bakunin considers numerous aspects of turbulent transport in plasma and fluids. This review is focused on scaling arguments for describing anomalous diffusion in the presence of complex structures. These topics are especially important for fusion plasma research, plasma astrophysics, discharge physics, and turbulence. Table of Contents: Preface -- 1. Mechanisma of Transverse Conductivity and Generation of Self-Consistent Electric Fields in Strongly Ionized Magnetized Plasma / V. Rozhansky -- 1.1. Introduction -- 1.2. Conductivity Tensor in Partially Ionized Plasma -- 1.3. Main Mechanisms of Perpendicular Conductivity in Fully Ionized Plasma: Currents Caused by Viscosity, Inertia, Collisions with Neutrals, and [down triangle, open]B, and Mass-Loading Currents -- 1.3.1. Inertia Currents -- 1.3.2. Currents Caused by Ion-Neutral Collisions -- 1.3.3. Diamagnetic Currents -- 1.3.4. Viscosity-Driven Currents -- 1.3.5. Mass-Loading Current -- 1.4. Inertial (Polarization) and [down triangle, open]B Currents. Acceleration of Plasma Clouds in an Inhomogeneous Magnetic Field -- 1.5. Alfven Conductivity -- 1.6. Perpendicular Viscosity, Radial Current, and Radial Electric Field in an Infinite Cylinder -- 1.7. Current Systems in Front of a Biased Electrode (Flush-Mounted Probe) and Spot of Emission -- 1.7.1. Viscosity-Driven Perpendicular Currents -- 1.7.2. Currents Driven by Ion-Neutral Collisions -- 1.7.3. Inertia Currents -- 1.7.4. General Situation -- 1.7.5. Spot of Emission -- 1.8. Currents in the Vicinity of a Biased Electrode That is Smaller Than the Ion Gyroradius -- 1.9. Neoclassical Perpendicular Conductivity in a Tokamak -- 1.9.1. Steady State Current -- 1.9.2. Time-Dependent Current -- 1.10. Transverse Conductivity in a Reversed Field Pinch -- 1.11. Modeling of Electric Field and Currents in the Tokamak Edge Plasma -- 1.12. Mechanisms of Anomalous Perpendicular Viscosity and Viscosity-Driven Currents -- 1.13. Transverse Conductivity in a Stochastic Magnetic Field -- 1.13.1. Nonstochastic Magnetic Field -- 1.13.2. Stochastic Magnetic Field -- 1.14. Electric Fields Generated in the Shielding Layer between Hot Plasma and a Solid State -- References -- 2. Correlations and Anomalous Transport Models / O. G. Bakunin -- 2.1. Introduction -- 2.2. Turbulent Diffusion and Transport -- 2.2.1. The Correlation Function and the Taylor Diffusivity -- 2.2.2. The Richardson Law -- 2.2.3. The Davydov Model of Turbulent Diffusion -- 2.2.4. The Batchelor Approximation for the Diffusion Coefficient -- 2.3. Nonlocal Effects and Diffusion Equations -- 2.3.1. The Functional Equation for Random Walks -- 2.3.2. Nonlocality and the Levy Distribution -- 2.3.3. The Monin Fractional Differential Equation -- 2.4. The Corrsin Conjecture -- 2.4.1. The Corrsin Independence Hypothesis -- 2.4.2. The Simplified Corrsin Conjecture -- 2.4.3. The Correlation Function and Scalings -- 2.5. Effects of Seed Diffusivity -- 2.5.1. Seed Diffusivity and Correlations -- 2.5.2. Returns and Correlations -- 2.5.3. The Stochastic Magnetic Field and Scalings -- 2.5.4. The Howells Result -- 2.6. The Diffusive Tracer Equation and Averaging -- 2.6.1. The Taylor Shear Flow Model -- 2.6.2. Generalization of the Taylor Model -- 2.6.3. The Zeldovich Flow and the Kubo Number -- 2.6.4. Advection and Zeldovich Scaling -- 2.7. The System of Random Shear Flows -- 2.7.1. The Dreizin-Dykhne Superdiffusion Regime -- 2.7.2. The Matheron-de Marsily Model -- 2.7.3. The Manhattan Grid Flow and Transport -- 2.8. The Quasi-Linear Approximation -- 2.8.1. Quasi-Linear Equations -- 2.8.2. Short-Range and Long-Range Correlations -- 2.8.3. The Telegraph Equation -- 2.8.4. Magnetic Diffusivity and the Kubo Number -- 2.9. The Diffusive Renormalization -- 2.9.1. The Dupree Approximation -- 2.9.2. The Dupree Theory Revisited -- 2.9.3. The Taylor-McNamara Correlation Function -- 2.9.4. The Kadomtsev-Pogutse Renormalization and the Stochastic Magnetic Field -- 2.10. Anomalous Transport and Convective Cells -- 2.10.1. Bohm Scaling and Electric Field Fluctuations -- 2.10.2. The Bohm Regime and Correlations -- 2.10.3. Convective Cells and Transport -- 2.10.4. Complex Structures and Convective Transport -- 2.11. Stochastic Instability and Transport -- 2.11.1. Stochastic Instability and Correlations -- 2.11.2. The Rechester-Rosenbluth Model -- 2.11.3. Collisional Effects and the Stix Formula -- 2.11.4. The Quasi-Isotropic Stochastic Magnetic Field and Transport -- 2.11.5. Quasi-Linear Scaling for the Stochastic Instability Increment -- 2.12. Fractal Conceptions and Turbulence -- 2.12.1. Fractality and Transport -- 2.12.2. The Richardson Law and Fractality -- 2.12.3. Intermittency and the Kolmogorov Law -- 2.13. Percolation and Scalings -- 2.13.1. Continuum Percolation and Transport -- 2.13.2. Renormalization and Percolation -- 2.13.3. Graded Percolation -- 2.14. Percolation and Turbulent Transport Scalings -- 2.14.1. Random Steady Flows and Seed Diffusivity -- 2.14.2. The Spatial Hierarchy of Scales and Stochastic Instability -- 2.14.3. Low Frequency Regimes -- 2.15. The Temporal Hierarchy of Scales and Correlations -- 2.15.1. The Spatial and Temporal Hierarchy of Scales -- 2.15.2. The Isichenko Intermediate Regime -- 2.15.3. Dissipation and Percolation Transport -- 2.16. The Stochastic Magnetic Field and Percolation Transport -- 2.16.1. The Stochastic Magnetic Field and Percolation Transport -- 2.16.2. Percolation and the Kadomtsev-Pogutse Scaling -- 2.16.3. Percolation Renormalization and the Stochastic Instability Increment -- 2.17. Percolation in Drift Flows -- 2.17.1. Graded Percolation and Drift Flows -- 2.17.2. Low Frequency Regimes and Drift Effects -- 2.17.3. Compressibility and Percolation -- 2.18. Multiscale Flows -- 2.18.1. The Nested Hierarchy of Scales and Drift Effects -- 2.18.2. The Brownian Landscape and Percolation -- 2.18.3. Correlations and Transport Scalings -- 2.18.4. The Diffusive Approximation and the Multiscale Model -- 2.18.5. Stochastic Instability and Time Scales -- 2.18.6. Isotropic and Anisotropic Turbulent Energy Spectra -- 2.18.7. The Multiscale Model of Transport in a Tangled Magnetic Field -- 2.19. Subdiffusion and Traps -- 2.19.1. The Balagurov and Vaks Model of Diffusion with Traps -- 2.19.2. Subdiffusion and Fractality -- 2.19.3. Comb Structures and Transport -- 2.20. Continuous Time Random Walks -- 2.20.1. The Montroll and Weiss Approach and Memory Effects -- 2.20.2. Fractional Differential Equations -- 2.20.3. The Taylor Definition and Memory Effects -- 2.21. Fractional Differential Equations and Scalings -- 2.21.1. The Klafter, Blumen, and Shlesinger Approximation -- 2.21.2. The Stochastic Magnetic Field and Balescu Approach -- 2.21.3. Longitudinal Correlations and the Diffusive Approximation -- 2.21.4. Vortex Structures and Trapping -- 2.21.5. Correlations and Trapping -- 2.22. Correlation and Phase-Space -- 2.22.1. The Corrsin Conjecture and Phase-Space -- 2.22.2. The Hamiltonian Nature of the Universal Hurst Exponent -- 2.22.3. The One-Flight Model and Transport -- 2.22.4. Correlations and Nonlocal Velocity Distribution -- 2.22.5. The Arrhenius Law and Phase-Space Distribution -- 2.23. Conclusion -- Acknowledgements -- References.