Reviews of plasma physics. Vol. 24

3540745750......Page 1
Reviews of Plasma Physics 24......Page 4
Contents......Page 8
Preface......Page 6
1.1 Introduction......Page 12
1.2 Conductivity Tensor in Partially Ionized Plasma......Page 15
1.3 Main Mechanisms of Perpendicular Conductivity in Fully Ionized Plasma: Currents Caused by Viscosity, Inertia, Collisions with Neutrals, and [ ] B, and Mass-Loading Currents......Page 17
1.3.2 Currents Caused by Ion–Neutral Collisions......Page 18
1.3.4 Viscosity-Driven Currents......Page 19
1.3.5 Mass-Loading Current......Page 21
1.4 Inertial (Polarization) and [ ] B, Currents. Acceleration of Plasma Clouds in an Inhomogeneous Magnetic Field......Page 22
1.5 Alfven Conductivity......Page 24
1.6 Perpendicular Viscosity, Radial Current, and Radial Electric Field in an Infinite Cylinder......Page 26
1.7 Current Systems in Front of a Biased Electrode (Flush-Mounted Probe) and Spot of Emission......Page 27
1.7.1 Viscosity-Driven Perpendicular Currents......Page 29
1.7.2 Currents Driven by Ion–Neutral Collisions......Page 33
1.7.3 Inertia Currents......Page 34
1.7.4 General Situation......Page 35
1.7.5 Spot of Emission......Page 36
1.8 Currents in the Vicinity of a Biased Electrode That is Smaller Than the Ion Gyroradius......Page 37
1.9.1 Steady State Current......Page 41
1.9.2 Time-Dependent Current......Page 48
1.10 Transverse Conductivity in a Reversed Field Pinch......Page 49
1.11 Modeling of Electric Field and Currents in the Tokamak Edge Plasma......Page 50
1.12 Mechanisms of Anomalous Perpendicular Viscosity and Viscosity-Driven Currents......Page 52
1.13 Transverse Conductivity in a Stochastic Magnetic Field......Page 54
1.13.1 Nonstochastic Magnetic Field......Page 55
1.13.2 Stochastic Magnetic Field......Page 56
1.14 Electric Fields Generated in the Shielding Layer between Hot Plasma and a Solid State......Page 57
References......Page 61
2.1 Introduction......Page 64
2.2 Turbulent Diffusion and Transport......Page 67
2.2.1 The Correlation Function and the Taylor Diffusivity......Page 68
2.2.2 The Richardson Law......Page 70
2.2.3 The Davydov Model of Turbulent Diffusion......Page 71
2.2.4 The Batchelor Approximation for the Diffusion Coefficient......Page 73
2.3 Nonlocal Effects and Diffusion Equations......Page 74
2.3.1 The Functional Equation for Random Walks......Page 75
2.3.2 Nonlocality and the Levy Distribution......Page 76
2.3.3 The Monin Fractional Differential Equation......Page 78
2.4.1 The Corrsin Independence Hypothesis......Page 80
2.4.2 The Simplified Corrsin Conjecture......Page 81
2.4.3 The Correlation Function and Scalings......Page 82
2.5 Effects of Seed Diffusivity......Page 83
2.5.1 Seed Diffusivity and Correlations......Page 84
2.5.2 \"Returns\" and Correlations......Page 85
2.5.3 The Stochastic Magnetic Field and Scalings......Page 86
2.5.4 The Howells Result......Page 88
2.6.1 The Taylor Shear Flow Model......Page 90
2.6.2 Generalization of the Taylor Model......Page 93
2.6.3 The Zeldovich Flow and the Kubo Number......Page 94
2.6.4 Advection and Zeldovich Scaling......Page 96
2.7 The System of Random Shear Flows......Page 97
2.7.1 The Dreizin–Dykhne Superdiffusion Regime......Page 98
2.7.2 The Matheron–de Marsily Model......Page 99
2.7.3 The \"Manhattan Grid\" Flow and Transport......Page 102
2.8.1 Quasi-Linear Equations......Page 104
2.8.2 Short-Range and Long-Range Correlations......Page 106
2.8.3 The Telegraph Equation......Page 107
2.8.4 Magnetic Diffusivity and the Kubo Number......Page 108
2.9 The Diffusive Renormalization......Page 109
2.9.1 The Dupree Approximation......Page 110
2.9.2 The Dupree Theory Revisited......Page 113
2.9.3 The Taylor–McNamara Correlation Function......Page 115
2.9.4 The Kadomtsev–Pogutse Renormalization and the Stochastic Magnetic Field......Page 117
2.10.1 Bohm Scaling and Electric Field Fluctuations......Page 119
2.10.2 The Bohm Regime and Correlations......Page 121
2.10.3 Convective Cells and Transport......Page 123
2.11 Stochastic Instability and Transport......Page 125
2.11.1 Stochastic Instability and Correlations......Page 126
2.11.2 The Rechester–Rosenbluth Model......Page 128
2.11.3 Collisional Effects and the Stix Formula......Page 130
2.11.4 The Quasi-Isotropic Stochastic Magnetic Field and Transport......Page 132
2.11.5 Quasi-Linear Scaling for the Stochastic Instability Increment......Page 134
2.12.1 Fractality and Transport......Page 136
2.12.2 The Richardson Law and Fractality......Page 138
2.12.3 Intermittency and the Kolmogorov Law......Page 140
2.13.1 Continuum Percolation and Transport......Page 141
2.13.2 Renormalization and Percolation......Page 143
2.13.3 Graded Percolation......Page 145
2.14 Percolation and Turbulent Transport Scalings......Page 146
2.14.1 Random Steady Flows and Seed Diffusivity......Page 147
2.14.2 The Spatial Hierarchy of Scales and Stochastic Instability......Page 148
2.14.3 Low Frequency Regimes......Page 149
2.15.1 The Spatial and Temporal Hierarchy of Scales......Page 151
2.15.2 The Isichenko Intermediate Regime......Page 153
2.15.3 Dissipation and Percolation Transport......Page 154
2.16.1 The Stochastic Magnetic Field and Percolation Transport......Page 157
2.16.2 Percolation and the Kadomtsev–Pogutse Scaling......Page 159
2.16.3 Percolation Renormalization and the Stochastic Instability Increment......Page 161
2.17.1 Graded Percolation and Drift Flows......Page 162
2.17.2 Low Frequency Regimes and Drift Effects......Page 164
2.17.3 Compressibility and Percolation......Page 166
2.18 Multiscale Flows......Page 167
2.18.1 The Nested Hierarchy of Scales and Drift Effects......Page 168
2.18.2 The Brownian Landscape and Percolation......Page 170
2.18.3 Correlations and Transport Scalings......Page 172
2.18.4 The Diffusive Approximation and the Multiscale Model......Page 174
2.18.5 Stochastic Instability and Time Scales......Page 176
2.18.6 Isotropic and Anisotropic Turbulent Energy Spectra......Page 177
2.18.7 The Multiscale Model of Transport in a Tangled Magnetic Field......Page 179
2.19 Subdiffusion and Traps......Page 180
2.19.1 The Balagurov and Vaks Model of Diffusion with Traps......Page 181
2.19.2 Subdiffusion and Fractality......Page 182
2.19.3 Comb Structures and Transport......Page 183
2.20 Continuous Time Random Walks......Page 184
2.20.1 The Montroll and Weiss Approach and Memory Effects......Page 185
2.20.2 Fractional Differential Equations......Page 187
2.20.3 The Taylor Definition and Memory Effects......Page 188
2.21.1 The Klafter, Blumen, and Shlesinger Approximation......Page 191
2.21.2 The Stochastic Magnetic Field and Balescu Approach......Page 192
2.21.3 Longitudinal Correlations and the Diffusive Approximation......Page 194
2.21.4 Vortex Structures and Trapping......Page 196
2.21.5 Correlations and Trapping......Page 198
2.22.1 The Corrsin Conjecture and Phase-Space......Page 200
2.22.2 The Hamiltonian Nature of the Universal Hurst Exponent......Page 202
2.22.3 The One-Flight Model and Transport......Page 204
2.22.4 Correlations and Nonlocal Velocity Distribution......Page 206
2.22.5 The Arrhenius Law and Phase-Space Distribution......Page 208
References......Page 209