Plasma Physics_Richard Fitzpatrick

Plasma Physics_Richard Fitzpatrick - Plasma Physics Richard...

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Plasma Physics Richard Fitzpatrick Professor of Physics The University of Texas at Austin Contents 1 Introduction 5 1.1 Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 What is Plasma? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Brief History of Plasma Physics . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4 Basic Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.5 Plasma Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.6 Debye Shielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.7 Plasma Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.8 Collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.9 Magnetized Plasmas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.10 Plasma Beta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2 Charged Particle Motion 17 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2 Motion in Uniform Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.3 Method of Averaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.4 Guiding Centre Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.5 Magnetic Drifts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.6 Invariance of Magnetic Moment . . . . . . . . . . . . . . . . . . . . . . . . 25 2.7 Poincar´ e Invariants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.8 Adiabatic Invariants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.9 Magnetic Mirrors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.10 Van Allen Radiation Belts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.11 Ring Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.12 Second Adiabatic Invariant . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.13 Third Adiabatic Invariant . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.14 Motion in Oscillating Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3 Plasma Fluid Theory 43 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
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2 PLASMA PHYSICS 3.2 Moments of the Distribution Function . . . . . . . . . . . . . . . . . . . . . 45 3.3 Moments of the Collision Operator . . . . . . . . . . . . . . . . . . . . . . . 47 3.4 Moments of the Kinetic Equation . . . . . . . . . . . . . . . . . . . . . . . . 49 3.5 Fluid Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 3.6 Entropy Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.7 Fluid Closure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.8 Braginskii Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.9 Normalization of the Braginskii Equations . . . . . . . . . . . . . . . . . . . 67 3.10 Cold-Plasma Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.11 MHD Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 3.12 Drift Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 3.13 Closure in Collisionless Magnetized Plasmas . . . . . . . . . . . . . . . . . 78 3.14 Langmuir Sheaths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4 Waves in Cold Plasmas 89 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.2 Plane Waves in a Homogeneous Plasma . . . . . . . . . . . . . . . . . . . . 89 4.3 Cold-Plasma Dielectric Permittivity . . . . . . . . . . . . . . . . . . . . . . 91 4.4 Cold-Plasma Dispersion Relation . . . . . . . . . . . . . . . . . . . . . . . . 93 4.5 Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4.6 Cutoff and Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4.7 Waves in an Unmagnetized Plasma . . . . . . . . . . . . . . . . . . . . . . 96 4.8 Low-Frequency Wave Propagation . . . . . . . . . . . . . . . . . . . . . . . 97 4.9 Parallel Wave Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 4.10 Perpendicular Wave Propagation . . . . . . . . . . . . . . . . . . . . . . . . 106 4.11 Wave Propagation Through Inhomogeneous Plasmas . . . . . . . . . . . . 107 4.12 Cutoffs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 4.13 Resonances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 4.14 Resonant Layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 4.15 Collisional Damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 4.16 Pulse Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 4.17 Ray Tracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 4.18 Radio Wave Propagation Through the Ionosphere . . . . . . . . . . . . . . 124 5 Magnetohydrodynamic Fluids 127 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 5.2 Magnetic Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 5.3 Flux Freezing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 5.4 MHD Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 5.5 The Solar Wind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 5.6 Parker Model of Solar Wind . . . . . . . . . . . . . . . . . . . . . . . . . . 136 5.7 Interplanetary Magnetic Field . . . . . . . . . . . . . . . . . . . . . . . . . 140 5.8 Mass and Angular Momentum Loss . . . . . . . . . . . . . . . . . . . . . . 144
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CONTENTS 3 5.9 MHD Dynamo Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 5.10 Homopolar Generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 5.11 Slow and Fast Dynamos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 5.12 Cowling Anti-Dynamo Theorem . . . . . . . . . . . . . . . . . . . . . . . . 154 5.13 Ponomarenko Dynamos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 5.14 Magnetic Reconnection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 5.15 Linear Tearing Mode Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 162 5.16 Nonlinear Tearing Mode Theory . . . . . . . . . . . . . . . . . . . . . . . . 169 5.17 Fast Magnetic Reconnection . . . . . . . . . . . . . . . . . . . . . . . . . . 171 5.18 MHD Shocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 5.19 Parallel Shocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 5.20 Perpendicular Shocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 5.21 Oblique Shocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 6 Waves in Warm Plasmas 187 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 6.2 Landau Damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 6.3 Physics of Landau Damping . . . . . . . . . . . . . . . . . . . . . . . . . . 194 6.4 Plasma Dispersion Function . . . . . . . . . . . . . . . . . . . . . . . . . . 197 6.5 Ion Sound Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 6.6 Waves in Magnetized Plasmas . . . . . . . . . . . . . . . . . . . . . . . . . 200 6.7 Parallel Wave Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 6.8 Perpendicular Wave Propagation . . . . . . . . . . . . . . . . . . . . . . . . 206
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4 PLASMA PHYSICS
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Introduction 5 1 Introduction 1.1 Sources The major sources for this course are: The Theory of Plasma Waves : T.H. Stix, 1st Ed. (McGraw-Hill, New York NY, 1962). Plasma Physics : R.A. Cairns (Blackie, Glasgow UK, 1985).
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