Space Physics. An Introduction to Plasmas and Particles in the Heliosphere and Magnetospheres. May-Britt Kallenrode. Springer

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1 May-Britt Kallenrode Space Physics An Introduction to Plasmas and Particles in the Heliosphere and Magnetospheres With 170 Figures, 9 Tables, Numerous Exercises and Problems Springer

2 Contents 1. Introduction Neutral Gases and Plasmas Plasmas in Space A Brief History of Space Research 4 Exercises and Problems 8 2. Charged Particles in Electromagnetic Fields Electromagnetic Fields Maxwell's Equations Transformation of Field Equations Generalized Ohm's Law Energy Equation of the Electromagnetic Field Particle Motion in Electromagnetic Fields Lorentz Force and Gyration Drifts of Particles in Electromagnetic Fields The Concept of the Guiding Center Crossed Magnetic and Electric Fields: E x B Drift Magnetic and Gravitational Fields Inhomogeneous Magnetic Fields Curvature Drift : Drifts Combined with Changes in Particle Energy Drift Currents in Plasmas Adiabatic Invariants First Adiabatic Invariant: The Magnetic Moment Magnetic Mirrors and Bottles Second Adiabatic Invariant: Longitudinal Invariant Third Adiabatic Invariant: Flux Invariant Summary 29 Exercises and Problems Magnetohydrodynamics Basic MHD Equations Momentum Balance Equation of Continuity 37

3 VIII Contents Equation of State Basic Equations of MHD Two-Fluid Description Magnetohydrostatics Magnetic Pressure Magnetic Tension Magnetohydrokinematics Frozen-in Magnetic Fields Dissipation of Fields Reconnection Deformation of the Field in a Plasma Flow The Magnetohydrodynamic Dynamo Debye Shielding Summary 65 Exercises and Problems Plasma Waves What is a Wave? Magnetohydrodynamic Waves Linearization of the Equations: Perturbation Theory Alfven Waves Magneto-Sonic Waves Electrostatic Waves in Non-Magnetic Plasmas Plasma Oscillations Electron Plasma Waves (Langmuir Waves) Ion-Acoustic Waves (Ion Waves) Electrostatic Waves in Magnetized Plasmas Electron Oscillations Perpendicular to B (Upper Hybrid Frequency) Electrostatic Ion Waves Perpendicular to B (Ion Cyclotron Waves) Lower Hybrid Frequency Electromagnetic Waves in Non-Magnetized Plasmas Electromagnetic Waves in Magnetized Plasmas Electromagnetic Waves Perpendicular to B o Waves Parallel to the Magnetic Field: Whistler (R-Waves) and L-Waves Summary 87 Exercises and Problems Kinetic Theory The Distributioh-Function Phase Space and Distribution Function Maxwell's Velocity Distribution Other Distributions 92

4 Contents IX Distribution Function and Measured Quantities Basic Equations of Kinetic Theory The Boltzmann Equation The Vlasov Equation The Fokker-Planck Equation Collisions Collisions Between Neutrals Collisions Between Charged Particles Summary 102 Exercises and Problems Diffusive Transport Diffusion Spatial Diffusion Pitch-Angle Diffusion Diffusion in Momentum Space Ill 6.2 Wave-Particle Interactions Quasi-Linear Theory Resonance Scattering Alfven Waves and Interplanetary Propagation Electromagnetic Waves Diffusion in Momentum Space Summary 117 Exercises and Problems Shock Waves What is a Shock Wave? Information, Dissipation, and Non-Linearity The Shock's Rest Frame Collisionless Shock Waves Shock Conservation Laws Rankine-Hugoniot Equations in Ordinary Shocks Rankine-Hugoniot Equations in MHD Shocks Jump Conditions and Discontinuities Shock Parameters Shock Geometry Fast and Slow Shocks The Coplanarity Theorem The Shock Normal Direction Particle Acceleration at Shocks Shock Drift Acceleration (SDA) Diffusive Shock Acceleration Diffusive Shock Acceleration and Self-Generated Turbulence Stochastic Acceleration 139

5 X Contents 7.5 The Shock as a Non-Linear System Summary 141 Exercises and Problems Sun and Solar Wind: Plasmas in the Heliosphere The Sun Nuclear Fusion Structure of the Sun The Solar Atmosphere The Coronal Magnetic Field The Solar Wind Properties Solar Wind Models The Problem: Coronal Heating and Solar Wind Acceleration The Interplanetary Magnetic Field Spiral Structure Sector Structure The Ballerina Model Corotating Interaction Regions Plasma Waves in Interplanetary Space Power-Density Spectrum Waves or Turbulence? The Three-Dimensional Heliosphere The Active Sun The Solar Cycle A Simple Model of the Solar Cycle The Heliosphere During the Solar Cycle Flares and Coronal Mass Ejections Electromagnetic Radiation Classes of Flares Coronal Mass Ejections Coronal Mass Ejections, Flares, and Coronal Shocks Models of Coronal Mass Ejections (CMEs) Models of Flares Magnetic Clouds: CMEs in Interplanetary Space Interplanetary Shocks Summary 186 Exercises and Problems 186

6 Contents 9. Energetic Particles in the Heliosphere Particle Populations in the Heliosphere Solar Energetic Particles Classes of Particle Events Interplanetary Propagation Particles and Traveling Interplanetary Shocks Low Energies (Tens of Kiloelectronvolts) High Energies (Megaelectronvolts) Forbush Decreases Particles at Planetary Bow Shocks Galactic Cosmic Rays Modulation Over the Poles Summary 210 Exercises and Problems The Terrestrial Magnetosphere The Terrestrial Magnetic Field The Dipole Field Variability The Terrestrial Dynamo Topology of the Magnetosphere The Magnetopause Polar Cusps The Tail Magnetosheath and Bow Shock Open or Closed? Magnetospheric Modeling Plasmas and Currents in the Magnetosphere The Ionosphere The Plasmasphere The Geosphere The Outer Magnetosphere Magnetosphere-Ionosphere Coupling Particles in the Magnetosphere The Radiation Belts Galactic Cosmic Rays - St0rmer Orbits Solar Energetic Particles - Polar Cap Absorption Summary 253 Exercises and Problems 254 XI

7 XII Contents 11. The Dynamic Magnetosphere Geomagnetic Variability Daily Variations Geomagnetic Disturbances Geomagnetic Indices Geomagnetic Activity Through the Solar Cycle Annual Variations and Recurrent Geomagnetic Activity Magnetic Storms in Response to Transient Phenomena A Simple Model of Geomagnetic Activity Substorms Aurorae Historical Excursion Beginning of the Scientific Analysis Modern Interpretation Summary Planetary Magnetospheres Overview The Planets Structures of Planetary Magnetospheres Sizes Plasma Sources Upstream of the Bow Shock: The Foreshocks Radiation Belts Planets with a Magnetic Field Mercury Jupiter Saturn Uranus Neptune Planets Without a Magnetic Field Summary 292 Exercises and Problems Solar-Terrestrial Relationships Solar-Terrestrial Relationships: Overview The Atmosphere Responses of the Upper Atmosphere to Solar Variability Polar Cap Absorptions and Ozone Thermospheric Circulation The Technical Environment and Solar Activity 303

8 Contents XIII 13.5 The Solar Cycle, Sector Boundaries, Droughts, and Thunderstorms Solar Activity, Climate, and Culture Sun and Weather Instrumentation Field Instruments The Magnetic Field Electric Field Measurements Wave Measurements Plasma Instruments Instruments for Dense Plasmas Instruments for Rarefied Plasmas Energetic Particle Instruments Supplementary Ground-Based Observations 323 Appendix 325 A.I List of Symbols 325 A.2 Useful Relations 327 A.2.1 Vector Identities 327 A.2.2 Vector Calculus 328 A.2.3 Cylindrical Coordinates 329 A.2.4 Spherical Coordinates 329 A.3 Useful Numbers 330 A.3.1 Fundamental Constants 330 A.3.2 Numbers in Plasmas 330 References 331 Index - 351

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