Dynamics of Geomagnetically Trapped Radiation

I. Particle Drifts and the First Adiabatic Invariant.- I.1 The Guiding Center Approximation.- I.2 Uniform Magnetic Field.- I.3 Zero Order Drifts.- I.4 First Order Drifts.- I.5 Second Order Drifts.- 1.6 The First Adiabatic Invariant.- I.7 Application I: Drift of Particles in the Geomagnetic Equator.- 1.8 Application II: Effect of an Electric Field on the Drift of Equatorial Particles.- II. Bounce Motion, the Second Adiabatic Invariant and Drift Shells.- II.1 Particle Trapping.- II.2 The Parallel Equation of Motion.- II.3 The Energy Equation.- II.4 Drift Shells.- II.5 The Second Adiabatic Invariant.- II.6 Application I: Particle Drifts in the Dipole Field.- II.7 Application II: Shell Tracing in a Magnetospheric Field Model.- II.8 Some Other Cases: Near-equatorial Particles; Effects of External Forces.- III. Periodic Drift Motion and Conservation of the Third Adiabatic Invariant.- III.1 Drift Shells in Time-dependent Magnetic Fields.- III.2 The Third Adiabatic Invariant.- III.3 Application I: Influence of a Ring Current Field on Equatorial Particle Drift Paths.- III.4 Application II: Effect of Sudden Compressions and Adiabatic Expansions of the Magnetosphere.- IV. Trapped Particle Distributions and Flux Mapping.- IV.1 Directional Flux.- IV.2 Flux Relations.- IV.3 Particle Distribution Functions.- IV.4 Application I: Trapped Particle Flux Mapping in the Inner Magnetosphere; B-L Coordinates.- IV.5 Application II: Particle Flux Mapping in the Outer Magnetosphere.- V. Violation of the Adiabatic Invariants and Trapped Particle Diffusion.- V.1 Diffusion Mechanisms.- V.2 Coordinates and Distribution Functions.- V.3 The Diffusion Equation.- V.4 Application I: Pure Radial Diffusion.- V.5 Application II: Pure Pitch Angle Diffusion in a Symmetric Field.- V.6 Application III: Pure Pitch Angle Diffusion in an Asymmetric Field.- V.7 Application IV: Simultaneous Radial and Pitch Angle Diffusion.- Appendices.- II. General Expression for the Bounce-average Drift Velocity.- III. Shell Tracing in Absence of External Forces.- IV. Conservation of the Third Adiabatic Invariant.- V. Conservation of the Magnetic Flux of a Tube of Field Lines Moving with Drifting Particles.- VII. A Different Expression for the Drift Velocity.- VIII. Derivation of the Fokker-Planck Equation.- References.- Subject-Index.