Since the discovery of geomagnetically trapped radiation by Van Allen in 1958, an impressive amount of experimental information on the earth's particle and field environment has nourished research work for scores of scientists and thesis work for their students. This quest has challenged space-age technology to produce better and more sophisticated instru ments and has challenged the international scientific community and governments to establish more, and more effective, cooperative programs of research and information exchange. As a result, an orderly picture of the principal physical mechanisms governing the earth's radiation environment is beginning to emerge. The interest in this topic has reached far beyond the domain of geo physics. Indeed, we find trapped radiation elsewhere in the universe: Jupiter's radiation belts, particle trapping in sunspot magnetic fields, cosmic rays confined in interstellar fields and, possibly, ultra-high-energy particles trapped in the magnetic fields of rotating neutron stars. There is abundant technical and scientific literature available on Van Allen radiation; comprehensive reviews are published regularly in journals or have been collected in book form*, and books have been written on the subject*. The aim of this monograph is to complement the existing literature with a concise discussion of the basic dynamical processes that control the earth's radiation belts. It is mainly intended to help a graduate student or a researcher new to this field to understand the underlying physics and to provide him with guidelines for quantita tive, numerical applications of the theory.

Inhalt
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.