Cosmic-Ray Propagation. I. Charged Particles in a Random Magnetic Field

A description of charged-particle motion in an irregular magnetic field is obtained. The magnetic field is taken to be the superposition of a constant field B6e, and a smaller fluctuating component B1 which is a homogeneous random function of position with zero mean. The Fokker-Planck coefficients, describing the evolution of the particle distribution in pitch angle and position, are derived explicitly in terms of the two-point correlation function of B1, or, alternatively, in terms of the Fourier spectrum of the irregular field. The time evolution of the distribution is found to depend on the irregular field in two ways: (1) A particle is scattered by those irregularities which are seen by the particle to be in resonance with its cyclotron frequency. (2) A particle follows the random walk of a field line in the X, Y-plane as it moves along the Z-axis. The diffusion limit of the Fokker-Planck equation, suppressing the pitchangle dependence, is then considered and a diffusion tensor is derived. The application to spacecraft magnetic field observations is discussed, and the Fokker-Planck coefficients are related to the observed power spectrum of interplanetary magnetic-field fluctuations.