Crude Approximations to Some Aspects of Three-Dimensional Magnetospheric Dynamics

Abstract

It is quite well understood in principle how to formulate and solve dynamical problems in a three-dimensional magnetosphere (i.e., one in which all three adiabatic invariants M, J, Φ come into play), given the relevant diffusion coefficients, loss rates, and so forth (Haerendel, 1968; Lanzerotti and Schulz, 1973). But there are very severe practical difficulties in carrying out a truly three-dimensional calculation, and practically none exist in the literature. Two-dimensional calculations abound: radial diffusion of equatorially-mirroring (J =0) particles, pitch angle scattering at fixed L (or fixed Φ). In many cases this is not good enough; for example, most data on energetic trapped α-particles (e.g., Fennell et al., 1973) are off-equatorial, but theory (e.g., Cornwall, 1972) has concentrated on J=0 particles.