On the effect of geomagnetic fluctuations on trapped particles

The effect of large-scale geomagnetic fluctuations on Van Allen belt particles with mirror points near the geomagnetic equatorial plane is studied in a model where a dipole field is perturbed by the sudden approach and adiabatic withdrawal of a perfectly conducting plane. The Fokker-Planck equation for the particle density is obtained by following the motions of the particle guiding centers, assuming that the first and second adiabatic invariants, but not the third, remain valid during the approach. Steady-state and transient solutions for several cases are obtained. The steady-state solution for the density of particles with a particular nonrelativistic energy E, due to a source producing the density KE−(8+1) at an intermediate radius with sinks at very large and very small radii, varies with radius r approximately as r−4−38 inside the source region and as r-11−38 outside it. The equations resemble, but are not identical with, those of Parker for the same problem, corresponding solutions differing in that his density at small radii is less.