On the theory of protons trapped in the Earth's magnetic field

Abstract

A differential equation of transport is written for protons losing energy in an atmosphere but not scattering. It is solved under the approximation that a proton loses a negligible amount of energy while it drifts once around the earth in longitude. Three cases are treated: the equilibrium, solution with input and loss rates equal; the solution for impulsive injection at t = 0, the intensity then dying away; and the solution for the intensity zero initially, the input mechanism being turned on at t = 0. No numerical work bearing on the geometry of the source function is included. The treatment is an improvement over previous ones in that it adequately treats the particles as moving along their actual trajectories. A detailed comparison with observations over South Africa shows that the altitude dependence of intensity is roughly consistent with the view that the particles seen by the unshielded Geiger tube on 1958e are protons supplied by a weak source (for example, by decay of albedo neutrons) which are lost to the detector when their energy is reduced below the detection threshold by absorption. The atmosphere required has a temperature of about 2000°K at 400 km if it is pure dissociated nitrogen. At some height between about 1100 and 1300 km the scale height sharply increases in a way consistent with the view that at this height the composition changes to pure dissociated hydrogen. Only relative intensities are used in these comparisons.