Effects of the secular magnetic variation on the distribution function of inner-zone protons

Abstract

The equation governing the distribution function of high-energy protons in the earth's radiation belt has been modified to include the effects of the secular change of the earth's magnetic dipole moment in addition to the effects of albedo neutron decay, collisional energy loss, and radial diffusion, which have been studied in the past. Because the time scale of the magnetic-field change (∼2000 years) is much longer than the time scale of proton trapping (∼200 years) an approximate solution of the equation can be obtained. This solution indicates that the shrinking dipole increases the distribution function at the geomagnetic equator for 1.15 < L < 1.7 and 15 < E < 160 Mev. The greatest increase occurs at L = 1.2, where it is as large as a factor of 5. The addition of this effect improves the agreement between the theoretically computed distribution function and the experimental data.