Cosmic ray diffusion, energy loss, and the diurnal variation

Abstract

The purpose of this paper is to consider a number of points pertaining to the origin of the observed mean diurnal variation of the cosmic ray intensity, which were not treated in the earlier papers on the subject. Following a brief review of the basic nature of the diurnal variation, the necessary diffusion across the lines of force is investigated. It is found that the values κ ⊥ κ ‖ ≅ 10 −2 deduced from the observed fluctuations inside the orbit of Earth give about the right amount of diffusion to account for the fact that the amplitude of the diurnal variation is approximately half the theoretical upper limit, which would apply if κ ⊥ were much larger. The calculations show that the geometry of the spiral form of the field beyond the orbit of Earth plays an essential role in providing sufficient diffusion across the lines of force. The calculations also show that variation in outer radius R and in κ ⊥ κ ‖ due to changing wind conditions may contribute to some of the observed changes in the amplitude of the diurnal variation. The diurnal variation is rederived for steady uniform wind conditions in order to include the effect of adiabatic deceleration. The effect is the addition of a small diurnal component with an amplitude proportional to the radial cosmic ray gradient in space. The effect is only a few per cent of the total diurnal variation above 1 GeV, and so may be neglected there. The effect is large at low energies, but is not subject to observation. The principal observable steady diurnal variation is, then, the rotation of the cosmic rays with the Sun. Appendix II gives a summary of the motion of a particle in an idealized smooth spiral interplanetary field, with a discussion of the energy loss from adiabatic expansion.