On the second spherical harmonies of the cosmic ray angular distribution

Explicit expressions describing the semi-diurnal variation of cosmic ray intensity are obtained in the frame of the convection-diffusion theory. Convection-diffusion equations are extended by introducing a symmetric traceless tensor accounting for the second harmonics of the cosmic ray angular distribution. Starting from the statistical Boltzmann equation a new transport equation is deduced which relates the second harmonics of the angular distribution to the gradients of cosmic ray streaming. Expressing the free space anisotropy in terms of geographical coordinates, the predicted diurnal and semi-diurnal variations are given. Arguments are brought forward that a sunward cosmic ray streaming along the interplanetary field lines gives rise to a pitch angle distribution with an excess of particles of large pitch angles.