On the second spherical harmonics of the cosmic ray angular distribution

Details On the second spherical harmonics of the cosmic ray angular distribution On the second spherical harmonics of the cosmic ray angular distribution

Aug 1975

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975jpha....8.1349k&link_type=abstract

Journal of Physics, Part A - Mathematical and General, vol. 8, Aug. 1975, p. 1349-1360.

Physics

5

Angular Distribution, Cosmic Rays, Diurnal Variations, Radiation Distribution, Spherical Harmonics, Anisotropy, Boltzmann Transport Equation, Interplanetary Magnetic Fields, Lines Of Force, Mean Free Path, Partial Differential Equations, Particle Diffusion

Scientific paper

Explicit expressions describing the semidiurnal 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. Thus, compared to models used hitherto, a more quantitative calculation is carried out. Expressing the free space anisotropy in terms of geographical coordinates, the predicted diurnal and semidiurnal variations are given. The results obtained are essentially in agreement with those of Quenby and Lietti but also differences arise as a result of the bending and divergence of the large-scale interplanetary magnetic field lines. 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.

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