Abstract. The kinetic equation describing cosmic-ray propagation in interplanetary space has been used to construct a consistent theory of cosmic-ray anisotropy including the second spherical harmonic of particle angular distribution. The amplitude and phase of semi-diurnal cosmic-ray variation have been calculated. Expressions describing the relationships of the semi-diurnal variation parameters to helio-latitude distribution of cosmic rays have been derived. The results obtained are compared with observational data.
Basic ConceptsPropagation of cosmic rays in interplanetary space is accompanied by not only a decrease in their intensity due their interactions with moving inhomogeneities of interplanetary magnetic field but also a deformation of angular distribution of charged particles. Despite the fact that the cosmic-ray distribution function is nearly isotropic, the small anisotropic addend to the distribution function gives rise to the cosmic-ray intensity variations (the diurnal and semi-diurnal cosmic-ray variations) observed with ground-based detectors. The mechanism of the diurnal variation has been studied in sufficient detail (Krymsky, 1964(Krymsky, , 1969. It has been shown by Kuzmin et al. (1965) or Ables etal. (1965) that a semi-diurnal cosmic-ray variation due to the second spherical harmonic in the cosmic-ray angular distribution exists simultaneously with the diurnal cosmic-ray variation. The observed cosmic-ray anisotropy is associated with spatial distribution of charged particle density.The spatial distribution of cosmic-ray density is determined by numerous factors, such as the helio-latitude distribution of solar activity and the geometry of interplanetary magnetic field. It has been known (Parker, 1964;Krymsky, 1969;Owens and Kash, 1976) that the field-aligned cosmic-ray diffusion coefficient is much in excess of the field-perpendicular diffusion coefficient. If interplanetary magnetic field can be described in terms of the Parker model (Parker, 1964), the distance along force line to the modulation region boundary near the helio-equator is much in excess of the same distance in the regions located far from the helio-equator. Therefore, the effective modulation parameter #(0) = uro/Z, where u is solar wind velocity; to, the distance from the modulation region center in a spherical coordinate system with origin at the Sun's center to the modulation region boundary; 0, the azimuthal angle measured from the Sun's northern semi-axis; and z(0) is the cosmic-ray diffusion coefficient) which is maximum at 0 ~ ~/2 (i.e., at the helio-equator); so that the cosmic-ray density near the Astrophysics and Space Science 93 (1983) 97-126. 0004-640X/83/0931-0097504.50.