The role of cyclic solar magnetic field variations in the long-term cosmic ray modulation

Updating the semi-empirical model of cosmic rays (CR) modulation proposed in our previous work has been discussed. In order to provide a description of long-term variations, in which the CR modulation would adequately reflect the complex interaction of global and local solar magnetic fields, we have supplemented the model with the following characteristics: the solar magnetic field polarity, the integral index, the partial indices, the tilt of the current sheet, and the index characterizing the X-ray flares. The role of each index in the CR modulation has been determined. In the multi-parameter description of long-term CR variations using the integral index or one of four partial indices, the best fit for the period 1977-1999 has been obtained for the integral index and the sector-odd index characterizing the inclined dipole. The discrepancy between the model and observations increases from the beginning of 2000. Therefore, the problematic features in the behavior and modeling of CR during cycle 23 have been discussed. It is suggested that the cycle-to-cycle decrease of the CR density in the minimum epochs of the past solar activity (SA) cycles could be explained by the decrease of the zone-odd index.