Bulg. J. Phys. vol.48 no.1 (2021), pp. 042-054

Cosmic-Ray Transport Equation: Solutions and Semi-Empirical Models

M. Buchvarova
Space Research and Technology Institute, Bulgarian Academy of Sciences, Acad. Georgy Bonchev Str., bl. 1, Sofia 1113, Bulgaria
Abstract. Galactic radiation is the most penetrating type of cosmic radiation in the Earth's atmosphere. The galactic cosmic rays (GCRs), passing through the heliosphere to reach to the upper atmosphere, change their energy, direction of propagation and may even be absorbed along the way. The galactic cosmic-ray transport in the heliosphere is described by the well-known transport equation developed by American solar astrophysicist Eugene Newman Parker. Parker has shown that – in the framework of statistical physics – the random walk of cosmic-ray particles is a Markoff process, describable by a Fokker–Planck equation (FPE). Gleeson and Axford (1967) subsequently rederived the Parker transport equation for cosmic rays starting with a Boltzmann type equation for a radial geometry.

In this work are discussed the most widely used analytical solutions to the Parker transport equation. It is also shown that an approximate solution of Fisk and Axford (1969) to the transport equation is the basis of widely used semi-empirical models. The further development of this type of models is related to finding functional dependencies between the parameters in the models and different heliospheric and solar variables. These studies are important for deriving more accurate semi-empirical models describing and predicting GCR spectra during the solar cycle.

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