# The Distribution Function of Solar Cosmic Rays under Prolonged Particle Injection

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**Abstract**—The propagation of solar cosmic rays (SCR) in the interplanetary medium is considered on the basis of the Fokker–Planck kinetic equation. It is known that the SCR distribution function averaged over a solar proton event contains valuable data on the scattering process for energetic charged particles by interplanetary magnetic fields. A steady-state solution for the kinetic equation in the small-angle approximation is obtained, and the dependence of the angular distribution function of cosmic rays on the distance to the particle source is examined. This solution is applicable if the distance to the particle source is short compared to the mean free path of cosmic rays and if particles are moving primarily in the radial direction. The angular distribution of particles at large (compared to the mean free path of cosmic rays) distances to the particle source is also analyzed. An analytical expression for the distribution function of cosmic rays in the form of a sum of an isotropic component and a small anisotropic one is derived. It is demonstrated that the angular distribution of cosmic rays depends to a considerable extent on the anisotropy of their scattering. The scattering characteristics of energetic charged particles by fluctuations of interplanetary magnetic fields are estimated based on observational data for several SCR flares.

*Keywords*: cosmic rays kinetic equation interplanetary magnetic field

## Notes

### FUNDING

This study was funded as part of the routine financing program for institutes of the National Academy of Sciences of Ukraine.

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