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Cosmic rays are an important factor of space weather determining radiation conditions near the Earth and it seems to be essential to clarify radiation conditions near extrasolar planets too. Last year a terrestrial planet candidate was discovered in an orbit around Proxima Centauri. Here we present our estimates on parameters of stellar wind from the Parker model, possible fluxes and fluencies of galactic and stellar cosmic rays based on the available data of the Proxima Centauri activity and its magnetic field. We found that galactic cosmic rays will be practically absent near Proxima b up to energies of 1 TeV due to the modulation by the stellar wind. Stellar cosmic rays may be accelerated in Proxima Centauri events, which are able to permanently maintain density of stellar cosmic rays in the astrosphere comparable to low energy cosmic ray density in the heliosphere. Maximal proton intensities in extreme Proxima events should be by 3–4 orders more than in solar events.

The work was partly supported by the Russian Foundation for Basic Research (grant 16-02-00328) and the Programm 1.7 P2 of the Russian Academy of Sciences.