Planets in close proximity to their parent star, such as those in the habitable zones around M dwarfs, could be subject to particularly high doses of particle radiation. We have carried out test-particle simulations of ∼GeV protons to investigate the propagation of energetic particles accelerated by flares or traveling shock waves within the stellar wind and magnetic field of a TRAPPIST-1-like system. Turbulence was simulated with small-scale magnetostatic perturbations with an isotropic power spectrum. We find that only a few percent of particles injected within half a stellar radius from the stellar surface escape, and that the escaping fraction increases strongly with increasing injection radius. Escaping particles are increasingly deflected and focused by the ambient spiraling magnetic field as the superimposed turbulence amplitude is increased. In our TRAPPIST-1-like simulations, regardless of the angular region of injection, particles are strongly focused onto two caps within the fast wind regions and centered on the equatorial planetary orbital plane. Based on a scaling relation between far-UV emission and energetic protons for solar flares applied to M dwarfs, the innermost putative habitable planet, TRAPPIST-1e, is bombarded by a proton flux up to 6 orders of magnitude larger than experienced by the present-day Earth. We note two mechanisms that could strongly limit EP fluxes from active stars: EPs from flares are contained by the stellar magnetic field; and potential CMEs that might generate EPs at larger distances also fail to escape.
