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Planets in close proximity to their parent star, such as those in thehabitable zones around M dwarfs, could be subject to particularly high doses ofparticle radiation. We have carried out test-particle simulations of ~GeVprotons to investigate the propagation of energetic particles accelerated byflares or travelling shock waves within the stellar wind and magnetic field ofa TRAPPIST-1-like system. Turbulence was simulated with small-scalemagnetostatic perturbations with an isotropic power spectrum. We find that onlya few percent of particles injected within half a stellar radius from thestellar surface escape, and that the escaping fraction increases strongly withincreasing injection radius. Escaping particles are increasingly deflected andfocused by the ambient spiralling magnetic field as the superimposed turbulenceamplitude is increased. In our TRAPPIST-1-like simulations, regardless of theangular region of injection, particles are strongly focused onto two capswithin the fast wind regions and centered on the equatorial planetary orbitalplane. Based on a scaling relation between far-UV emission and energeticprotons for solar flares applied to M dwarfs, the innermost putative habitableplanet, TRAPPIST-1e, is bombarded by a proton flux up to 6 orders of magnitudelarger than experienced by the present-day Earth. We note two mechanisms thatcould strongly limit EP fluxes from active stars: EPs from flares are containedby the stellar magnetic field; and potential CMEs that might generate EPs atlarger distances also fail to escape.

Stellar energetic particles in the magnetically turbulent habitable zones of TRAPPIST-1-like planetary systems