  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 travelling 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 spiralling 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.
