Effects of adiabatic focusing and free-escape boundaries in coronal shock acceleration

Solar energetic particles (SEPs) are considered a serious radiation threat to space technologies and humans in space. SEPs are accelerated to high energies by solar explosive phenomena such as solar flares and in particular by shocks driven by coronal mass ejections (CMEs). We aim to better understand the effects of magnetic field gradient-induced adiabatic focusing on the coronal acceleration of SEPs and to test whether free-escape boundaries produce the same effects as focusing. We present results from a one-dimensional oblique shock model with a mean free path similar to Bell's (1978) theory using Monte Carlo simulations. We show that the momentum spectrum at a shock and far upstream will attain a steady state in a model with adiabatic focusing, whereas it does not in a non-focusing model. However, the effects of focusing can be mimicked in a non-focused simulation by introducing a free-escape boundary ahead of the shock close to the position where the particles will escape from the shock by focusing in a focused transport simulation. This provides a promising avenue for constructing computationally efficient codes that can model the particle emission from shocks.