Accelerated particle beams in a 3D simulation of the quiet Sun. Effects of advanced beam propagation modelling

Charged particles are constantly accelerated to non-thermal energies by the reconnecting magnetic field in the solar atmosphere. Our understanding of the interactions between the particles and their environment can benefit from three-dimensional atmospheric simulations accounting for non-thermal particle beams. In a previous publication, we presented the first results from such a simulation. However, the original treatment of beam propagation ignores potentially important phenomena. Here, we present a more general beam propagation model incorporating magnetic gradient forces, the return current, acceleration by the ambient electric field, and temperature-dependent collision rates. Neglecting collisional velocity randomisation makes the model sufficiently lightweight to simulate millions of beams. We investigate how each new physical effect changes beam energy transport in a three-dimensional atmosphere. We applied the method of characteristics to the steady-state continuity equation for electron flux to derive ordinary differential equations for the mean evolution of energy, pitch angle, and flux with distance. For each beam, we solved these numerically for a range of initial energies to obtain the evolving flux spectrum, from which we computed the energy deposited into the ambient plasma. Magnetic gradient forces significantly influence the deposition of beam energy. The strong magnetic field convergence leads to a small coronal deposition peak followed by a heavy dip caused by the onset of magnetic mirroring. Mirrored electrons carry away 5 to 10% of the injected beam energy on average. The transition region peak produced by the remaining energetic electrons occurs slightly deeper than in a uniform magnetic field. An initial diverging magnetic field enhances the subsequent impact of mirroring. The other new physical effects are less significant for the studied atmospheric conditions.