Trapping and Precipitation of Protons during Stochastic Acceleration in Magnetic Loops

Abstract

We study confinement of particles during the stochastic acceleration in coronal magnetic loops. Analytic solutions and Monte Carlo simulations of the coordinate-dependent focused-diffusion transport and acceleration are employed to deduce the effective leaky-box escape time, τ_esc. The rigorously correct expression of the escape time yields the leaky-box-model spectrum of accelerated particles, which exactly coincides with the high-energy asymptote of a spectrum deduced by including all spatial dependencies into the diffusion equation. Besides the application to the acceleration studies, the deduced escape time allows one to relate the spectra of protons generating neutrons and γ-rays in the coronal portion of the loop to the spectra in and below the chromosphere. As an illustration, we discuss the model implications for γ-ray and neutron observations of the behind-the-limb flares.