Particle spectrum N(E) outside a Fermi reservoir in an illustrative case α₀T = 3/4. The thin upper line is the analytical scaling N(E) ~ E^-2, predicted by Eq. (13) in the range 1 ≤ E/E₀ ≤ 4 for regular Fermi acceleration (q = 0). The lower curve is the numerically evaluated stochastic acceleration solution of Eq. (25) with the parameter q = 1/4 that corresponds to Fermi acceleration in three dimensions.