Effect of synchtrotron losses on multiple diffusive shock acceleration

The effect of synchrotron losses on diffusive shock acceleration (DSA) at many shocks is treated numerically. Synchrotron losses determine a maximum energy to which electrons can be accelerated through DSA, and this is referred to as the synchrotron cutoff, p_c . The distribution of accelerated electrons after many shocks is found (a) for a distribution injected at the initial shock, to tend to a plateau [f(p) independent of p ≲ 0.1p_c ], and (b) for the cumulative distribution from injection at each shock to tend to f(p) ∝ p^-b with b ≈ 3 well below the synchrotron cutoff with a peak in the slope (b _min ≈ 2) at p ≲ 0.1p_c . It is suggested that the latter result might account for the flat synchrotron spectra observed in some Galactic Centre sources.