In Fig. 4.24.1 are shown distribution functions for a set of parameters and with vthms = 0 (left panel) and vMCs = 4«2 (right panel). In both panels, the solid curves are the Monte Carlo results and the dashed curves are the semi-analytical results where E,sa has been chosen to provide the best match to the Monte Carlo spectra.
In Fig. 4.24.2 is shown the low energy portions of the spectra along with the distributions of injected particles in the Monte Carlo model (dotted histograms). The vertical solid lines are at pinj and they show the transition between the
Maxwellian and the super-thermal population in the semi-analytical results.
Ellison et al. (2005) underlined the following important aspects of the plots in Fig. 4.24.1 and 4.24.2:
(i) The broad-band match between the two very different calculations is quite good, particularly for vthres = 0. Both models show the important characteristics of nonlinear diffusive shock acceleration, i.e., r >> 4, concave spectra, and a sharp reduction in the shocked temperature from test-particle values.
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