Fig. 4.29.2. Accelerated particle spectra at the super-luminal shock wave (u1 = 0.5c, = 75° and uB1 = 1.93c) for (a) the flat (Eq. 4.29.1) and (b) the Kolmogorov (Eq. 4.29.2) wave spectrum of magnetic field perturbations. The upstream perturbation amplitude ¿B/Bcu = 0.3, 1.0, and 3.0 are given near the respective results. According to Niemiec and Ostrowski (2003a).
For the low amplitude turbulence (¿B/B0j = 0.3) Niemiec and Ostrowski
(2003a) approximately reproduce results of Begelman and Kirk (1990), with a 'super-adiabatic' compression of injected particles, but hardly any power-law spectral tail. At larger turbulence amplitudes power-law sections in the spectra are produced again, but the steepening and the cut-off occur at lower energies compared with the subluminal shocks (compare with Fig. 4.29.1).
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