Fig. 4.29.1. Accelerated particle spectra at the sub-luminal shock wave ( u1 = 0.5c, y/1 = 45° and ub1= 0.71c) 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/B01 = 0.3, 1.0, and 3.0 are given near the respective results. Linear fits to the power-law parts of the spectra are presented and values of the phase space distribution function spectral indices a = 3.08, 3.24, and 3.55 for (a) and a = 3.16, 3.43, and 3.69 for (b) are given. particles of energies in the range indicated by arrows can effectively interact with the magnetic field inhomogeneities (kmin < kres < kmax ). From Niemiec and Ostrowski (2003a).

The following features are visible in the spectra from Fig. 4.29.1:

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