at a >> 1. The relative role of shock wave regular and statistical accelerations is mostly determined by the ratio T¡Tst ~ a. If a << 1 the main role is played regular shock wave acceleration, and the accelerated particle distribution (see Eq. 4.21.43) and the index y in the power spectrum (see Eq. 4.21.46) will be about the same as that considered in Section 4.21.5. Only in the region 2 (behind the shock front) on the big distances from the front x >> K2/^a2 will be a sufficient role of statistical acceleration (according to Eq. 4.21.43): the density of accelerated particles will be increased. In the opposite case when a >> 1 statistical acceleration will be more important, and it will form the power spectrum with the index y determined by Eq. 4.21.47.
In the case of Alfvén turbulence when the diffusion coefficient in the momentum space is determined by Eq. 4.21.38, we obtain «12 = (ualu1 2) For the fast shock waves u 2 >> ua , then a << 1, and the main role will be played by the regular acceleration. For slow shock waves U12 = ua can had and in this case the relative role of regular and statistical accelerations may be comparable.
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