Y

where the index of the power spectrum of accelerated particles is

The Eq. 4.21.29 differs from Eq. 4.21.21 by the factor [1 - exp(- R^/ K1 )]-1> 1. It means that the limiting of the shock wave dimension leads to an increase of y. As was shown in Chapters 1 and 2, with increasing particle momentum p usually increases diffusion coefficient. It means that at p > pmax, where pmax is determined by the relation

the value of y quickly increases with increasing p. Therefore the value of pmax can be considered, according to Berezhko et al. (M1988), as the effective upper threshold of the momentum spectrum of particles accelerated by a shock wave with finite dimension Rs .

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