ultrahigh energy region E > 10 eV and provides the flattening of the spectrum. In other words, in this model the 'ankle' in primary CR spectrum is also due to the 'Levy flights' of the CR particles.
Thus, the differential flux Jt (E) of the particles of the type i from all Galactic sources may be presented in the form:
2.32.3. Parameters of the model and numerical calculations
The first free path distribution of CR particle traveling through highly inhomogeneous medium of fractal type was investigated by Lagutin et al. (2005) numerically. It was obtained that first free path distribution in the medium with mass fractal dimension 0 < dm < 2 has power-law asymptotic P(r) ^ r_a-1. The index a dependence on fractal dimension of the medium under different assumptions on cross-section of particle interaction with elementary structures of the medium (parameter p/xo) is shown in Fig. 2.32.1. In case of small cross-sections the relation, obtained in Isliker and Vlahos (2003), a + 1 = 3 - dM, (2.32.14)
is confirmed by calculations of Lagutin et al. (2005). The violation of linear dependence of a(dM) appears with increasing cross-section as a consequence of finiteness of medium and also overlapping inhomogeneities of the medium. Thus, assuming fractal dimension of the Galaxy as dM ~ 1.7 (according to Combes, 2000), from Eq. 2.32.14 follows a~ 0.3 (Lagutin et al., 2004). The other parameters of the model (p, S, ß, Ko) were evaluated from experimental data. There were found as follows (in accordance with Lagutin and Tyumentsev, 2004):
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