of an infinite plane front (see Section 4.21.3). Both these processes sufficiently decrease the effectiveness of particle acceleration. The relative role of these processes is mostly determined by the values of the parameters gi = uiro K and g2 = U2roIk which are called modulation parameters: Eq. 4.21.54 and Eq. 4.21.55 show that they characterize the possibility of accelerated particles propagating against the plasma flux in regions 1 and 2, correspondingly. It is easy to see that if gi ^ 0 or g2 ^ 0 we obtain
at g1 << min(1, g23 at g2 << min(1, g1).
The bigger y is means that in there cases particle acceleration to high energies becomes non-effective.
With increase of the modulation parameter g1 the role of adiabatic particle energy decreasing falls sufficiently and at g1 ^ ^ the value of the distribution function f rc (p/po )3g1/8 ^ 0 . This occurs because at g1 >> 1 the diffusion length of particles going inside region 2 with adiabatic cooling is very small: L ~ k/U1 << ro . In Fig. 4.21.2 are shown results of calculations of expected momentum spectra at different distances from the standing shock front (for rjro from 0.01 to 100) at two values of modulation parameters: weak, g1 = g2 = g = 01, and very large, g1 = g2 = g = 10.
From Fig. 4.21.2 it can be seen that with increasing the modulation parameter g the relative role of particle deceleration (p < po) decreases sufficiently. At g1 >> 1 the spectral index of accelerated particles differs only little from the index Y = 3j/(j -1) for particle acceleration by the infinite plane shock wave (see Section 4.21.3); the difference is caused mainly by the finites of the standing spherical shock wave:
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