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If Ri < AmpOUijZe (i.e. if Xi < 1) the integration of Eq. 4.6.22 in the region x <1 gives

2 Ui x31 x3

1 _ 2(3 + 2) x2 + 23(3 + 2) x4 _ 3(3 + 4) i 45(3 + 6) i "

It follows from Eq. 4.6.23 that within a short time 4x_3

1 _ 3 _ 2(3+2) ( _ xf+4)+ 23(3+2) ( _ 3)_ i 3(3+ 4) i ' 45(3+ 6) i '

a particle gains rigidity AmpCu^jZe, i.e. x = 1. We shall consider, therefore, the particle acceleration at Ri > AmpcuijZe (i.e. when Xi > 1). It then follows approximately from Eq. 4.6.22:

Since according to Eq. 4.6.25

then taking account of Eq. 4.2.7 and Eq. 4.6.19 we shall obtain for the particle rigidity spectrum i(R)dR ~ R23+1 exp

Cosmic Ray Acceleration in Space Plasmas The spectrum determined by Eq. 4.6.27 exhibits a peak maximum at

Rmax Ri

The Eq. 4.6.27 may be presented in the form of the power function n(R) — R Y with the variable power exponent

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