is satisfied, the spectrum described by Eq. 4.6.38 exhibits a peak maximum at

nmax

8(2ß-1)(1 -ß)uiri (l + 0.2(iWR ) ) f ^ 34(ß + l)RilRoi )

Let it now be assumed that 3= 1; then it follows from Eq. 4.6.31 that t = 34 (i/^i )ln(R/R2 ); dt « R _1dR .

whence, considering Eq. 4.2.7 and Eq. 4.6.19, we shall obtain the rigidity spectrum of accelerated particles in the power form n(RR~r, but with the variable exponent

It can be seen from Eq. 4.6.42 that when the condition

is satisfied the accelerated particle spectrum exhibits a maximum peak at

Rmax Ri

If, however, the condition Eq. 4.6.43 is not satisfied, then already from R = Ri the spectrum will descend with ever increasing power exponent y

(3) The case 0 < S< 1; fiis arbitrary. It will be assumed that Xi < 1 (i.e. Ri < Ro^i).

Since in the case examined //(1 _/)> 0 the value of x> 1. Therefore the acceleration will take place first from x = xi to x = x_ //(1 /) according to Eq.

4.6.20 for x < x_ //(1 /), and then up to high values also according to Eq. 4.6.20 but for x > x,

is attained within a time dy

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