Rr lsllkis tRoR e25

k?0 R- i) 5k {R. IR0l 31k tß - 25 + i - 2kRi - S))

If R >> Ri it is possible in Eq. 4.6.50 to be limited to the first term; then the dependence R(() will be determined by the relations

where ¿1 is determined by Eq. 4.6.46 and Eq. 4.6.47. It follows from Eq. 4.6.51 based on Eq. 4.2.7 and including Eq. 4.6.19 that at R >> Ri the accelerated particle spectrum is n(R<

28+1

8u t

8uiT

where b = 34 (R1/R01 )[(R/R )ß-28+1 -(Roi/Ri )(ß-28+1)(1-8))+ 8ulh.. b2 = 34 (Ri/Roi)[ln(RR)+ ln (Roi/Ri )(1 - /))■+ 8uit1.

It will now be assumed that xi = 1 (i.e. Rl = Roi). Then xi/(( 8) and the acceleration will be completely determined by the second expression in Eq. 4.6.20.

< 1, the acceleration will

If Xi > 1 (i.e. Ri > R0i) then, since in this case xi also be completely determined by the second expression in Eq. 4.6.20. Thus at Xi > 1 and including the boundary condition X t=0 = Xi we obtain

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