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The Eq. 4.6.9 seems to be rather cumbersome for further analysis. Within a relative error of less than 0.1, it follows from Eq. 4.6.9 that

(((3/2 + R?/r2)exp(8ut/32)-3/2//2 if t < tT, [[8u(i - tT )/32 + l] if t > tT,

where

It follows from Eq. 4.6. ll that the particle rigidity must rapidly (within time tl) increase from Rj to Rp; the time tl is a weak function of Rj, namely it varies from 0.l92(2/u) at Ri/Rp = 0 to 0.l34(2/u) at Ri/Rp = 0.5, and to 0.058(2/u) at Rj/R0 = 08. Further, the particle's rigidity increase is directly proportional to t (see Eq. 4.6.ll).

If, however, Rj > Rp (i.e. Vj > u ), then, after integrating Eq. 4.6.7, we find that

arctg

8utR0 3/

whence approximately

The accelerated particle spectrum will be found from Eq. 4.2.7 and Eq. 4.6. l4 in the case where t is independent of R in the form n(R exp(- 32(R - Rj R8uRpT).

If, however, the expected variations of t with R (even at constant 2 and u) are taken into account according to Eq. 4.6.6, then

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