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Cosmic Ray Acceleration in Space Plasmas Resolving the Eq. 4.11.20 relative to E we shall find

(i + a )xo + i)exp(at/r) +1 + a - xo (xo + 1)exp(at/r)+1+«1 - xo

It can be easily seen that in the non-relativistic energy range where 1 - m2accA/E2 << 1 the Eq. 4.11.20 turns out to be xo«1+0^. x, 1

2macc2

2macc2

and Eq. 4.11.22 is transformed into Eq. 4.11.16 for dE^/d . In the ultra-relativistic

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