where Ri is the rigidity of injected particles (at t = 0); ut is the velocities of the inhomogeneities effectively scattering the particles with rigidity Ri; A is the transport scattering path of such particles; R1 is determined by Eq. 4.6.61. Integration of Eq. 4.6.75 gives
Consider individual cases.
(1) The case R << R1 (and hence Ri << R1). Here it follows from Eq. 4.6.76 that
Since in this case
we shall obtain, in accordance with Eq. 4.4.7, for the accelerated particle spectrum:
It follows from Eq. 4.6.79 that at 3_ 25 + 1 = 0 the spectrum will be of power form only if 3 + 1 = 0; 5 = 0. Here it follows from Eq. 4.6.76 that
(l + 2u2t(3- 2¿)/c4 f (¡ 1S) if 3- 28* 0, exp^t/cO,) if 3- 28 = 0.
If 3 _ 25 * 0 then since it follows from Eq. 4.6.80 and Eq. 4.6.4 that
and including Eq. 4.2.7, we shall obtain for the rigidity spectrum of accelerated particles in their sources:
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