4.11.4. Formation of the energy and rigidity spectra in the case of particle acceleration by magnetic pumping

Let the mean lifetime of particles in the acceleration region be determined by one of the following expressions:

T = To(Ek/Eko) T = To(R/RoT = To(E/Eo)) . (4.11.26)

Taking into account the Eq. 4.2.7 describing the distribution of the accelerated particle number n() over the particle lifetime t in the acceleration region and considering that, according to Eq. 4.11.16,

t = — ln—^, dt =-k; t = — ln—, dt =-; (4.11.27)

we shall obtain for the kinetic energy and rigidity spectra of the particles respectively:

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