On the energy spectrum of galactic primary cosmic rays: Results from the transport equation

The spectrum of galactic primary cosmic rays at relativistic monenta is calculated. The primaries are assumed to be accelerated continuously from the thermal galactic background medium by first- and second-order Fermi acceleration. We show that the observed spectrum is readily obtained from the transport equation conventionally invoked to discuss propagation and loss of cosmic rays in our Galaxy from a distribution of sources. We have previously (Lerche and Schlickeiser, 1985) shown that the observed secondary to primary ratio is satisfactorily explained by a similar use of the transport equation, allowing for secondary production from the primaries. Accordingly, when the results of this paper are added to those concerning the secondary/primary ratio behaviour, it would seem that continuous Fermi acceleration accounts, in a quantitative fashion, for the spectral behaviours observed at Earth.