Origin of Primary Cosmic Radiation and Its Antiproton Component

Abstract

We have solved a Fokker-Planck diffusion equation for the diffusion and acceleration of cosmic rays. A time-independent solution is obtained by assuming that the contributions to the present intensity of particles injected at a uniform rate during all past times is equivalent to summing the intensities over all future time of particles injected at a given time. Contrary to the usual dependence upon an average acceleration, we have used continuous deceleration and fluctuations in acceleration to explain the energy spectrum. This gives us a general expression for a power-law spectrum in which the exponent varies as $\ensuremath{\gamma}=0.093\mathrm{ln}(\frac{E}{m})+1.75$, thus allowing a very good fit to the experimental energy spectrum. We then apply a previously developed expression for the production of antiprotons to obtain an injection spectrum. This and the above solutions are then applied to three extreme cases of possible origin. The resulting antiproton spectra depend upon whether the material encountered by primary cosmic-ray protons is mostly inside or outside the regions of acceleration. The relative ratio of antiprotons to protons with $E>10$ GeV is expected to be about ${10}^{\ensuremath{-}6}$ if the protons have passed through 2-3 g/${\mathrm{cm}}^{2}$ of material.