Model for the origin and properties of the cosmic‐ray rigidity spectrum
Authors: Kaplon M. F. , Skadron G. 
Published: February 2008

We propose a model to explain a number of features of the differential rigidity spectra of the nuclear component of the primary cosmic radiation. A supernova explosion is assumed to result in the acceleration of nuclei to a pure power law rigidity spectrum and a composition relatively rich in heavy and medium weight nuclei. The supernova remnant into which these particles are injected is characterized as a large‐scale trapping region resulting from predominantly closed magnetic field lines that partially isolate the region from the surrounding galactic space. This feature of the supernova region is represented by a dipole‐like field. We assume that, superimposed on this field, magnetic irregularities produce a certain amount of distortion of the field lines in the interior of the source, and that irregularities along the periphery of the source lead to local distortions of the field and, hence, a mixing of galactic and source field lines in the neighborhood of these irregularities.

The observed large‐scale regularity of the magnetic field in the Crab leads us to treat the particle motion within the source region in the guiding center approximation (except at very high rigidities), so that these particles are capable of guiding outward to the source boundary and returning inward to the interior along the source's predominantly closed magnetic lines of force. The well defined inward field gradient and field curvature, however, cause the particles to drift longitudinally as they spiral along the periphery of the source region, and accordingly they have a certain probability of drifting into a neighborhood of field mixing and onto a galactic field line which guides them out of the source region.

During their confinement within the source region, the particles necessarily undergo nuclear interactions and ionization loss, and, therefore, the differential rigidity spectrum of particles escaping from the source boundary into the galaxy is jointly determined by their injection spectrum, their escape probability, and the extent to which they suffer loss processes. A continuity equation combining these various processes is constructed and then averaged over the entirety of active sources in the galaxy. The solutions of the averaged continuity equation for each charge group then give us the differential rigidity spectra with which the cosmic radiation is injected into the galactic medium.

The additional effects of intragalactic motion on the cosmic‐ray spectrum are treated in the approximation that the particles escaping from source regions undergo magnetic diffusion in the galactic volume with a rigidity independent scattering mean free path. The differential rigidity spectra of the various charge groups incident on the solar system are thereby obtained. The effects of solar modulation on the galactic cosmic‐ray spectrum are treated in accordance with the solar wind theory. The resulting differential rigidity spectra are derived and compared with data taken near solar minimum, and it is found that the calculated spectra, as well as the rigidity dependence of various abundance ratios, are in reasonable agreement with the available data.