Acceleration of cosmic rays in the solar wind termination shock. I - A steady state technique in a spherically symmetric model

Abstract

In this paper, it is shown that a steady state model for the combined acceleration and modulation of cosmic rays in the heliosphere is possible. In this first of a series of papers, a spherically symmetric heliosphere with a termination shock at 50 AU is adopted. It is shown that the accelerated spectrum develops naturally from the shock boundary condition and that the low-energy source of particles to be accelerated need not be specified explicitly. The demonstration solutions on the shock are the expected power laws, and it is shown where shock curvature and acceleration time scale effects set in. Some of the basic features of the anomalous cosmic-ray component are explained by the solutions, but, as expected, a detailed comparison with observations must await more extensive and realistic models. 25 references.