Interplanetary and Interacting Protons Accelerated in a Parallel Shock Wave
R. Vainio, L. Kocharov, T. Laitinen
We present a test-particle model of diffusive shock acceleration on open coronal field lines based on one-dimensional diffusion- convection equation with finite upstream and downstream diffusion regions. We calculate the energy spectrum of protons escaping into the interplanetary space and that of protons interacting with the subcoronal material producing observable secondary emissions. Our model can account for the observed power-law and broken power-law energy spectra as well as the values of the order of unity for the ratio of the interplanetary to interacting protons. We compare our model to Monte Carlo simulations of parallel shock acceleration including the effects of the diverging magnetic field. A good agreement between the models is found if (i) the upstream diffusion length is much smaller than the scale length L$_B$ of the large-scale magnetic field, \ensuremath\kappa$_1$/U$_1$< ApJ, 528, 1015-1025, 2000