Interplanetary and interacting protons accelerated in a parallel shock wave

We present a test-particle model of diffusive shock acceleration on open co ronal field lines based on one-dimensional diffusion-convection equation wi th finite upstream and downstream diffusion regions. We calculate the energ y spectrum of protons escaping into the interplanetary space and that of pr otons interacting with the subcoronal material producing observable seconda ry emissions. Our model can account for the observed power-law and broken p ower-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 t o Monte Carlo simulations of parallel shock acceleration including the effe cts 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 held, kappa(1)/U-1 much less than L- B, where U-1 is the upstream scattering center speed and kappa(1)(p) is the momentum dependent upstream diffusion coefficent; (ii) the downstream diff usion length is much smaller than the length of the downstream diffusive re gion L-2, for which L-2 much less than L-B has to be satisfied; and (iii) m ost of the particles are injected to the acceleration process within a coup le of L-B's above the solar surface. We emphasize that concurrently produce d interplanetary and interacting protons can be used as probes of turbulenc e in the vicinity of the shock; our model has two turbulence parameters, th e scattering-center compression ratio at the shock and the number of diffus ion lengths in the upstream region, that may be experimentally determined i f the interplanetary and interacting proton spectra are measured.