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Published in

American Astronomical Society, Astrophysical Journal, 2(528), p. 1015-1025, 2000

DOI: 10.1086/308202

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Interplanetary and Interacting Protons Accelerated in a Parallel Shock Wave

Journal article published in 2000 by R. Vainio ORCID, L. Kocharov, T. Laitinen ORCID
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

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 LB of the large-scale magnetic field, kappa1/U1