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Momentum-dependent diffusive particle acceleration in modified shock fronts

G. M. WebbDepartment of Planetary Sciences, Lunar and Planetary Laboratory, University of Arizona, Tucson, AZ 85721, USAT. J. BogdanHigh Altitude Observatory, National Center for Atmospheric Research, PO Box 3000, Boulder CO 80307, USAM. A. LeeSpace Science Center, University of New Hampshire, Durham, NH 03824, USA;I. LercheDepartment of Geology, University of South Carolina, Columbia, SC 29208 USA
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In the presently derived analytic solutions of the steady transport equation for diffusive particle acceleration in a modified, planar shock front having free escape boundaries, the fluid velocity profile through the shock transition decreases monotonically between the upstream and downstream boundaries. The spatial diffusion coefficient's spatial dependence is linked to that of the fluid velocity profile. Attention is given to the solution corresponding to monoenergetic particle injection at the shock front, with free particle escape at finite distances both upstream and downstream of the shock. The accelerated particle spectrum is dominated at high energies by an exponential cutoff, due to the competition between acceleration by the first-order Fermi mechanism and particle loss through the free escape boundaries.

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