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A Numerical Model of a Coronal Mass Ejection: Shock Development with Implications for the Acceleration of GeV Protons

The initiation and evolution of the coronal mass ejection, which occurred on 1998 May 2 in NOAA Active Region 8210, are modeled using a fully three-dimensional, global MHD code. The initial magnetic field for the model is based on magnetogram data from the Wilcox Solar Observatory, and the solar eruption is initiated by slowly evolving the boundary conditions until a critical point is reached where the configuration loses equilibrium. At this time, the field erupts, and a flux rope is ejected that achieves a maximum speed in excess of 1000 km s-1. The shock that forms in front of the rope reaches a fast-mode Mach number in excess of 4 and a compression ratio greater than 3 by the time it has traveled a distance of 5 R☉ from the surface. For such values, diffusive shock acceleration theory predicts a distribution of solar energetic protons with a cutoff energy of about 10 GeV. For this event, there appears to be no need to introduce an additional acceleration mechanism to account for solar energetic protons with energies below 10 GeV.