Propagation of particles injected from interplanetary shocks: A black box model and its consequences for acceleration theory and data interpretation

Energetic protons in the hundreds of keV to the tens of MeV range frequently are observed in connection with traveling interplanetary shocks. Occasionally, the particle energies can extend up to about 100 MeV. The intensity time profiles at the observer's site are a superposition of the continuous, spatially and temporally variable acceleration at the shock and the subsequent interplanetary propagation. To gain a better understanding of both processes and to derive their relevant parameters, we extend a numerical solution of the model of focused transport to accommodate the shock as a moving source. No assumptions about the acceleration mechanism are made; the shock is treated as a black box. In this paper we introduce the model, discuss its validity, and present model results which have implications for acceleration theory and data interpretation. The main results concerning acceleration and propagation are as follows: (1) In the limit of strong scattering and low particle speeds our model converges toward diffusive shock acceleration. (2) For weak scattering or fast particles, spatial diffusion is an insufficient approximation for particle transport; in this case, the physical consequence is a fast escape from the shock, and the formal consequence is that the standard description of diffusive shock acceleration is insufficient. (3) Because of this fast escape, even a turbulent foreshock region, while it is perfectly capable of keeping 100 keV protons confined to the shock, would allow 10 MeV protons to stream away easily. Important results for data interpretation are as follows: (1) A quasi‐exponential intensity increase upstream of the shock is not necessarily indicative of diffusive shock acceleration. (2) The intensity at the time of shock passage is a crude measure for the local acceleration efficiency as long as it stays constant or continues to rise.