A numerical simulation of the spatial profiles of energetic particles upstream and downstream of interplanetary shocks
Abstract
The spatial distribution of energetic particle accelerated at shocks depends on the transport properties of those particles. In the case of standard diffusion, it can be easily shown that an exponetial decay for the energetic particle intensity is obtained upstream of the shock, and a constant profile downstream. However, these kind of profiles are rarely observed by spacecraft at interplanetary shocks. We set up a numerical simulation to compute the energetic particle profile both upstream and downstream of the shock: particles are injected at the shock and then propagate according to a Gaussian random walk in the case of normal diffusion and according to a Levy random walk in the case of superdiffusion. The latter is characterized by a nonlinear growth of the mean square displacement of particles and by a power law distribution of free path lengths. A Langevin type equation is solved numerically, and energetic particle spatial profiles are obtained by means of a further integration over time. A number of solutions are obtained while varying the exponent of superdiffusion, and it is found that power law upstream profiles and nonconstant downstream profiles are obtained. These results are compared with previous analytical and numerical studies, and with interplanetary shock observations by the ACE spacecraft.
- Publication:
-
42nd COSPAR Scientific Assembly
- Pub Date:
- July 2018
- Bibcode:
- 2018cosp...42E2728P