Anomalous Transport of Cosmic Rays in a Nonlinear Diffusion Model
Abstract
We investigate analytically and numerically the transport of cosmic rays following their escape from a shock or another localized acceleration site. Observed cosmic-ray distributions in the vicinity of heliospheric and astrophysical shocks imply that anomalous, superdiffusive transport plays a role in the evolution of the energetic particles. Several authors have quantitatively described the anomalous diffusion scalings, implied by the data, by solutions of a formal transport equation with fractional derivatives. Yet the physical basis of the fractional diffusion model remains uncertain. We explore an alternative model of the cosmic-ray transport: a nonlinear diffusion equation that follows from a self-consistent treatment of the resonantly interacting cosmic-ray particles and their self-generated turbulence. The nonlinear model naturally leads to superdiffusive scalings. In the presence of convection, the model yields a power-law dependence of the particle density on the distance upstream of the shock. Although the results do not refute the use of a fractional advection-diffusion equation, they indicate a viable alternative to explain the anomalous diffusion scalings of cosmic-ray particles.
- Publication:
-
The Astrophysical Journal
- Pub Date:
- May 2017
- DOI:
- 10.3847/1538-4357/aa71ba
- Bibcode:
- 2017ApJ...841...57L
- Keywords:
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- cosmic rays;
- diffusion;
- turbulence