Litvinenko, Yuri E.Fichtner, HorstWalter, Dominik2017-07-2420172017-07-242017Litvinenko, Y. E., Fichtner, H., & Walter, D. (2017). Anomalous transport of cosmic rays in a nonlinear diffusion model. The Astrophysical Journal, 841(1). https://doi.org/10.3847/1538-4357/aa71bahttps://hdl.handle.net/10289/11218We 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.application/pdfenThis article has been published in the Astronomical Journal. © 2017 The American Astronomical Society.mathematicscosmic raysdiffusionturbulenceJournal Article10.3847/1538-4357/aa71ba1538-4357