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 cosmicray 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 cosmicray transport: a nonlinear diffusion equation that follows from a selfconsistent treatment of the resonantly interacting cosmicray particles and their selfgenerated turbulence. The nonlinear model naturally leads to superdiffusive scalings. In the presence of convection, the model yields a powerlaw 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 cosmicray particles.
 Authors:
 Department of Mathematics, University of Waikato, P. B. 3105, Hamilton 3240 (New Zealand)
 Institut für Theoretische Physik IV, RuhrUniversität Bochum, Universitätsstrasse 150, D44780 Bochum (Germany)
 Publication Date:
 OSTI Identifier:
 22663570
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Astrophysical Journal; Journal Volume: 841; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACCELERATION; ASTROPHYSICS; COMPUTERIZED SIMULATION; CONVECTION; COSMIC RADIATION; DENSITY; DIFFUSION; DIFFUSION EQUATIONS; DISTRIBUTION; EVOLUTION; NONLINEAR PROBLEMS; TRANSPORT THEORY; TURBULENCE
Citation Formats
Litvinenko, Yuri E., Fichtner, Horst, and Walter, Dominik. Anomalous Transport of Cosmic Rays in a Nonlinear Diffusion Model. United States: N. p., 2017.
Web. doi:10.3847/15384357/AA71BA.
Litvinenko, Yuri E., Fichtner, Horst, & Walter, Dominik. Anomalous Transport of Cosmic Rays in a Nonlinear Diffusion Model. United States. doi:10.3847/15384357/AA71BA.
Litvinenko, Yuri E., Fichtner, Horst, and Walter, Dominik. 2017.
"Anomalous Transport of Cosmic Rays in a Nonlinear Diffusion Model". United States.
doi:10.3847/15384357/AA71BA.
@article{osti_22663570,
title = {Anomalous Transport of Cosmic Rays in a Nonlinear Diffusion Model},
author = {Litvinenko, Yuri E. and Fichtner, Horst and Walter, Dominik},
abstractNote = {We investigate analytically and numerically the transport of cosmic rays following their escape from a shock or another localized acceleration site. Observed cosmicray 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 cosmicray transport: a nonlinear diffusion equation that follows from a selfconsistent treatment of the resonantly interacting cosmicray particles and their selfgenerated turbulence. The nonlinear model naturally leads to superdiffusive scalings. In the presence of convection, the model yields a powerlaw 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 cosmicray particles.},
doi = {10.3847/15384357/AA71BA},
journal = {Astrophysical Journal},
number = 1,
volume = 841,
place = {United States},
year = 2017,
month = 5
}

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