PoS - Proceedings of Science
Volume 395 - 37th International Cosmic Ray Conference (ICRC2021) - CRD - Cosmic Ray Direct
A perturbative approach to a nonlinear advection-diffusion equation of particle transport
D. Walter*, H. Fichtner and Y. Litvinenko
Full text: pdf
Pre-published on: July 03, 2021
Published on: March 18, 2022
We explore analytical techniques for modeling the nonlinear cosmic ray transport in various
astrophysical environments which is of significant current research interest. While nonlinearity
is most often described by coupled equations for the dynamics of the thermal plasma and the
cosmic ray transport or for the transport of the plasma waves and the cosmic rays, we study
the case of a single but nonlinear advection-diffusion equation. The latter can be approximately
solved analytically or semi-analytically, with the advantage that these solutions are easy to use and,
thus, can facilitate a quantitative comparison to data. We present our previous work in a twofold
manner. First, instead of employing an integral method to the case of pure nonlinear diffusion,
we apply an expansion technique to the advection-diffusion equation. We use the technique
systematically to analyze the effect of nonlinear diffusion for the cases of constant and spatially
varying advection combined with time-varying source functions. Second, we extend the study
from the one-dimensional, Cartesian geometry to the radially symmetric case, which allows us to
treat more accurately the nonlinear diffusion problems on larger scales away from the source. The
results are compared to numerical solutions, which are also extended to more complex situations.
DOI: https://doi.org/10.22323/1.395.0139
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