An Implicit Conservative Finite Volume Scheme with Poisson Brackets for the Steady-State Transport of Galactic Cosmic Rays
Abstract
Galactic cosmic rays (GCRs) pose a persistent radiation hazard to astronauts and spacecraft in the heliosphere. Modeling their transport is essential for understanding how the solar wind and heliospheric magnetic field shape their spatial distributions and energy spectra. Timely predictions require solving for the particle distribution function much faster than real time, but explicit numerical schemes are restricted by the stability limit on the time step. In this Letter, we present an implicit conservative finite-volume scheme for kinetic equations formulated with Poisson brackets. This scheme conserves particle number, maintains the total-variation-diminishing property, achieves second-order spatial accuracy, and remains stable for time steps far beyond the explicit limit, while reaching quasi-steady states in less than ~1/100 of the computational time required for the explicit scheme, as demonstrated by numerical tests. We apply this scheme to the Parker transport equation along magnetic field lines in the background solar wind during Carrington rotation 2211, where it reaches steady-state GCR distributions within 10 iterations, about 1000 times faster than the explicit scheme. The GCR proton spectrum averaged over 27 days agrees with AMS-02 measurements to within 10%. The simulation also yields a realistic radial intensity gradient and captures the Forbush decrease features associated with three stream interaction regions observed at Earth.
Related
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BibTeX
@misc{liu2026implicit,
title = {{An Implicit Conservative Finite Volume Scheme with Poisson Brackets for the Steady-State Transport of Galactic Cosmic Rays}},
author = {Weihao Liu and Igor V. Sokolov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30091},
eprint = {2610.30091},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30091},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - An Implicit Conservative Finite Volume Scheme with Poisson Brackets for the Steady-State Transport of Galactic Cosmic Rays
AU - Weihao Liu
AU - Igor V. Sokolov
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.30091
UR - https://arxiv.org/abs/2610.30091
AB - Galactic cosmic rays (GCRs) pose a persistent radiation hazard to astronauts and spacecraft in the heliosphere. Modeling their transport is essential for understanding how the solar wind and heliospheric magnetic field shape their spatial distributions and energy spectra. Timely predictions require solving for the particle distribution function much faster than real time, but explicit numerical schemes are restricted by the stability limit on the time step. In this Letter, we present an implicit conservative finite-volume scheme for kinetic equations formulated with Poisson brackets. This scheme conserves particle number, maintains the total-variation-diminishing property, achieves second-order spatial accuracy, and remains stable for time steps far beyond the explicit limit, while reaching quasi-steady states in less than ~1/100 of the computational time required for the explicit scheme, as demonstrated by numerical tests. We apply this scheme to the Parker transport equation along magnetic field lines in the background solar wind during Carrington rotation 2211, where it reaches steady-state GCR distributions within 10 iterations, about 1000 times faster than the explicit scheme. The GCR proton spectrum averaged over 27 days agrees with AMS-02 measurements to within 10%. The simulation also yields a realistic radial intensity gradient and captures the Forbush decrease features associated with three stream interaction regions observed at Earth.
ER -