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A reduced speed-of-light formulation of the magnetohydrodynamic-particle-in-cell method

Ji, Suoqing and Hopkins, Philip F. (2022) A reduced speed-of-light formulation of the magnetohydrodynamic-particle-in-cell method. Monthly Notices of the Royal Astronomical Society, 516 (4). pp. 5143-5147. ISSN 0035-8711. doi:10.1093/mnras/stac2523.

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A reduced speed-of-light (RSOL) approximation is a useful technique for magnetohydrodynamic (MHD)-particle-in-cell (PIC) simulations. With an RSOL, some 'in-code' speed-of-light c~ is set to much lower values than the true c, allowing simulations to take larger time-steps (which are restricted by the Courant condition given the large CR speeds). However, due to the absence of a well-formulated RSOL implementation from the literature, with naive substitution of the true c with a RSOL, the CR properties in MHD-PIC simulations (e.g. CR energy or momentum density, gyro radius) vary artificially with respect to each other and with respect to the converged (⁠c~ → c⁠) solutions, with different choices of a RSOL. Here, we derive a new formulation of the MHD-PIC equations with an RSOL and show that (1) it guarantees all steady-state properties of the CR distribution function, and background plasma/MHD quantities are independent of the RSOL c~ even for c~ ≪ c⁠; (2) it ensures that the simulation can simultaneously represent the real physical values of CR number, mass, momentum, and energy density; (3) it retains the correct physical meaning of various terms like the electric field; and (4) it ensures the numerical time-step for CRs can always be safely increased by a factor ∼ c/c~⁠. This new RSOL formulation should enable greater self-consistency and reduced CPU cost in simulations of CR–MHD interactions.

Item Type:Article
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URLURL TypeDescription
Ji, Suoqing0000-0001-9658-0588
Hopkins, Philip F.0000-0003-3729-1684
Additional Information:The authors thank the referee and editor for their constructive suggestions that improve this work. SJ is supported by a Sherman Fairchild Fellowship from Caltech, the Natural Science Foundation of China (grants 12133008, 12192220, and 12192223) and the science research grants from the China Manned Space Project (No. CMS-CSST-2021-B02). Support for PFH was provided by NSF research grants 1911233 and 20009234, NSF CAREER grant 1455342, and NASA grants 80NSSC18K0562 and HST-AR-15800.001-A. Numerical calculations were run on the Caltech compute cluster ‘Wheeler’, allocations FTA-Hopkins supported by the NSF and TACC, and NASA HEC SMD-16-7592, and the High Performance Computing Resource in the Core Facility for Advanced Research Computing at Shanghai Astronomical Observatory.
Group:Astronomy Department, TAPIR
Funding AgencyGrant Number
Natural Science Foundation of China12133008
Natural Science Foundation of China12192220
Natural Science Foundation of China12192223
China Manned SpaceCMS-CSST-2021-B02
Issue or Number:4
Record Number:CaltechAUTHORS:20221010-454096500.10
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:117296
Deposited By: Research Services Depository
Deposited On:14 Oct 2022 21:15
Last Modified:14 Oct 2022 21:15

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