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Accurately Incorporating a Reduced-Speed-of-Light in Magnetohydrodynamic-Particle-in-Cell Simulations

Ji, Suoqing and Hopkins, Philip F. (2021) Accurately Incorporating a Reduced-Speed-of-Light in Magnetohydrodynamic-Particle-in-Cell Simulations. . (Unpublished)

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A reduced-speed-of-light (RSOL) approximation is usually adopted in magnetohydrodynamic (MHD)-particle-in-cell (PIC) simulations, in which relativistic cosmic ray (CR) particles moving at nearly the speed of light c and background (non-relativistic) plasma are evolved concurrently. With a RSOL, some "in-code" speed-of-light c̃ is set to much lower values than the true c, allowing simulations to take larger timesteps (which are restricted by the Courant condition given the large CR speeds). However, due to the absence of a well-formulated RSOL implementation in the literature for MHD-PIC simulations, the CR properties in simulations (e.g.\ CR energy or momentum density, gyro radius) vary artificially with respect to each other and with respect to the converged (c̃ →c) solutions with different implementations of a RSOL, breaking the correspondence between simulation results and physical reality. Here, we derive a new formulation of the MHD-PIC equations with a 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 c̃ even for c̃ ≪c, (2) ensures that the simulation can simultaneously represent the real physical values of CR number, mass, momentum, and energy density, (3) retains the correct physical meaning of various terms like the electric field, and (4) ensures the numerical timestep for CRs can always be safely increased by a factor ∼c/c̃ . This should enable greater self-consistency and reduced CPU cost in simulations of CR-MHD interactions.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Ji, Suoqing0000-0001-9658-0588
Hopkins, Philip F.0000-0003-3729-1684
Additional Information:SJ is supported by a Sherman Fairchild Fellowship from Caltech. Support for PFH was provided by NSF Research Grants 1911233 & 20009234, NSF CAREER grant 1455342, NASA grants 80NSSC18K0562, 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. DATA AVAILABILITY STATEMENT. There are no new data associated with this article.
Group:TAPIR, Astronomy Department
Funding AgencyGrant Number
Sherman Fairchild FoundationUNSPECIFIED
Subject Keywords:cosmic rays — plasmas — methods: numerical — MHD — galaxies: evolution — ISM: structure
Record Number:CaltechAUTHORS:20220228-183302037
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:113648
Deposited By: George Porter
Deposited On:28 Feb 2022 23:28
Last Modified:28 Feb 2022 23:28

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