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Abstract A variety of high-energy astrophysical phenomena are powered by the release—via magnetic reconnection—of the energy stored in oppositely directed fields. Single-fluid resistive magnetohydrodynamic (MHD) simulations with uniform resistivity yield dissipation rates that are much lower (by nearly 1 order of magnitude) than equivalent kinetic calculations. Reconnection-driven phenomena could be accordingly modeled in resistive MHD employing a nonuniform, “effective” resistivity informed by kinetic calculations. In this work, we analyze a suite of fully kinetic particle-in-cell (PIC) simulations of relativistic pair-plasma reconnection—where the magnetic energy is greater than the rest mass energy—for different strengths of the guide field orthogonal to the alternating component. We extract an empirical prescription for the effective resistivity, , whereB0is the reconnecting magnetic field strength,Jis the current density,ntis the lab-frame total number density,eis the elementary charge, andcis the speed of light. The guide field dependence is encoded inαandp, which we fit to PIC data. This resistivity formulation—which relies only on single-fluid MHD quantities—successfully reproduces the spatial structure and strength of nonideal electric fields and thus provides a promising strategy for enhancing the reconnection rate in resistive MHD simulations.
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A reduced speed-of-light formulation of the magnetohydrodynamic-particle-in-cell method
ABSTRACT 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 $$\tilde{c}$$ 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 ($$\tilde{c} \rightarrow c$$) 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 $$\tilde{c}$$ even for $$\tilde{c} \ll c$$; (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 $$\sim c/\tilde{c}$$. This new RSOL formulation should enable greater self-consistency and reduced CPU cost in simulations of CR–MHD interactions.
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- PAR ID:
- 10443253
- Date Published:
- Journal Name:
- Monthly Notices of the Royal Astronomical Society
- Volume:
- 516
- Issue:
- 4
- ISSN:
- 0035-8711
- Page Range / eLocation ID:
- 5143 to 5147
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript
- Journal Article:
- https://doi.org/10.1093/mnras/stac2523
