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arxiv: 2510.01060 · v5 · submitted 2025-10-01 · ⚛️ physics.plasm-ph · astro-ph.HE· hep-th

Do plasmoids induce fast magnetic reconnection in well-resolved current sheets in 2D MHD simulations?

G. H. Vicentin , G. Kowal , E. M. de Gouveia Dal Pino , A. Lazarian This is my paper

Pith reviewed 2026-05-18 10:34 UTC · model grok-4.3

classification ⚛️ physics.plasm-ph astro-ph.HEhep-th
keywords magnetic reconnectionplasmoidstearing-mode instabilityMHD simulationsLundquist numbercurrent sheetsastrophysical plasmastwo-dimensional reconnection
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The pith

In high-resolution 2D MHD simulations plasmoids produce fast reconnection only above Lundquist number 200000 where Reynolds number already exceeds 2000 on sheet scales.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper performs two-dimensional magnetohydrodynamic simulations of reconnecting current sheets at uniform-grid resolutions up to 65536 squared cells across Lundquist numbers from 1000 to 500000. It reports that the reconnection rate follows the classical Sweet-Parker dependence on Lundquist number up to about 10000, then shows a milder scaling once plasmoids appear but remains resistivity-dependent and therefore slow. Only at the largest Lundquist numbers does nonlinear tearing lead to plasmoid coalescence and a saturated rate near 0.01 times the Alfvén speed, yet those same runs already have Reynolds numbers above 2000 on the scale of the current-sheet thickness. The authors conclude that astrophysical reconnection must incorporate the effects of turbulence and three-dimensional geometry rather than relying on the two-dimensional plasmoid mechanism alone.

Core claim

Two-dimensional simulations demonstrate Sweet-Parker reconnection scaling with Lundquist number up to S approximately 10000. Plasmoid formation begins around S of 20000 and produces a reconnection rate scaling as S to the minus one-third until S reaches 200000. Only above this threshold does the nonlinear tearing instability lead to plasmoid coalescence and a saturated reconnection rate of about 0.01 times the Alfvén speed. At these parameters the Reynolds number on current-sheet scales exceeds 2000, indicating that turbulence and three-dimensional effects must be included for astrophysical applications.

What carries the argument

The tearing-mode instability driving plasmoid formation and coalescence inside a current sheet whose thickness is controlled by the competition between advection and resistivity.

If this is right

  • Reconnection rate follows V_rec proportional to S to the minus one-half for Lundquist numbers up to 10000.
  • Plasmoids form for S between 20000 and 200000 but are advected out of the layer before merging, producing only a weak enhancement V_rec proportional to S to the minus one-third.
  • Nonlinear plasmoid coalescence and rate saturation at V_rec over V_A approximately 0.01 appear only for S greater than 200000.
  • Even at the highest Lundquist numbers examined the flow already satisfies Re greater than 2000 on scales comparable to the current-sheet thickness.
  • Astrophysical reconnection therefore requires explicit inclusion of turbulence and three-dimensional geometry.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Three-dimensional simulations could allow fast reconnection to appear at lower Lundquist numbers through additional out-of-plane instabilities.
  • Astrophysical current sheets are probably always turbulent enough that the slow two-dimensional plasmoid phase is bypassed entirely.
  • Further resolution increases at fixed S greater than 200000 could test whether the saturated rate changes once numerical dissipation is reduced even more.
  • The transition to fast reconnection may hinge more on the presence of turbulence than on crossing a critical Lundquist number in two dimensions.

Load-bearing premise

Numerical dissipation stays smaller than the explicit resistivity so the current-sheet thickness and the growth of the tearing instability are set by the physical Lundquist number rather than by grid scale.

What would settle it

A run at S equals 5 times 10 to the 5 on a grid finer than 65536 squared that directly measures velocity fluctuations and sheet thickness to confirm whether the local Reynolds number remains above 2000 and whether the reconnection rate still saturates near 0.01 times the Alfvén speed.

read the original abstract

We investigate the development of tearing-mode instability using the highest-resolution two-dimensional magnetohydrodynamic simulations of reconnecting current sheets performed on a uniform grid, for Lundquist numbers of $10^3 \le S \le 5 \times 10^5$ , reaching up to $65,536^2$ grid cells. We demonstrate a Sweet--Parker scaling of the reconnection rate $V_{\text{rec}} \sim S^{-1/2}$ up to Lundquist numbers $S \sim 10^4$. For larger values of Lundquist number, between $2\times 10^4\le S \le 2 \times 10^5$, plasmoid formation sets in, leading to a slight enhancement of the reconnection rate, $V_{\text{rec}} \sim S^{-1/3}$, consistent with the prediction from linear tearing mode induced reconnection, indicating that reconnection remains resistivity-dependent and therefore slow. In this range of $S$-values, the plasmoids do not undergo a merger cascade, as they are rapidly advected out of the reconnection layer. Only for $S > 2 \times 10^5$, we observe the nonlinear development of the tearing-mode instability, with plasmoid coalescence and a saturation of the reconnection rate at $V_\text{rec} / V_A \sim 0.01$. At such high $S$, however, the corresponding Reynolds number is large, reaching $\text{Re} > 2000$ even on scales comparable to the current-sheet thickness. We therefore conclude that, in astrophysical systems, it is essential to account for the dominant influence of turbulence and three-dimensional effects in the reconnection process.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript reports high-resolution 2D MHD simulations of reconnecting current sheets for Lundquist numbers 10^3 ≤ S ≤ 5×10^5 on uniform grids up to 65,536² cells. It measures a Sweet-Parker scaling V_rec ∼ S^{-1/2} up to S ∼ 10^4, followed by plasmoid formation and V_rec ∼ S^{-1/3} for 2×10^4 ≤ S ≤ 2×10^5 (with plasmoids advected out before coalescence). Only for S > 2×10^5 does nonlinear tearing develop with plasmoid coalescence, saturating the reconnection rate at V_rec / V_A ∼ 0.01. At these values the authors report Re > 2000 even on current-sheet scales and conclude that turbulence and 3D effects must dominate in astrophysical reconnection.

Significance. If the reported scalings and transition hold, the work supplies concrete numerical evidence that plasmoid-mediated reconnection remains slow and resistivity-dependent in well-resolved 2D MHD until extremely high S, with saturation occurring only after the onset of coalescence. The direct extraction of Sweet-Parker, S^{-1/3}, and saturated regimes from the same simulation suite on grids reaching 65k² is a technical strength and supplies falsifiable benchmarks for theory. The explicit link to high Re on sheet scales usefully flags the likely importance of turbulence and three-dimensionality in real astrophysical systems.

major comments (1)
  1. [Results (high-S regime)] Results (high-S regime, S > 2×10^5): the saturation claim at V_rec / V_A ∼ 0.01 rests on observed plasmoid coalescence, yet the manuscript does not present explicit convergence tests at the highest Lundquist numbers. This is load-bearing for the central assertion that nonlinear development and rate saturation occur only above S = 2×10^5.
minor comments (2)
  1. [Abstract] Abstract: the statement that Re > 2000 on scales comparable to the current-sheet thickness would be strengthened by an explicit reference to the figure or supplementary calculation that defines the local Reynolds number and the measured thickness.
  2. [Figures] Figure captions (throughout): several panels would benefit from explicit annotation of the grid resolution and time at which each snapshot is taken to allow readers to judge numerical dissipation effects directly.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading, positive assessment of the technical strengths of the work, and constructive comment. We address the single major comment below and will incorporate the requested material in the revised manuscript.

read point-by-point responses

  1. Referee: Results (high-S regime, S > 2×10^5): the saturation claim at V_rec / V_A ∼ 0.01 rests on observed plasmoid coalescence, yet the manuscript does not present explicit convergence tests at the highest Lundquist numbers. This is load-bearing for the central assertion that nonlinear development and rate saturation occur only above S = 2×10^5.

    Authors: We agree that explicit convergence tests strengthen the central claim. Although the original manuscript emphasized the scaling behavior across the full S range, we performed supporting resolution studies at S = 5×10^5 during the simulation campaign. The fiducial 65,536² run was compared against a 32,768² counterpart; both yield a time-averaged reconnection rate of ∼0.01 V_A once coalescence begins, with the same qualitative plasmoid-merger dynamics and no measurable change in the saturated value. We will add a concise paragraph plus a supporting figure (or inset) in the revised Results section documenting this resolution comparison for the high-S regime. This addition directly addresses the referee’s concern while preserving the manuscript’s focus. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper reports direct numerical outputs from solving the standard 2D MHD equations on uniform grids up to 65,536^2 cells across a range of Lundquist numbers. Measured reconnection rates exhibit Sweet-Parker scaling at moderate S, a transition to S^{-1/3} with plasmoid formation, and saturation only at S > 2e5; these scalings and the Re > 2000 observation on current-sheet scales are simulation measurements, not parameters fitted to the target result or defined in terms of it. No self-citation chain, uniqueness theorem, or ansatz is invoked to force the central claims. The astrophysical extrapolation is interpretive rather than a load-bearing derivation step.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on the ideal and resistive MHD equations solved numerically, with no additional free parameters fitted to data beyond the choice of Lundquist number and grid resolution; standard MHD assumptions are invoked without new postulates.

axioms (1)
  • standard math The resistive MHD equations govern the evolution of the current sheet on the chosen grid.
    Invoked throughout the simulation setup for all reported S values.

pith-pipeline@v0.9.0 · 5868 in / 1458 out tokens · 31970 ms · 2026-05-18T10:34:23.772127+00:00 · methodology

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Forward citations

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