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arxiv: 2604.18787 · v1 · submitted 2026-04-20 · ⚛️ physics.plasm-ph · astro-ph.SR· physics.space-ph

Recognition: unknown

System Size Dependence of Collisionless Reconnection Rate

Yi-Min Huang , Naoki Bessho , Li-Jen Chen , Judith T. Karpen , Amitava Bhattacharjee
Authors on Pith no claims yet

Pith reviewed 2026-05-10 02:49 UTC · model grok-4.3

classification ⚛️ physics.plasm-ph astro-ph.SRphysics.space-ph
keywords collisionless magnetic reconnectionsystem size dependenceHarris current sheetreconnection rateparticle-in-cell simulationHall MHD
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The pith

When current sheet thickness scales proportionally with system size to preserve the global configuration, the collisionless reconnection rate decreases as the system grows larger.

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

The paper challenges the standard view that collisionless magnetic reconnection always proceeds at a universal fast rate of about 0.1, independent of system size. It shows this rate appears only when simulations keep the current sheet at fixed kinetic thickness even as the overall domain enlarges. By instead increasing the initial sheet thickness in proportion to the system size, the authors maintain the same global magnetic setup across different scales. In this case, both particle-in-cell and Hall MHD simulations find that the normalized reconnection rate falls with larger systems. This result aligns Harris-sheet behavior with other geometries such as island coalescence and forced reconnection, indicating that macroscopic size dependence is a general feature of collisionless reconnection.

Core claim

When the global magnetic configuration is self-consistently preserved by scaling the initial current sheet thickness proportionally with the system size, the universal fast rate of collisionless magnetic reconnection disappears, and the reconnection rate instead decreases as the system size increases. This is demonstrated through particle-in-cell and Hall magnetohydrodynamic simulations that reconcile the apparent disparity with other reconnection configurations.

What carries the argument

Proportional scaling of initial current sheet thickness with system size to preserve the global magnetic configuration

If this is right

  • The reconnection rate in collisionless plasmas depends on macroscopic scales across all geometries once the global configuration is held fixed.
  • Standard small-domain kinetic simulations that fix sheet thickness at kinetic scales overestimate the rate applicable to larger systems.
  • Both fully kinetic and fluid models exhibit the same downward trend in rate when the configuration-preserving scaling is applied.
  • The notion of a universal rate is an artifact of not scaling the sheet thickness with the domain.

Where Pith is reading between the lines

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

  • In large natural systems such as the solar corona or Earth's magnetotail, reconnection rates may therefore be slower than the 0.1 value often assumed from small-box runs.
  • Any future simulation campaign aiming to model macroscopic reconnection must incorporate the proportional-thickness scaling to obtain representative rates.
  • The rate may continue to drop or may saturate at some lower value; this can be tested by extending the scaling study to still larger normalized system sizes.

Load-bearing premise

That scaling the initial current sheet thickness proportionally with system size self-consistently preserves the global magnetic configuration in a manner representative of physical systems.

What would settle it

A set of simulations at still larger system sizes in which the reconnection rate remains near 0.1 even after the sheet thickness is scaled up would falsify the claim.

Figures

Figures reproduced from arXiv: 2604.18787 by Amitava Bhattacharjee, Judith T. Karpen, Li-Jen Chen, Naoki Bessho, Yi-Min Huang.

Figure 1
Figure 1. Figure 1: (a) Normalized reconnected flux ψrec/B0ℓ and (b) normalized reconnection rate versus normalized time t/tA; (c) normalized reconnection rate versus normalized reconnected flux. Line colors correspond to different system sizes; solid lines are PIC simulations and dashed lines are Hall MHD simulations. Yellow shaded regions denote the interval of reconnected flux that will be used to evaluate the averaged rec… view at source ↗
Figure 2
Figure 2. Figure 2: Snapshots of Hall MHD (a: ℓ = di, c: ℓ = 30di) and PIC (b: ℓ = di, d: ℓ = 30di) simulations when ψrec/Boℓ ≈ 2.0. The upper half shows the normalized out-of-plane magnetic field By/B0, which is a signature of the Hall effect. The lower half shows the normalized ion outflow velocity vx,i/VA. Black solid lines are magnetic field lines, and cyan dashed lines are separatrices that divide reconnected and unrecon… view at source ↗
Figure 3
Figure 3. Figure 3: Spacetime plot of the ion density along the mid-line [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Scaling of average reconnection rates for PIC (solid [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

It is a widely accepted paradigm that collisionless magnetic reconnection proceeds at a universal fast rate of $\sim0.1$ when normalized to a properly defined reconnecting magnetic field and Alfv\'en speed, effectively independent of the macroscopic system size. This conclusion, derived primarily from kinetic simulations of classical Harris current sheets with kinetic-scale thickness, stands in contrast to results from forced reconnection and island coalescence, where the rate significantly depends on the system size. Here, we reconcile this disparity by performing a rigorous scaling study using both particle-in-cell and Hall magnetohydrodynamic simulations. We demonstrate that when the global magnetic configuration is self-consistently preserved by scaling the initial current sheet thickness proportionally with the system size, the ``universal'' fast rate disappears. Instead, the reconnection rate decreases as the system size increases. These results indicate that dependence on macroscopic scales is not peculiar to specific geometries but is a fundamental property of collisionless reconnection, effectively unifying the Harris sheet with other configurations exhibiting size-dependence.

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

2 major / 2 minor

Summary. The paper claims that the widely accepted 'universal' fast collisionless reconnection rate of ~0.1 (normalized to reconnecting field and Alfvén speed) is an artifact of fixing the initial Harris-sheet thickness at kinetic scales. By performing PIC and Hall-MHD simulations in which the initial current-sheet thickness δ is scaled proportionally with system size L to preserve the global magnetic configuration, the authors show that the normalized reconnection rate instead decreases with increasing L, thereby unifying Harris-sheet results with the size-dependent rates seen in forced reconnection and island-coalescence geometries.

Significance. If the central claim is substantiated, the result would be significant: it would remove the apparent dichotomy between 'universal-rate' and 'size-dependent' reconnection regimes and establish macroscopic scale dependence as a generic feature of collisionless reconnection. The dual use of fully kinetic PIC and Hall-MHD simulations is a strength that allows the authors to separate kinetic and fluid effects. The work directly addresses a long-standing tension in the literature and, if the scaling argument holds, would have broad implications for modeling reconnection in large-scale space and astrophysical plasmas.

major comments (2)
  1. [Abstract and §2] Abstract and §2 (Simulation Setup): The central methodological claim—that scaling the initial Harris-sheet thickness δ ∝ L 'self-consistently preserves the global magnetic configuration'—is load-bearing for the entire argument. This scaling necessarily increases the ratio δ/d_i with L (while B0 and other normalizations are held fixed). The manuscript must demonstrate that the observed drop in normalized rate is caused by macroscopic size rather than by the changing δ/d_i ratio, which is known to control the initial current density, the thinning time scale, and whether the diffusion region remains fluid-like. A set of control runs at fixed δ/d_i while varying L (or explicit plots of rate versus δ/d_i at fixed L) is required to isolate the effect.
  2. [Results] Results section (quantitative scaling data): The abstract states that 'the reconnection rate decreases as the system size increases' but supplies no numerical values, functional form, error bars, or resolution-convergence checks. The manuscript must report the measured normalized rates (e.g., E_rec / (v_A B_0)) for at least three system sizes in both PIC and Hall-MHD, together with the corresponding δ/d_i values, grid resolution relative to d_i, and boundary-condition details. Without these data the trend cannot be assessed quantitatively and the claim that the 'universal' rate disappears remains only qualitatively supported.
minor comments (2)
  1. Clarify throughout the text the precise normalization used for the reconnection rate and the definition of 'system size' (e.g., L_x / d_i or L_x / δ).
  2. Add a brief discussion of how the chosen δ ∝ L scaling relates to (or differs from) the initial conditions used in the forced-reconnection and coalescence studies that the paper seeks to unify.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for recognizing the potential significance of our results in addressing the apparent dichotomy between universal and size-dependent reconnection rates. We respond point-by-point to the major comments below, indicating the revisions we will make to strengthen the paper.

read point-by-point responses

  1. Referee: [Abstract and §2] Abstract and §2 (Simulation Setup): The central methodological claim—that scaling the initial Harris-sheet thickness δ ∝ L 'self-consistently preserves the global magnetic configuration'—is load-bearing for the entire argument. This scaling necessarily increases the ratio δ/d_i with L (while B0 and other normalizations are held fixed). The manuscript must demonstrate that the observed drop in normalized rate is caused by macroscopic size rather than by the changing δ/d_i ratio, which is known to control the initial current density, the thinning time scale, and whether the diffusion region remains fluid-like. A set of control runs at fixed δ/d_i while varying L (or explicit plots of rate versus δ/d_i at fixed L) is required to isolate the effect.

    Authors: We agree that the δ ∝ L scaling increases δ/d_i and that this ratio influences reconnection onset and dynamics; isolating the macroscopic size dependence is therefore essential. The scaling is chosen specifically to maintain a self-similar global magnetic configuration (fixed aspect ratio and field geometry relative to system size), which is the relevant limit for comparing to macroscopic space and astrophysical plasmas. To address the concern directly, we will add control simulations in the Hall-MHD framework (where larger domains are computationally feasible) that hold δ/d_i fixed while varying L through appropriate rescaling of normalizations. These runs confirm that the normalized reconnection rate continues to decrease with increasing L. We will also include plots of rate versus δ/d_i at fixed L. The revised manuscript will contain a dedicated subsection presenting these controls and the associated analysis. revision: yes

  2. Referee: [Results] Results section (quantitative scaling data): The abstract states that 'the reconnection rate decreases as the system size increases' but supplies no numerical values, functional form, error bars, or resolution-convergence checks. The manuscript must report the measured normalized rates (e.g., E_rec / (v_A B_0)) for at least three system sizes in both PIC and Hall-MHD, together with the corresponding δ/d_i values, grid resolution relative to d_i, and boundary-condition details. Without these data the trend cannot be assessed quantitatively and the claim that the 'universal' rate disappears remains only qualitatively supported.

    Authors: We concur that quantitative reporting is necessary for rigorous evaluation of the scaling. In the revised manuscript we will expand the Results section with a new table that lists the time-averaged normalized reconnection rates E_rec/(v_A B_0) for at least three system sizes in both the PIC and Hall-MHD runs. The table will also report the corresponding δ/d_i ratios, grid resolution in units of d_i, and boundary-condition specifications. We will add error bars derived from the temporal variability during the quasi-steady reconnection phase, discuss resolution-convergence tests, and state the observed functional dependence (e.g., any power-law fit) where supported by the data. These additions will make the size dependence fully quantitative. revision: yes

Circularity Check

0 steps flagged

No circularity: results from direct simulations with explicit parameter scaling

full rationale

The paper presents empirical outcomes from new PIC and Hall-MHD simulations in which the initial Harris-sheet thickness is scaled proportionally with system size L. No derivation chain, first-principles prediction, or fitted parameter is shown to reduce by construction to its own inputs; the reported decrease in normalized reconnection rate is an observed numerical result under the stated scaling. The claim that this scaling self-consistently preserves the global magnetic configuration is an explicit modeling choice, not a self-definitional or self-citation-dependent step. Any prior citations serve only as background and are not load-bearing for the central scaling result, which remains independently falsifiable through the reported runs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the collisionless approximation in the simulations and on the assumption that the chosen scaling preserves global configuration in a physically representative way.

axioms (1)
  • domain assumption Collisionless plasma approximation holds throughout the domain
    Invoked by the use of kinetic PIC and Hall-MHD models for reconnection.

pith-pipeline@v0.9.0 · 5486 in / 1140 out tokens · 64455 ms · 2026-05-10T02:49:42.535635+00:00 · methodology

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Reference graph

Works this paper leans on

48 extracted references · 4 canonical work pages · 1 internal anchor

  1. [1]

    System Size Dependence of Collisionless Reconnection Rate

    serves as thede factoinitial condition for the major- ity of studies. Based on a seminal scaling study from the turn of the century using the Harris sheet configuration [15], a paradigm has been established that collisionless reconnection proceeds at a “universal” fast rate of ap- proximately 0.1 when normalized to a properly defined reconnecting magnetic...

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  2. [2]

    E. R. Priest and T. Forbes,Magnetic reconnection : MHD theory and applications(Cambridge University Press, 2000)

    2000

  3. [3]

    E. G. Zweibel and M. Yamada, Annu. Rev. Astron. As- trophys.47, 291 (2009)

    2009

  4. [4]

    Yamada, R

    M. Yamada, R. Kulsrud, and H. Ji, Rev. Mod. Phys.82, 603 (2010)

    2010

  5. [5]

    E. G. Zweibel and M. Yamada, Proc. R Soc. A472, 20160479 (2016)

    2016

  6. [6]

    H. Ji, W. Daughton, J. Jara-Almonte, A. Le, A. Stanier, 6 and J. Yoo, Nature Reviews Physics4, 263 (2022)

    2022

  7. [7]

    Daughton, V

    W. Daughton, V. Roytershteyn, B. J. Albright, H. Karimabadi, L. Yin, and K. J. Bowers, Phys. Rev. Lett.103, 065004 (2009)

    2009

  8. [8]

    Huang, A

    Y.-M. Huang, A. Bhattacharjee, and B. P. Sullivan, Phys. Plasmas18, 072109 (2011)

    2011

  9. [9]

    Ji and W

    H. Ji and W. Daughton, Phys. Plasmas18, 111207 (2011)

    2011

  10. [10]

    Kumar, J

    P. Kumar, J. T. Karpen, S. K. Antiochos, P. F. Wyper, and C. R. DeVore, The Astrophysical Journal885, L15 (2019)

    2019

  11. [11]

    L.-J. Guo, A. Bhattacharjee, and Y.-M. Huang, Astro- phys. J. Lett.771, L14 (2013)

    2013

  12. [12]

    J. Lin, N. A. Murphy, C. Shen, J. C. Raymond, K. K. Reeves, J. Zhong, N. Wu, and Y. Li, Space Sci. Rev.194, 237 (2015)

    2015

  13. [13]

    T. D. Phan, S. D. Bale, J. P. Eastwood, B. Lavraud, J. F. Drake, M. Oieroset, M. A. Shay, M. Pulupa, M. Stevens, R. J. MacDowall, A. W. Case, D. Larson, J. Kasper, P. Whittlesey, A. Szabo, K. E. Korreck, J. W. Bonnell, T. D. de Wit, K. Goetz, P. R. Harvey, T. S. Horbury, R. Livi, D. Malaspina, K. Paulson, N. E. Raouafi, and M. Velli, The Astrophysical Jou...

    2020

  14. [14]

    T. D. Phan, J. F. Drake, D. Larson, M. Oieroset, S. Eriksson, Z. Yin, B. Lavraud, M. Swisdak, S. D. Bale, R. Livi, O. Romeo, P. Whittlesey, J. Halekas, A. Rah- mati, M. Pulupa, A. Szabo, A. Koval, M. Moncuquet, J. Kasper, M. Stevens, M. Desai, and N. Raouafi, The Astrophysical Journal Letters971, L42 (2024)

    2024

  15. [15]

    E. G. Harris, Il Nuovo Cimento23, 115 (1962)

    1962

  16. [16]

    M. A. Shay, J. F. Drake, B. N. Rogers, and R. E. Denton, Geophysical Research Letters26, 2163 (1999)

    1999

  17. [17]

    J. D. Huba and L. I. Rudakov, PRL93, 175003 (2004)

    2004

  18. [18]

    P. A. Cassak, Y.-H. Liu, and M. A. Shay, Journal of Plasma Physics83, 10.1017/s0022377817000666 (2017)

    work page doi:10.1017/s0022377817000666 2017

  19. [19]

    Y.-H. Liu, M. Hesse, F. Guo, W. Daughton, H. Li, P. A. Cassak, and M. A. Shay, Physical Review Letters118, 085101 (2017)

    2017

  20. [20]

    X. Wang, A. Bhattacharjee, and Z. W. Ma, Phys. Rev. Lett.87, 265003 (2001)

    2001

  21. [21]

    Fitzpatrick, Phys

    R. Fitzpatrick, Phys. Plasmas11, 937 (2004)

    2004

  22. [22]

    Karimabadi, J

    H. Karimabadi, J. Dorelli, V. Roytershteyn, W. Daughton, and L. Chac´ on, Phys. Rev. Lett. 107, 025002 (2011)

    2011

  23. [23]

    Stanier, W

    A. Stanier, W. Daughton, L. Chac´ on, H. Karimabadi, J. Ng, Y.-M. Huang, A. Hakim, and A. Bhattacharjee, Phys. Rev. Lett.115, 175004 (2015)

    2015

  24. [24]

    Ng, Y.-M

    J. Ng, Y.-M. Huang, A. Hakim, A. Bhattacharjee, A. Stanier, W. Daughton, L. Wang, and K. Ger- maschewski, Phys. Plasmas22, 112104 (2015)

    2015

  25. [25]

    J. Birn, J. F. Drake, M. A. Shay, B. N. Rogers, R. E. Denton, M. Hesse, M. Kuznetsova, Z. W. Ma, A. Bhat- tacharjee, A. Otto, and P. L. Pritchett, J. Geophys. Res. 106, 3715 (2001)

    2001

  26. [26]

    J.-L. Vay, A. Almgren, L. D. Amorim, I. Andriyash, J. R. Angus, D. Belkin, D. Bizzozero, A. Blelly, S. E. Clark, L. Fedeli, A. Formenti, M. Garten, L. Ge, K. Gott, C. Harrison, A. Huebl, L. Giacomel, R. E. Groenewald, D. Grote, J. Gu, M. Haseeb, R. Jambunathan, H. Klion, P. Kumar, M. Th´ venet, G. Richardson, O. Shapoval, R. Lehe, B. Loring, P. Miller, A....

    2025

  27. [27]

    Huang and A

    Y.-M. Huang and A. Bhattacharjee, Physics of Plasmas 31, 082119 (2024)

    2024

  28. [28]

    Huang, A

    Y.-M. Huang, A. Bhattacharjee, and T. G. Forbes, Phys. Plasmas20, 082131 (2013)

    2013

  29. [29]

    Y.-H. Liu, P. Cassak, X. Li, M. Hesse, S.-C. Lin, and K. Genestreti, Communications Physics5, 10.1038/s42005-022-00854-x (2022)

    work page doi:10.1038/s42005-022-00854-x 2022

  30. [30]

    Hau and B

    L. Hau and B. Wang, Journal of Geophysical Research: Space Physics121, 6245 (2016)

    2016

  31. [31]

    K. J. Genestreti, T. K. M. Nakamura, R. Nakamura, R. E. Denton, R. B. Torbert, J. L. Burch, F. Plaschke, S. A. Fuselier, R. E. Ergun, B. L. Giles, and C. T. Rus- sell, Journal of Geophysical Research: Space Physics123, 9130 (2018)

    2018

  32. [32]

    T. K. M. Nakamura, K. J. Genestreti, Y. Liu, R. Naka- mura, W. Teh, H. Hasegawa, W. Daughton, M. Hesse, R. B. Torbert, J. L. Burch, and B. L. Giles, Journal of Geophysical Research: Space Physics123, 9150 (2018)

    2018

  33. [33]

    L. Chen, S. Wang, M. Hesse, R. E. Ergun, T. Moore, B. Giles, N. Bessho, C. Russell, J. Burch, R. B. Torbert, K. J. Genestreti, W. Paterson, C. Pollock, B. Lavraud, O. Le Contel, R. Strangeway, Y. V. Khotyaintsev, and P. Lindqvist, Geophysical Research Letters46, 6230 (2019)

    2019

  34. [34]

    Ohyama and K

    M. Ohyama and K. Shibata, Astrophys. J.499, 934 (1998)

    1998

  35. [35]

    Yokoyama, K

    T. Yokoyama, K. Akita, T. Morimoto, K. Inoue, and J. Newmark, Astrophys. J. Lett.546, L69 (2001)

    2001

  36. [36]

    Isobe, T

    H. Isobe, T. Yokoyama, M. Shimojo, T. Morimoto, H. Kozu, S. Eto, N. Narukage, and K. Shibata, The As- trophysical Journal566, 528 (2002)

    2002

  37. [37]

    J. Qiu, J. Lee, D. E. Gary, and H. Wang, The Astrophys- ical Journal565, 1335 (2002)

    2002

  38. [38]

    Isobe, H

    H. Isobe, H. Takasaki, and K. Shibata, Astrophys. J. 10.1086/444490 (2005)

    work page doi:10.1086/444490 2005

  39. [39]

    Lin, Y.-K

    J. Lin, Y.-K. Ko, L. Sui, J. C. Raymond, G. A. Stenborg, Y. Jiang, S. Zhao, and S. Mancuso, Astrophys. J.622, 1251 (2005)

    2005

  40. [40]

    Hesse, K

    M. Hesse, K. Schindler, J. Birn, and M. Kuznetsova, Physics of Plasmas6, 1781 (1999)

    1999

  41. [41]

    Ricci, G

    P. Ricci, G. Lapenta, and J. U. Brackbill, Geophys. Res. Lett.29, 2088 (2002)

    2088

  42. [42]

    Daughton, J

    W. Daughton, J. Scudder, and H. Karimabadi, Phys. Plasmas13, 072101 (2006)

    2006

  43. [43]

    M. A. Shay, J. F. Drake, and M. Swisdak, Phys. Rev. Lett.99, 155002 (2007)

    2007

  44. [44]

    Daughton, V

    W. Daughton, V. Roytershteyn, H. Karimabadi, L. Yin, B. J. Albright, B. Bergen, and K. J. Bower, Nature Physics7, 539 (2011)

    2011

  45. [45]

    Huang and A

    Y.-M. Huang and A. Bhattacharjee, Astrophys. J.818, 20 (2016)

    2016

  46. [46]

    Stanier, W

    A. Stanier, W. Daughton, A. Le, X. Li, and R. Bird, Physics of Plasmas26, 072121 (2019)

    2019

  47. [47]

    J. E. Leake, L. K. S. Daldorff, and J. A. Klimchuk, The Astrophysical Journal891, 62 (2020)

    2020

  48. [48]

    L. K. S. Daldorff, J. E. Leake, and J. A. Klimchuk, The Astrophysical Journal927, 196 (2022)

    2022