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Reconnection-Driven Turbulent Fluctuations in the Magnetically Dominated Collisionless Regime

T0 review · 3 major / 5 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read In kinetic simulations of collisionless magnetic reconnection, velocity fluctuations follow a Kolmogorov-like 1/3 structure-function slope while magnetic fluctuations are systematically steeper, near 2/3, and steepen further when a guide fi

desk verdict First systematic 3D PIC characterization of reconnection-driven turbulence—likely real, but the structure functions are computed on raw fields and the x/y slopes may be partially contaminated by mean gradients. read the letter →

arxiv 2512.12516 v2 pith:IO5FAUN5 submitted 2025-12-14 astro-ph.GA physics.plasm-ph

Yue Hu , Luca Comisso , Lorenzo Sironi , Siyao Xu This is my paper
classification astro-ph.GAphysics.plasm-ph
keywords magneticreconnectioncollisionlessplasmaturbulencestructurefunctionsintermittencyguidefieldpairparticle-in-cellsimulations
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper aims to establish that magnetic reconnection in a collisionless, magnetically dominated plasma does not merely convert magnetic energy but also self-generates a broadband turbulent cascade with measurable statistical signatures. Using large three-dimensional particle-in-cell simulations of a pair plasma, it reports that the square root of the second-order velocity structure function scales with a slope close to 1/3 along the inflow, outflow, and guide-field directions, matching Kolmogorov expectations. The magnetic structure function is steeper, with slopes around 0.6 to 0.8, and grows steeper as a guide field is added. The paper also reports that magnetic fluctuations are strongly intermittent along the outflow direction and that both velocity and magnetic fluctuations become more anisotropic as the guide field increases. A sympathetic reader would care because these scalings are the input needed to model plasma heating and particle acceleration in reconnection events.

What carries the argument

The analysis rests on large-scale 3D particle-in-cell simulations that resolve scales from the system size down to the electron skin depth, a characteristic kinetic plasma scale, with a magnetization of 10 and guide fields from zero up to the full reversing field. Within the reconnection region, defined by a 1% mixing-threshold mask between the two inflow populations, the paper computes second- and higher-order structure functions of velocity and magnetic field along the inflow, outflow, and guide-field directions, fitting power-law slopes over separations of 2 to 30 electron skin depths. It also decomposes structure functions parallel and perpendicular to the local magnetic field to quantif

What would settle it

Compute the same structure functions in a simulation with a domain at least twice as large in the outflow direction and repeat at several steady-state times; if the fitted slopes over 2 to 30 electron skin depths change systematically with box length or time, the inertial-range identification fails. A simpler check is to recompute the structure functions without the reconnection-region mask: if the slopes flatten or disappear, the fluctuations are a boundary effect of the mask rather than a self-similar cascade.

Watch

Extended reading notes

Core claim

The central discovery is a systematic statistical characterization of reconnection-driven turbulence in the collisionless regime: inside the reconnection layer, the square root of the second-order velocity structure function follows a power law with slope approximately 1/3 at intermediate to large scales, robust to guide-field strength, while the magnetic equivalent is steeper, with mean slopes typically near 2/3 but varying between about 0.6 and 0.8. A finite guide field leaves the velocity slope nearly unchanged but progressively steepens the magnetic slope in the guide-field and inflow directions. Higher-order structure functions show that magnetic intermittency is strongest along the out

Load-bearing premise

The paper assumes that the 2-to-30 electron-skin-depth range inside the mixing-defined reconnection region is a stationary, self-similar scaling range; if those separations are instead dominated by the finite geometry of the current sheet, coherent flux ropes, or net inflow and outflow, the reported power-law exponents are not turbulence scalings.

Editorial extensions

If this is right

  • If these scalings hold, collisionless reconnection layers are intrinsically multiscale: the velocity cascade is Kolmogorov-like, so kinetic-scale energy transfer resembles hydrodynamic turbulence.
  • Magnetic fluctuations are steeper than Kolmogorov, meaning magnetic energy is concentrated at smaller scales, which affects how the magnetic field dissipates and how particles interact with magnetic structures.
  • The guide field acts as a control parameter: it does not alter velocity scaling but steepens magnetic scaling and enhances anisotropy, so environments with stronger guide fields should show different fluctuation statistics.
  • The strong magnetic intermittency along the outflow direction implies that rare, intense magnetic structures dominate high-order moments, relevant for localized dissipation and particle energization.
  • These statistical signatures can serve as diagnostics connecting reconnection to turbulence in astrophysical plasmas, including where reconnection outflows and guide fields are present.
  • These statistical signatures can serve as diagnostics connecting reconnection to turbulence in astrophysical plasmas, including where reconnection outflows and guide fields are present.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A natural extension is to apply the same structure-function analysis to ion-electron reconnection, since the pair-plasma setup leaves open whether the 1/3 velocity slope and the steep magnetic slope persist with proton-scale physics.
  • The steep magnetic scaling reported here resembles intermittency-corrected MHD turbulence, suggesting a possible bridge between collisionless reconnection and broader magnetized-turbulence phenomenology that the paper does not itself draw.
  • The mixing-threshold definition of the reconnection region is one choice among several; testing whether the reported exponents are stable when the mask is widened or narrowed would sharpen the claim that the fitted range is a true inertial range.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper uses large-scale 3D particle-in-cell simulations of collisionless reconnection in magnetically dominated pair plasmas (σ=10) with guide-field strengths from 0 to B0. It computes second- and higher-order structure functions of the velocity and magnetic field inside a reconnection region defined by a 1% mixing-factor threshold, and reports that the square root of the second-order velocity structure function follows a slope near 1/3, while the magnetic counterpart is steeper, 0.6–0.8, with guide-field-dependent steepening in the inflow/guide-field directions. It further analyzes intermittency via higher-order structure functions and scale-dependent anisotropy through local-field decomposition. The central claim is that collisionless reconnection self-generates a broadband turbulent cascade with distinct velocity and magnetic statistics.

Significance. If the reported scaling laws are robust, the paper provides the first systematic 3D kinetic characterization of reconnection-driven turbulence and will be a useful reference for models of particle acceleration and energy partition in high-energy astrophysical plasmas. The study benefits from large simulation domains (L=800 d_e), a guide-field scan, and a second-time robustness check in the Appendix. The measured quantities are outputs of the simulations, not derived from a fitted model, so the empirical separation between velocity and magnetic slopes is a genuine observational result rather than a consequence of parameter choices. However, the interpretation depends critically on the assumption that the structure functions inside the highly inhomogeneous reconnection layer represent inertial-range turbulence.

major comments (3)
  1. [Sec. 3.2, Eq. (1)] The structure functions are computed directly on the raw fields v and B without subtracting a large-scale mean flow or mean magnetic-field gradient. The reconnection region is a thin layer with B_x reversing across y, reconnection outflow accelerating along x, and inflow advecting along y. A mean gradient contributes to the structure function a term of order (∇<f>)^2 r^2, whose square root scales as r (slope 1 in log-log), which can mimic or bias the reported slopes. The paper itself notes 'an effect of the net outflow' (Sec. 3.2.2) and 'some memory of the net inflow motion' (Sec. 3.2.3), indicating that mean gradients are present near the fitted range. To support the claim that the exponents describe turbulent fluctuations, the authors should recompute the structure functions after subtracting a spatially varying mean (e.g., a local average over scales >30 d_e), or otherwise quantify th
  2. [Sec. 3.2 (Figs. 2–5), Appendix] The power-law slopes are fitted over only 2–30 d_e, which is roughly 1.2 decades and includes the smallest resolved scale (2 d_e) after downsampling. The abstract's phrase 'intermediate to large scales' overstates the range: the plots show that the structure functions flatten or steepen for separations above ~30 d_e (e.g., the velocity SF in the x-direction 'flattens in all cases' for ≳30 d_e, Sec. 3.2.2; the magnetic SF in the z-direction 'gradually flattens' at large scales, Sec. 3.2.1). The second-time check in the Appendix does not extend the inertial-range fit. The authors should either restrict the claims to the 2–30 d_e range, or demonstrate robustness by fitting over alternate ranges (e.g., 4–30, 5–50, 10–100 d_e) and reporting the resulting spread. They should also state the goodness of fit or the scatter about the power law; the wide slope distributions in Figs. 2–4 suggest sen
  3. [Sec. 3.3, Eq. (2), Fig. 6] The higher-order structure functions (n=1 to 10) are fitted over the same 2–30 d_e range, which is very short for reliably determining high-order exponents. With a single analysis time (plus the Appendix check) and a limited number of independent point-pairs inside the reconnection region, high-order moments are likely dominated by a few intense coherent structures (flux ropes) rather than representing statistical convergence of inertial-range intermittency. The claim of 'strong magnetic intermittency along the outflow direction' is plausible but needs support: the authors should provide convergence tests (e.g., varying the sample by splitting the domain, or bootstrap estimates) or at least quantify the uncertainty in the high-order exponents. Without such tests, the intermittency conclusions are not yet robust.
minor comments (5)
  1. [Figure 4] The caption and text state that the left panels show the case without a guide field (B_g=0), but the left panel in the displayed figure is labeled '(a) B_g = 0.1B0'. Either the label or the caption is incorrect; this should be fixed. If the intent was to use B_g=0.1 as a substitute for the zero-guide-field case, that needs to be stated explicitly because the text and Figure 5 treat B_g=0 separately.
  2. [Abstract] The phrase 'intermediate to large scales' conflicts with the actual fitting range (2–30 d_e) and with the observed flattening at larger separations. Please revise to 'intermediate scales' or explicitly qualify the range.
  3. [Sec. 3.2.4] There is a typo in 'the mean slope of p SFv∆x, y, z)' — a missing parenthesis and a malformed expression. Please rephrase and ensure all structure-function notation is consistent throughout.
  4. [Sec. 2] The sentence 'Future work should assess the degree of self-similarity in these results...' acknowledges that the scale separation is limited; this limitation should also be noted in the Conclusion, where the paper currently implies broad applicability.
  5. [Fig. 1] The caption defines ρ=n0m, but the figure shows velocity and magnetic field fluctuations; the density definition is not needed and may confuse. Consider clarifying the normalization of the plotted fluctuations.

Circularity Check

0 steps flagged · score 1.0 of 10

Empirical structure-function slopes are measured simulation outputs; no circular derivation chain found.

full rationale

The paper's central claims are direct measurements from first-principles 3D PIC simulations: the second-order velocity and magnetic structure functions are computed with Eq. (1) inside the reconnection region, and their power-law slopes are fit over 2–30 d_e. These slopes are the reported outputs, not quantities obtained by fitting a parameter to some data and then presented as a prediction of closely related data. The Kolmogorov 1/3 and 2/3 reference lines are external interpretive benchmarks, not inputs that force the measured exponents. The paper itself flags the main physical caveats — 'some memory of the net inflow motion' and 'an effect of the net outflow' — which shows that the potential contamination by mean gradients is acknowledged rather than hidden; that concern affects interpretation, not circularity. The self-citations (e.g., Zhang et al. 2021 for large domains, Sironi et al. 2025b for the relativistic regime, Daughton et al. 2014 for the mixing-factor criterion) are contextual and not load-bearing for the central scaling result. No uniqueness theorem from the authors' prior work is invoked to forbid alternatives, and no ansatz is smuggled in via self-citation. The Appendix's second analysis time (t = 6.75 L/c) provides an independent check that the slopes are stable, further showing the result is not constructed from its own premises. Hence the derivation chain is self-contained; the only minor circularity-adjacent feature is a small amount of self-citation for context, which does not rise to circularity.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new entities or fitted physical constants; its main outputs are measured scaling exponents. The free choices are the fit range, the reconnection-region criterion, and the analysis time, all of which control the reported slopes. The axioms are standard domain assumptions for PIC plasma simulations plus the unvalidated inertial-range hypothesis.

free parameters (3)
  • slope fit interval = 2–30 d_e
    All scaling exponents are least-squares fits over this hand-selected range; the text reports deviations (flattening/steepening) outside it, so the fitted slopes depend on this choice.
  • reconnection-region mixing threshold = 1% contribution from each inflow population
    Defines the volume in which all structure functions are computed; changing the threshold would change the statistical sample and likely the exponents.
  • analysis time = t = 5.625 L/c (checks at 6.75 L/c)
    The steady-state claim is verified at only two times for a subset of cases; the exponents could evolve with the system-size/light-crossing time.
assumptions (4)
  • domain assumption TRISTAN-MP PIC simulations accurately capture collisionless reconnection and kinetic-scale turbulence in a pair plasma at sigma=10.
    Used throughout Sec. 2; the central measurements are outputs of this code, so its fidelity is assumed.
  • ad hoc to paper The 2–30 d_e interval is an inertial range where structure functions follow power laws.
    Invoked in Sec. 3.2 when fitting slopes; the paper does not establish inertial-range separation (L/d_e=800 but output is resolved only above 2 d_e and scaling flattens beyond about 30 d_e).
  • domain assumption The mixing-factor criterion identifies the reconnection region for statistical analysis.
    Taken from prior literature (Daughton et al. 2014), but the 1% threshold is a convention and affects the sample volume.
  • domain assumption Periodic, outflow, and injector boundary conditions do not dominate fluctuations on 2–30 d_e scales.
    Assumed in Secs. 2 and 3; no convergence study with box size or boundary conditions is provided.

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Cite this review

Pith. "Pith review of Reconnection-Driven Turbulent Fluctuations in the Magnetically Dominated Collisionless Regime." pith.science (2026). https://pith.science/paper/IO5FAUN5

@misc{pith2026251212516,
  author       = {Pith},
  title        = {Pith review of: Reconnection-Driven Turbulent Fluctuations in the Magnetically Dominated Collisionless Regime},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IO5FAUN5}},
  note         = {Machine review of arXiv:2512.12516}
}
abstract

Magnetic reconnection is a fundamental plasma process that converts magnetic energy into bulk flow energy, thermal energy, and nonthermal particle acceleration. Despite its importance, the statistical properties of the turbulent fluctuations generated by collisionless reconnection, which are essential for understanding how this energy conversion proceeds, remain poorly understood. Here, we employ large-scale 3D particle-in-cell simulations to investigate the turbulence characteristics of velocity and magnetic field fluctuations generated by collisionless reconnection in a magnetically dominated pair plasma. We characterize their statistical properties by computing structure functions along different directions within the reconnection layer. We find that the square root of the second-order velocity structure function follows a power-law scaling with a slope $\sim1/3$ at intermediate to large scales. The square root of the second-order magnetic structure function consistently exhibits a steeper slope, in the range $\sim 0.6 - 0.8$. The presence of a finite guide field does not systematically modify the slope of the velocity fluctuations, while it progressively steepens the scaling of the magnetic fluctuations in the guide-field and inflow directions. We measure higher-order structure functions, which reveal strong magnetic intermittency along the outflow direction and weaker intermittency in the inflow and guide-field directions. Additionally, the local anisotropies of both velocity and magnetic field fluctuations are greater for stronger guide fields. These results provide a systematic characterization of the multiscale nature of turbulence in collisionless and magnetically dominated reconnection layers, with important implications for plasma heating and particle acceleration.

Figures

Figures reproduced from arXiv: 2512.12516 by the authors.

Figure 1
Figure 1. Velocity slices (top two rows) and magnetic field slices (bottom two rows), respectively, taken at the z location where the flux ropes are visually most prominent, and taken at the center of the y axis. The left panels do not include a guide field, whereas the middle and right panels include a guide field of strength Bg = 0.3B0 or Bg = B0 (oriented along the z-axis), respectively. ρ = n0m is the mass density and Bg … view at source ↗
Figure 2
Figure 2. Top and middle panels: Square root of the second-order structure function (SF) for the velocity (red) and magnetic field (blue). The SF is computed for separations along the z-axis at each position (x, ymid), where ymid denotes the midpoint in y for each x within the reconnection region. The resulting SF(x, ymid, ∆z) are then averaged over all x values, denoted as ⟨SF(∆z)⟩x,ymid . The shaded area represents the stan… view at source ↗
Figure 3
Figure 3. Top and middle panels: Square root of the second-order structure function (SF) for the velocity (red) and magnetic field (blue). The SF is computed for separations along the x-axis at each position (y, z). The resulting SF(∆x, y, z) are then averaged over all y and z values, denoted as ⟨SF(∆x)⟩y,z. The shaded area represents the standard deviation. The black dashed line indicates the expected slope for Kolmogorov-ty… view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Top and middle panels: Square root of the second-order structure function (SF) for the velocity (red) and magnetic field (blue). The SF is computed for separations along the y-axis at each position (x, z). The resulting SF(∆y, x, z) are then averaged over all x and z v…
Figure 5
Figure 5. Figure 5: Mean slopes of p SF(x, ymid, ∆z) (left), p SF(∆x, y, z) (middle), p SF(x, ∆y, z) (right) as a function of the guide field strength. The slope is fitted over separations in the range 2–30 de. The black dashed line indicates the expected slope for Kolmogorov-type fluctua…
Figure 6
Figure 6. Figure 6: Slopes of the n-th order structure functions: ⟨SFn (∆z)⟩x,ymid (left), ⟨SFn (∆y)⟩x,z (middle), ⟨SFn (∆x)⟩y,z (right). The slope is fitted over separations in the range 2–30 de. Intermittency is reflected in departures from linear, self-similar scaling. The black dashed…
Figure 7
Figure 7. Figure 7: Square root of the second-order structure function (SF) for the velocity (red) and magnetic field (blue) decomposed into components parallel and perpendicular to the local magnetic field. The black dashed and dotted lines indicate the scaling slopes of 1/3 and 1/2, res…
Figure 8
Figure 8. Figure 8: First and second rows: Square root of the second-order velocity structure functions, p ⟨SFv(∆x)⟩y,z (left), p ⟨SFv(∆y)⟩x,z (middle), and p ⟨SFv(∆z)⟩x,ymid (right), for Bg = 0 and Bg = B0. The shaded areas represent the standard deviation. The black dashed lines indicat…
Figure 9
Figure 9. Figure 9: Mean slopes of p SF(x, ymid, ∆z) (left), p SF(∆x, y, z) (middle), p SF(x, ∆y, z) (right) as a function of the guide field strength. The slope is fitted over separations in the range 2–30 de. The black dashed line indicates the expected slope for Kolmogorov-type fluctua…
Figure 10
Figure 10. Figure 10: Slopes of the n-th order structure functions: ⟨SFn (∆z)⟩x,ymid (left), ⟨SFn (∆y)⟩x,z (middle), ⟨SFn (∆x)⟩y,z (right). The slope is fitted over separations in the range 2–30 de. Intermittency is reflected in departures from linear, self-similar scaling. The black dashe…

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Works this paper leans on

41 extracted references · 6 canonical work pages

  1. [1]

    A., Verscharen, D., Wicks, R

    Agudelo Rueda, J. A., Verscharen, D., Wicks, R. T., et al. 2021, Journal of Plasma Physics, 87, 905870228, doi: 10.1017/S0022377821000404

    work page doi:10.1017/s0022377821000404 2021

  2. [2]

    J., & Kuijpers, J

    Aly, J. J., & Kuijpers, J. 1990, A&A, 227, 473

    1990

  3. [3]

    P., Larson, D., et al

    Angelopoulos, V ., McFadden, J. P., Larson, D., et al. 2008, Science, 321, 931, doi: 10.1126/science.1160495

    doi:10.1126/science.1160495 2008

  4. [4]

    Beloborodov, A. M. 2017, ApJ, 850, 141, doi: 10.3847/1538-4357/aa8f4f

    doi:10.3847/1538-4357/aa8f4f 2017

  5. [5]

    K., & Langdon, B

    Birdsall, C. K., & Langdon, B. 1985, Plasma Physics via Computer Simulation (McGraw-Hill)

    1985

  6. [6]

    1993, Computer Space Plasma Physics: Simulation Techniques and Softwares 13

    Buneman, O. 1993, Computer Space Plasma Physics: Simulation Techniques and Softwares 13

    1993

  7. [7]

    Cho, J., & Vishniac, E. T. 2000, ApJ, 539, 273, doi: 10.1086/309213

    doi:10.1086/309213 2000

  8. [8]

    2019, ApJ, 886, 122, doi: 10.3847/1538-4357/ab4c33 —

    Comisso, L., & Sironi, L. 2019, ApJ, 886, 122, doi: 10.3847/1538-4357/ab4c33 —. 2022, ApJL, 936, L27, doi: 10.3847/2041-8213/ac8422

    doi:10.3847/1538-4357/ab4c33 2019

Show all 41 references
  1. [9]

    2020, ApJL, 895, L40, doi: 10.3847/2041-8213/ab93dc

    Comisso, L., Sobacchi, E., & Sironi, L. 2020, ApJL, 895, L40, doi: 10.3847/2041-8213/ab93dc

    2020 doi

  2. [10]

    T., Drake, J

    Dahlin, J. T., Drake, J. F., & Swisdak, M. 2017, Physics of Plasmas, 24, 092110, doi: 10.1063/1.4986211

    2017 doi

  3. [11]

    Daughton, W., Nakamura, T. K. M., Karimabadi, H., Roytershteyn, V ., & Loring, B. 2014, Physics of Plasmas, 21, 052307, doi: 10.1063/1.4875730

    2014 doi

  4. [12]

    2011, Nature Physics, 7, 539, doi: 10.1038/nphys1965

    Daughton, W., Roytershteyn, V ., Karimabadi, H., et al. 2011, Nature Physics, 7, 539, doi: 10.1038/nphys1965

    2011 doi

  5. [13]

    1995, ApJ, 438, 763, doi: 10.1086/175121

    Goldreich, P., & Sridhar, S. 1995, ApJ, 438, 763, doi: 10.1086/175121

    1995 doi

  6. [14]

    2021, ApJ, 919, 111, doi: 10.3847/1538-4357/ac0918

    Guo, F., Li, X., Daughton, W., et al. 2021, ApJ, 919, 111, doi: 10.3847/1538-4357/ac0918

    2021 doi

  7. [15]

    2021, ApJ, 911, 37, doi: 10.3847/1538-4357/abea18

    Hu, Y ., Xu, S., & Lazarian, A. 2021, ApJ, 911, 37, doi: 10.3847/1538-4357/abea18

    2021 doi

  8. [16]

    2016, ApJ, 818, 20, doi: 10.3847/0004-637X/818/1/20 —

    Huang, Y .-M., & Bhattacharjee, A. 2016, ApJ, 818, 20, doi: 10.3847/0004-637X/818/1/20 —. 2024, Physics of Plasmas, 31, 082119, doi: 10.1063/5.0216561

    2016 doi

  9. [17]

    2022, Nature Reviews Physics, 4, 263, doi: 10.1038/s42254-021-00419-x

    Ji, H., Daughton, W., Jara-Almonte, J., et al. 2022, Nature Reviews Physics, 4, 263, doi: 10.1038/s42254-021-00419-x

    2022 doi

  10. [18]

    A., & Pneuman, G

    Kopp, R. A., & Pneuman, G. W. 1976, SoPh, 50, 85, doi: 10.1007/BF00206193

    1976 doi

  11. [19]

    A., Lazarian, A., & Vishniac, E

    Kowal, G., Falceta-Gonc ¸alves, D. A., Lazarian, A., & Vishniac, E. T. 2017, ApJ, 838, 91, doi: 10.3847/1538-4357/aa6001

    2017 doi

  12. [20]

    L., Jafari, A., et al

    Lazarian, A., Eyink, G. L., Jafari, A., et al. 2020, Physics of Plasmas, 27, 012305, doi: 10.1063/1.5110603

    2020 doi

  13. [21]

    Lazarian, A., & Vishniac, E. T. 1999, ApJ, 517, 700, doi: 10.1086/307233

    1999 doi

  14. [22]

    2019, ApJ, 884, 118, doi: 10.3847/1538-4357/ab4268

    Li, X., Guo, F., Li, H., Stanier, A., & Kilian, P. 2019, ApJ, 884, 118, doi: 10.3847/1538-4357/ab4268

    2019 doi

  15. [23]

    2025, arXiv e-prints, arXiv:2510.09978, doi: 10.48550/arXiv.2510.09978

    Liang, S.-M., Zhang, J.-F., Gao, N.-N., & Yi, N.-Y . 2025, arXiv e-prints, arXiv:2510.09978, doi: 10.48550/arXiv.2510.09978

    2025 doi

  16. [24]

    Lyubarsky, Y ., & Kirk, J. G. 2001, ApJ, 547, 437, doi: 10.1086/318354

    2001 doi

  17. [25]

    1994, Nature, 371, 495, doi: 10.1038/371495a0

    Masuda, S., Kosugi, T., Hara, H., Tsuneta, S., & Ogawara, Y . 1994, Nature, 371, 495, doi: 10.1038/371495a0

    1994 doi

  18. [26]

    Nagai, T., Fujimoto, M., Saito, Y ., et al. 1998, J. Geophys. Res., 103, 4419, doi: 10.1029/97JA02190

    1998 doi

  19. [27]

    Narayan, R., & Medvedev, M. V . 2001, ApJL, 562, L129, doi: 10.1086/338325

    2001 doi

  20. [28]

    S., Mac Low, M.-M., Collins, D

    Oishi, J. S., Mac Low, M.-M., Collins, D. C., & Tamura, M. 2015, ApJL, 806, L12, doi: 10.1088/2041-8205/806/1/L12 OpenAI. 2022, Introducing ChatGPT, doi: https://openai.com/index/chatgpt/

    2015 doi

  21. [29]

    Parker, E. N. 1957, J. Geophys. Res., 62, 509, doi: 10.1029/JZ062i004p00509

    1957 doi

  22. [30]

    Petschek, H. E. 1964, in NASA Special Publication, ed. W. N

    1964

  23. [31]

    E., Sironi, L., & Narayan, R

    Rowan, M. E., Sironi, L., & Narayan, R. 2017, ApJ, 850, 29, doi: 10.3847/1538-4357/aa9380

    2017 doi

  24. [32]

    A., Cowley, S

    Schekochihin, A. A., Cowley, S. C., Dorland, W., et al. 2009, ApJS, 182, 310, doi: 10.1088/0067-0049/182/1/310

    2009 doi

  25. [33]

    2016, MNRAS, 462, 48, doi: 10.1093/mnras/stw1620

    Sironi, L., Giannios, D., & Petropoulou, M. 2016, MNRAS, 462, 48, doi: 10.1093/mnras/stw1620

    2016 doi

  26. [34]

    2014, ApJL, 783, L21, doi: 10.1088/2041-8205/783/1/L21

    Sironi, L., & Spitkovsky, A. 2014, ApJL, 783, L21, doi: 10.1088/2041-8205/783/1/L21

    2014 doi

  27. [35]

    A., & Giannios, D

    Sironi, L., Uzdensky, D. A., & Giannios, D. 2025a, ARA&A, 63, 127, doi: 10.1146/annurev-astro-020325-115713 —. 2025b, arXiv e-prints, arXiv:2506.02101, doi: 10.48550/arXiv.2506.02101

    doi arXiv

  28. [36]

    2005, in AIP Conf

    Spitkovsky, A. 2005, in AIP Conf. Ser., V ol. 801, Astrophysical Sources of High Energy Particles and Radiation, ed. T. Bulik, B. Rudak, & G. Madejski, 345, doi: 10.1063/1.2141897

    2005 doi

  29. [37]

    2019, Physics of Plasmas, 26, 072121, doi: 10.1063/1.5100737

    Stanier, A., Daughton, W., Le, A., Li, X., & Bird, R. 2019, Physics of Plasmas, 26, 072121, doi: 10.1063/1.5100737

    2019 doi

  30. [38]

    Sweet, P. A. 1958, The Observatory, 78, 30 Van Rossum, G., & Drake, F. L. 2009, Python 3 Reference Manual (Scotts Valley, CA: CreateSpace)

    1958

  31. [39]

    G., & Maruca, B

    Verscharen, D., Klein, K. G., & Maruca, B. A. 2019, Living Reviews in Solar Physics, 16, 5, doi: 10.1007/s41116-019-0021-0

    2019 doi

  32. [40]

    2021, ApJ, 922, 261, doi: 10.3847/1538-4357/ac2e08

    Zhang, H., Sironi, L., & Giannios, D. 2021, ApJ, 922, 261, doi: 10.3847/1538-4357/ac2e08

    2021 doi

  33. [41]

    2023a, ApJL, 956, L36, doi: 10.3847/2041-8213/acfe7c —

    Zhang, H., Sironi, L., Giannios, D., & Petropoulou, M. 2023a, ApJL, 956, L36, doi: 10.3847/2041-8213/acfe7c —. 2023b, ApJL, 956, L36, doi: 10.3847/2041-8213/acfe7c

    doi

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