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arxiv: 2606.21505 · v1 · pith:ZHAQFFAZnew · submitted 2026-06-19 · ⚛️ physics.plasm-ph

Linear Tearing Growth and Onset of Relativistic Magnetic Reconnection in the Presence of Shear Flows and a Guide Field

Sarah Peery , Yi-Hsin Liu This is my paper

Pith reviewed 2026-06-26 12:39 UTC · model grok-4.3

classification ⚛️ physics.plasm-ph
keywords relativistic magnetic reconnectiontearing instabilityshear flowguide fieldparticle-in-cell simulationKelvin-Helmholtz instabilitylinear growth rate
0
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The pith

Shear flows and guide fields slow the linear growth of the relativistic tearing instability and delay magnetic reconnection onset.

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

The paper examines the effects of shear flows and guide magnetic fields on the onset of relativistic magnetic reconnection through kinetic particle-in-cell simulations. It introduces a numerical solver for the growth rate of the relativistic linear tearing instability that accounts for the motional electric field. Findings indicate that both shear flows and guide field strength reduce the tearing growth rate, while sufficiently strong shear flows cause a transition to linear Kelvin-Helmholtz instability. A sympathetic reader would care because reconnection controls energy conversion and particle acceleration in many relativistic plasma systems, so changes to its onset time alter predictions for those systems.

Core claim

Using particle-in-cell simulations, the authors show that shear flows slow the linear phase of relativistic tearing instability and can delay the onset of magnetic reconnection, with analogous slowing from guide field strength; at higher shear the system passes through an intermediate regime into linear Kelvin-Helmholtz instability. The results are obtained with a new numerical solver for the relativistic tearing growth rate that includes the previously omitted motional electric field.

What carries the argument

Numerical solver for the growth rate of the relativistic linear tearing instability that incorporates the motional electric field.

If this is right

  • Reconnection onset is delayed by the presence of shear flows.
  • Increasing guide field strength also reduces the tearing growth rate.
  • Above a threshold shear the instability switches to Kelvin-Helmholtz.
  • These modifications to onset time apply inside relativistic plasma regimes.

Where Pith is reading between the lines

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

  • The reported dependence on shear and guide field could be tested in laboratory relativistic plasma experiments that control flow shear.
  • The solver might be extended to predict onset times in three-dimensional or pair-plasma configurations not examined here.
  • Similar slowing effects may appear in other current-sheet instabilities when motional electric fields are retained.

Load-bearing premise

The numerical solver for the relativistic linear tearing instability growth rate accurately incorporates the effects of the motional electric field.

What would settle it

Direct comparison of simulated linear growth rates against the numerical solver predictions across a range of shear-flow speeds and guide-field strengths; systematic mismatch would falsify the reported slowing and transition behaviors.

Figures

Figures reproduced from arXiv: 2606.21505 by Sarah Peery, Yi-Hsin Liu.

Figure 1
Figure 1. Figure 1: FIG. 1. Reconnection rates as a function of time [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The scaling of the tearing growth rate with [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Linear growth rates for [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The real and imaginary parts of the per [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Reconnection rates for simulations with [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The set of main simulations used, guide field is normalized to [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: a shows undisturbed tearing modes and a chain of plasmoids form, Fig. 7b also shows plasmoid formation but with some vortex-like distortion in the current sheet, which is greatly enhanced in Fig. 7c. As plasmoids form here, they are also rotated, but the dominant behav￾ior is still tearing. In Fig. 7d the current sheet is very distorted. While the run evolves to have a fast reconnection phase, as [PITH_FU… view at source ↗
Figure 8
Figure 8. Figure 8: shows plots of the maximum value of log(B2 z ) along the neutral line, for three val￾ues of shear flow, Vsh =0, 0.3c, and 0.7c with Bg = Bx0 and LB = 2de. We plot the magnetic energy to better identify the signal. Similar to what was observed by Schoeffler [77] for rela￾tivistic tearing modes, in Fig. 8a and b, there are two main growing phases. The first is the early linear growth phase, which happens bef… view at source ↗
Figure 9
Figure 9. Figure 9: shows the growth rates from the sim￾ulation and solver calculated in several ways, with no shear flow first so we may discuss the differences in these values. Both LB = 2de and 4de are shown. We plot results of the main rel￾ativistic solver (blue lines) and Jet (black lines) which were also shown in [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Linear growth rates from the solver [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Growth rates as a function of [PITH_FULL_IMAGE:figures/full_fig_p012_11.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. An example of vortex induced reconnec [PITH_FULL_IMAGE:figures/full_fig_p013_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. The average growth rate for the [PITH_FULL_IMAGE:figures/full_fig_p014_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Panel a) scaling of the inertial tearing growth rate with guide field for; the relativistic solver using [PITH_FULL_IMAGE:figures/full_fig_p018_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. Panel a) shows scaling of KHI with uniform [PITH_FULL_IMAGE:figures/full_fig_p019_16.png] view at source ↗
read the original abstract

It has been shown in non-relativistic tearing theory that shear flows will slow the linear phase of tearing instability and can delay onset of magnetic reconnection. We find using kinetic particle-in-cell simulations that shear flow as well as guide field strength affect the onset time of relativistic magnetic reconnection. To model this we develop a numerical solver for the growth rate of the relativistic linear tearing instability, including effects of the motional electric field which has not previously been done. We find slowing of growth due to both shear flows and guide field, and at higher flow shear, transition through an intermediate regime to linear Kelvin-Helmholtz instability.

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 manuscript develops a numerical solver for the relativistic linear tearing instability growth rate that includes motional electric field effects (previously unaddressed) and uses kinetic PIC simulations to show that both shear flow and guide-field strength slow the linear phase and delay the onset of relativistic magnetic reconnection, with a transition to Kelvin-Helmholtz instability at sufficiently high shear.

Significance. If the solver implementation and its predictions are confirmed, the work would advance understanding of reconnection onset conditions in relativistic plasmas with flows, relevant to astrophysical environments such as pulsar winds or AGN jets. The explicit treatment of motional E in the linear solver is a technical contribution that could be reusable.

major comments (2)
  1. [solver description and results section] The central claim that shear flow and guide field affect onset time rests on the new relativistic tearing solver (including motional E). No benchmarks are reported against the incompressible MHD tearing mode with flow (standard literature) or the zero-guide-field relativistic limit; without such tests the reported slowing and KH transition cannot be verified as physical rather than numerical artifacts.
  2. [simulation results] The PIC simulation results on onset times are presented without accompanying error analysis, resolution studies, or demonstration that post-hoc parameter choices (e.g., box size, particle number) do not shift the reported transition thresholds; this is load-bearing for the quantitative statements about onset delay.
minor comments (2)
  1. [linear solver] Notation for the motional electric field term and its insertion into the dispersion relation should be made explicit with an equation number for reproducibility.
  2. [figures] Figure captions should state the exact shear parameter values and guide-field strengths used so that the transition to KH can be directly compared with the linear solver output.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive feedback on our manuscript. We address each major comment below and will revise the manuscript accordingly to strengthen the validation of the solver and the robustness of the simulation results.

read point-by-point responses

  1. Referee: [solver description and results section] The central claim that shear flow and guide field affect onset time rests on the new relativistic tearing solver (including motional E). No benchmarks are reported against the incompressible MHD tearing mode with flow (standard literature) or the zero-guide-field relativistic limit; without such tests the reported slowing and KH transition cannot be verified as physical rather than numerical artifacts.

    Authors: We agree that explicit benchmarks would strengthen confidence in the solver. Although the motional-E term is a novel addition without direct prior literature for benchmarking, the solver reduces to known limits (non-relativistic MHD with flow and relativistic tearing without guide field) that can be compared against established analytical and numerical results. We will add these benchmark comparisons in a revised section to demonstrate that the reported slowing and KH transition are physical. revision: yes

  2. Referee: [simulation results] The PIC simulation results on onset times are presented without accompanying error analysis, resolution studies, or demonstration that post-hoc parameter choices (e.g., box size, particle number) do not shift the reported transition thresholds; this is load-bearing for the quantitative statements about onset delay.

    Authors: We acknowledge the need for quantitative assessment of numerical uncertainties. In the revised manuscript we will include resolution studies, error estimates on onset times, and explicit checks showing that the reported transition thresholds remain stable under variations in box size and particle number. revision: yes

Circularity Check

0 steps flagged

No significant circularity; results from independent solver and simulations

full rationale

The paper develops a new numerical solver for relativistic linear tearing growth rates (including motional E) and reports PIC simulation results on onset times. No quoted equations or claims show growth rates or onset times reducing to fitted parameters from the same data, self-definitions, or load-bearing self-citations. The derivation chain is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides insufficient detail to identify specific free parameters, axioms, or invented entities used in the solver or simulations.

pith-pipeline@v0.9.1-grok · 5634 in / 1203 out tokens · 37277 ms · 2026-06-26T12:39:05.572752+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

93 extracted references · 2 canonical work pages

  1. [1]

    and include for the first time, the effects of the motional electric field, which is not negli- gible when the guide field is finite. Consistent with previous studies of tearing instability, we find that the growth in the linear phase is slowed by shear flow, leading to a long buildup phase before magnetic reconnection can onset. The solver also allows fo...

  2. [2]

    T earing Instability As validation of the solver in this section we compare to some familiar limits in literature. Figure 15 shows scaling results forB g =B x0, in both the relativistic and the non-relativistic regimes, which may be compared to the analytic growth rates derived in multiple previous studies of linear tearing. For that reason non-relativist...

  3. [3]

    Kelvin Helmholtz Instability While we focus mainly on the tearing instability in this work, it is useful to discuss the tran- sition between to KHI, especially as many previous studies of relativistic KHI focus on uniform magnetization [17, 28, 71]. FIG. 16. Panel a) shows scaling of KHI with uniformB x0 for a smooth velocity profile withkL s = 0.2, (blue...

    2048

  4. [4]

    2014, Physics of Plasmas, 21, 052312

    Ali, A., Li, J., & Kishimoto, Y. 2014, Physics of Plasmas, 21, 052312

    2014

  5. [5]

    2012, Space Science Reviews, 173, 341

    Arons, J. 2012, Space Science Reviews, 173, 341

    2012

  6. [6]

    D., Bhattacharjee, A., & Huang, Y.-M

    Baalrud, S. D., Bhattacharjee, A., & Huang, Y.-M. 2012, Physics of Plasmas, 19, 022101

    2012

  7. [7]

    V., & Komissarov, S

    Barkov, M. V., & Komissarov, S. S. 2016, Monthly Notices of the Royal Astronomical Society, 458, 1939

    2016

  8. [8]

    2017, Monthly Notices of the Royal Astronomical Society, 469, 4957

    Barniol Duran, R., Tchekhovskoy, A., & Giannios, D. 2017, Monthly Notices of the Royal Astronomical Society, 469, 4957

    2017

  9. [9]

    2019, Monthly Notices of the Royal Astronomical Society, 485, 908

    Berlok, T., & Pfrommer, C. 2019, Monthly Notices of the Royal Astronomical Society, 485, 908

    2019

  10. [10]

    2020, Physics of Plasmas, 27, 102106

    Betar, H., Del Sarto, D., Ottaviani, M., & Ghizzo, A. 2020, Physics of Plasmas, 27, 102106

    2020

  11. [11]

    2022, Journal of Plasma Physics, 88, 925880601

    —. 2022, Journal of Plasma Physics, 88, 925880601

    2022

  12. [12]

    A., Nakamura, T

    Blasl, K. A., Nakamura, T. K. M., Plaschke, F., et al. 2022, Physics of Plasmas, 29, 012105

    2022

  13. [13]

    P., Bach, U., et al

    Boccardi, B., Krichbaum, T. P., Bach, U., et al. 2016, A&A, 585, A33

    2016

  14. [14]

    J., Albright, B

    Bowers, K. J., Albright, B. J., Yin, L., et al. 2009, 180, 012055

    2009

  15. [15]

    A., & Begelman, M

    Cerutti, B., Uzdensky, D. A., & Begelman, M. C. 2012, The Astrophysical Journal, 746, 148

    2012

  16. [16]

    R., Uzdensky, D

    Cerutti, B., Werner, G. R., Uzdensky, D. A., & Begelman, M. C. 2014, The Astrophysical Journal, 782, 104

    2014

  17. [17]

    1961, Hydrodynamic and hydromagnetic stability (Oxford-Clarendon Press and New York-Oxford Univ

    Chandrasekhar, S. 1961, Hydrodynamic and hydromagnetic stability (Oxford-Clarendon Press and New York-Oxford Univ. Press)

    1961

  18. [18]

    1997, Journal of Geophysical Research: Space Physics, 102, 151

    Chen, Q., Otto, A., & Lee, L. 1997, Journal of Geophysical Research: Space Physics, 102, 151

    1997

  19. [19]

    1990, Physics of Fluids B Plasma Physics, 2, 495

    Chen, X., & Morrison, P. 1990, Physics of Fluids B Plasma Physics, 2, 495

    1990

  20. [20]

    E., Sironi, L., et al

    Chow, A., Rowan, M. E., Sironi, L., et al. 2023, Monthly Notices of the Royal Astronomical Society, 524, 90

    2023

  21. [21]

    1976, Resistive internal kink modes, Tech

    Coppi, B., Galvao, R., Pellat, R., Rosenbluth, M., & Rutherford, P. 1976, Resistive internal kink modes, Tech. rep., Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States).https: //www.osti.gov/biblio/7268294

    arXiv 1976

  22. [22]

    Coroniti, F. V. 1990, Astrophys. J., 349, 538

    1990

  23. [23]

    2024, Physics of Plasmas, 31, 032106

    De Jonghe, J., & Keppens, R. 2024, Physics of Plasmas, 31, 032106

    2024

  24. [24]

    2016, Monthly Notices of the Royal Astronomical Society, 460, 3753

    Del Zanna, L., Papini, E., Landi, S., Bugli, M., & Bucciantini, N. 2016, Monthly Notices of the Royal Astronomical Society, 460, 3753

    2016

  25. [25]

    2024, Journal of Plasma Physics, 90, 905900619

    Demidov, I., & Lyubarsky, Y. 2024, Journal of Plasma Physics, 90, 905900619

    2024

  26. [26]

    2025, The Astrophysical Journal, 979, 104

    —. 2025, The Astrophysical Journal, 979, 104

    2025

  27. [27]

    Drenkhahn, G., & Spruit, H. C. 2002, A&A, 391, 1141

    2002

  28. [28]

    1986, The Physics of Fluids, 29, 2563 22

    Einaudi, G., & Rubini, F. 1986, The Physics of Fluids, 29, 2563 22

    1986

  29. [29]

    2010, Physics of Plasmas, 17, 062102

    Faganello, M., Pegoraro, F., Califano, F., & Marradi, L. 2010, Physics of Plasmas, 17, 062102

    2010

  30. [30]

    2021, Plasma Physics and Controlled Fusion

    Faganello, M., Sisti, M., Califano, F., & Lavraud, B. 2021, Plasma Physics and Controlled Fusion

    2021

  31. [31]

    1980, Monthly Notices of the Royal Astronomical Society, 193, 469

    Ferrari, A., Trussoni, E., & Zaninetti, L. 1980, Monthly Notices of the Royal Astronomical Society, 193, 469

    1980

  32. [32]

    2024, AA, 690, A389

    Figueiredo, E., Cerutti, B., Mehlhaff, J., & Scepi, N. 2024, AA, 690, A389

    2024

  33. [33]

    P., Killeen, J., & Rosenbluth, M

    Furth, H. P., Killeen, J., & Rosenbluth, M. N. 1963, The Physics of Fluids, 6, 459

    1963

  34. [34]

    N., & Hollerbach, R

    Gourgouliatos, K. N., & Hollerbach, R. 2016, Monthly Notices of the Royal Astronomical Society, 463, 3381

    2016

  35. [35]

    2009, Nonlinear Processes in Geophysics, 16, 241

    Grasso, D., Borgogno, D., Pegoraro, F., & Tassi, E. 2009, Nonlinear Processes in Geophysics, 16, 241. https://npg.copernicus.org/articles/16/241/2009/

    2009

  36. [36]

    1996, Journal of Atmospheric and Terrestrial Physics, 58, 613

    Gudkov, M., & Troshichev, O. 1996, Journal of Atmospheric and Terrestrial Physics, 58, 613

    1996

  37. [37]

    2014, Phys

    Guo, F., Li, H., Daughton, W., & Liu, Y.-H. 2014, Phys. Rev. Lett., 113, 155005

    2014

  38. [38]

    2015, The Astrophysical Journal, 806, 167

    Guo, F., Liu, Y.-H., Daughton, W., & Li, H. 2015, The Astrophysical Journal, 806, 167

    2015

  39. [39]

    Hamlin, N. D. 2012, Phd thesis, UCLA

    2012

  40. [40]

    D., & Newman, W

    Hamlin, N. D., & Newman, W. I. 2013, Phys. Rev. E, 87, 043101

    2013

  41. [41]

    1975, Plasma Physics, 17, 143.https://dx.doi.org/10.1088/0032-1028/17/2/005

    Hofman, I. 1975, Plasma Physics, 17, 143.https://dx.doi.org/10.1088/0032-1028/17/2/005

    work page doi:10.1088/0032-1028/17/2/005 1975

  42. [42]

    2021, Physics of Plasmas, 28, 062106

    Hoshino, M. 2021, Physics of Plasmas, 28, 062106

    2021

  43. [43]

    2012, Space Science Reviews, 173, 521–533

    Hoshino, M., & Lyubarsky, Y. 2012, Space Science Reviews, 173, 521–533

    2012

  44. [44]

    2018, Physics of Plasmas, 25, 102117

    Hosseinpour, M., Chen, Y., & Zenitani, S. 2018, Physics of Plasmas, 25, 102117

    2018

  45. [45]

    2015, Journal of Plasma Physics, 81, 905810606

    Jain, N., & Buchner, J. 2015, Journal of Plasma Physics, 81, 905810606

    2015

  46. [46]

    2015, Space Science Reviews, 191, 545

    Kagan, D., Sironi, L., Cerutti, B., & Giannios, D. 2015, Space Science Reviews, 191, 545

    2015

  47. [47]

    Keppens, R., Toth, G., Westermann, R. H. J., & Goedbloed, J. P. 1999, Journal of Plasma Physics, 61, 1–19

    1999

  48. [48]

    G., & Skjæraasen, O

    Kirk, J. G., & Skjæraasen, O. 2003, Astrophys. J., 591, 366

    2003

  49. [49]

    2009, The Astrophysical Journal, 696, 2220

    Koide, S. 2009, The Astrophysical Journal, 696, 2220

    2009

  50. [50]

    S., Barkov, M., & Lyutikov, M

    Komissarov, S. S., Barkov, M., & Lyutikov, M. 2006, Monthly Notices of the Royal Astronomical Society, 374, 415

    2006

  51. [51]

    1983, Plasma Physics and Controlled Fusion, 89, 293

    Landi, S., Papini, E., Del Zanna, L., Tenerani, A., & Pucci, F. 1983, Plasma Physics and Controlled Fusion, 89, 293

    1983

  52. [52]

    H., & Ma, Z

    Li, J. H., & Ma, Z. W. 2010, Journal of Geophysical Research: Space Physics, 115

    2010

  53. [53]

    C., Liu, Y.-H., & Qi, Y

    Li, T. C., Liu, Y.-H., & Qi, Y. 2021, The Astrophysical Journal Letters, 909, L28

    2021

  54. [54]

    2020, The Astrophysical Journal Letters, 890, L15

    Liu, D., Lu, S., Lu, Q., Ding, W., & Wang, S. 2020, The Astrophysical Journal Letters, 890, L15

    2020

  55. [55]

    2014, Physics of Plasmas, 21

    Liu, Y.-H., Daughton, W., Karimabadi, H., Li, H., & Peter Gary, S. 2014, Physics of Plasmas, 21

    2014

  56. [56]

    2020, The Astrophysical Journal, 892, L13

    Liu, Y.-H., Lin, S.-C., Hesse, M., et al. 2020, The Astrophysical Journal, 892, L13

    2020

  57. [57]

    F., Cowley, S

    Loureiro, N. F., Cowley, S. C., Dorland, W. D., Haines, M. G., & Schekochihin, A. A. 2005, Phys. Rev. Lett., 95, 235003

    2005

  58. [58]

    2013, Plasma Physics and Controlled Fusion, 55, 085019

    Lu, Q., Lu, S., Huang, C., Wu, M., & Wang, S. 2013, Plasma Physics and Controlled Fusion, 55, 085019

    2013

  59. [59]

    Lyubarsky, Y., & Kirk, J. G. 2001, Astrophys. J., 547, 437

    2001

  60. [60]

    2002, The Astrophysical Journal, 580, L65

    Lyutikov, M. 2002, The Astrophysical Journal, 580, L65

    2002

  61. [61]

    2003, The Astrophysical Journal, 589, 893–901

    Lyutikov, M., & Uzdensky, D. 2003, The Astrophysical Journal, 589, 893–901

    2003

  62. [62]

    2018, Journal of Plasma Physics, 84, 905840501

    MacTaggart, D. 2018, Journal of Plasma Physics, 84, 905840501

    2018

  63. [63]

    2020, The Tearing Instability of Resistive Magnetohydrodynamics, ed

    —. 2020, The Tearing Instability of Resistive Magnetohydrodynamics, ed. D. MacTaggart & A. Hillier (Cham: Springer International Publishing), 37–67

    2020

  64. [64]

    2021, Physics of Plasmas, 28, 072103

    Mahapatra, J., Bokshi, A., Ganesh, R., & Sen, A. 2021, Physics of Plasmas, 28, 072103

    2021

  65. [65]

    2025, Journal of Plasma Physics, 91, E62

    Mallet, A., Eriksson, S., Swisdak, M., & Juno, J. 2025, Journal of Plasma Physics, 91, E62

    2025

  66. [66]

    2025, Journal of Plasma Physics, 91, E146

    —. 2025, Journal of Plasma Physics, 91, E146

    2025

  67. [67]

    2022, Physical Review Letters, 128

    Mbarek, R., Haggerty, C., Sironi, L., Shay, M., & Caprioli, D. 2022, Physical Review Letters, 128

    2022

  68. [68]

    Miura, A., & Pritchett, P. L. 1982, Journal of Geophysical Research: Space Physics, 87, 7431

    1982

  69. [69]

    2013, Journal of Geophysical Research, 118, 5742

    Nakamura, T., Daughton, W., Karimabadi, H., & Eriksson, S. 2013, Journal of Geophysical Research, 118, 5742

    2013

  70. [70]

    Nakamura, T. K. M., Hasegawa, H., Shinohara, I., & Fujimoto, M. 2011, Journal of Geophysical Research (Space Physics), 116, A03227 23

    2011

  71. [71]

    Nakamura, T. K. M., Blasl, K. A., Hasegawa, H., et al. 2022, Physics of Plasmas, 29, 012901

    2022

  72. [72]

    J., & Steinolfson, R

    Ofman, L., Morrison, P. J., & Steinolfson, R. S. 1993, Physics of Fluids B: Plasma Physics, 5, 376

    1993

  73. [73]

    1972, Planetary and Space Science, 20, 1

    Ong, R., & Roderick, N. 1972, Planetary and Space Science, 20, 1

    1972

  74. [74]

    2008, AA, 490, 493

    Osmanov, Z., Mignone, A., Massaglia, S., Bodo, G., & Ferrari, A. 2008, AA, 490, 493

    2008

  75. [75]

    1993, Phys

    Ottaviani, M., & Porcelli, F. 1993, Phys. Rev. Lett., 71, 3802.https://link.aps.org/doi/10.1103/ PhysRevLett.71.3802

    1993

  76. [76]

    2024, The Astrophysical Journal, 964, 144

    Peery, S., Liu, Y.-H., & Li, X. 2024, The Astrophysical Journal, 964, 144

    2024

  77. [77]

    2025, Physics of Plasmas, 32, 042112

    Peyrichon, G., El-Rabii, H., Ripoll, J.-F., et al. 2025, Physics of Plasmas, 32, 042112

    2025

  78. [78]

    Roychoudhury, S., & Lovelace, R. V. E. 1986, Astrophys. J., 302, 188

    1986

  79. [79]

    2008, Physics of Plasmas, 15, 082901

    Roytershteyn, V., & Daughton, W. 2008, Physics of Plasmas, 15, 082901

    2008

  80. [80]

    2025, Journal of Plasma Physics, 91, E42

    Schoeffler, K., Eichmann, B., Pucci, F., & Innocenti, M. 2025, Journal of Plasma Physics, 91, E42

    2025

Showing first 80 references.