Pith. sign in

REVIEW 2 major objections 2 minor 58 references

A rising current expels plasma to form an expanding magnetic bubble whose front advances at the Alfvén speed set by the inner magnetic field and outer plasma density.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · grok-4.3

2026-06-26 11:31 UTC pith:PLZ26MFO

load-bearing objection The paper shows PIC simulations and laser experiments producing expanding magnetic bubbles from rising currents, with a claimed velocity scaling to a non-local Alfvén speed, but the force balance behind that specific form is not derived. the 2 major comments →

arxiv 2606.21853 v1 pith:PLZ26MFO submitted 2026-06-20 physics.plasm-ph astro-ph.HEastro-ph.SRphysics.space-ph

Plasma Flow Generation and Particle Acceleration from Expanding Magnetic Bubbles

Yang Zhang , Brandon K. Russell , Geoffrey Pomraning , Lan Gao , Xiaocan Li , Adam Stainer , William Daughton , Chuanfei Dong
show 4 more authors
Liang Wang Peiyun Shi Kian Orr Hantao Ji
This is my paper
classification physics.plasm-ph astro-ph.HEastro-ph.SRphysics.space-ph
keywords plasma flowmagnetic bubbleparticle accelerationAlfvén speedcurrent drivekinetic simulationlaser experiment
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper establishes that an impulsive rise in electric current through a plasma pushes the surrounding material outward, creating a magnetic bubble that expands and accelerates charged particles. The speed of the bubble's leading edge follows a specific scaling given by the Alfvén velocity constructed from the magnetic field strength at the bubble's inner boundary and the plasma density just ahead of the front. Kinetic particle-in-cell simulations together with laser-driven capacitor-coil experiments both reproduce this behavior. A sympathetic reader would care because the result identifies a basic, controllable process for producing directed plasma flows and energetic particles inside laboratory devices, without requiring external drivers beyond the current itself.

Core claim

Through fully kinetic particle-in-cell simulations and laser-driven capacitor-coil experiments the authors demonstrate that a rising current expels plasma and forms an expanding magnetic bubble while accelerating particles. The expansion front velocity scales directly with the Alfvén speed evaluated using the magnetic field at the inner edge of the bubble and the plasma density at its outer edge. This scaling holds across the range of conditions examined and positions impulsive current drive as a fundamental mechanism for generating plasma flows and particle acceleration in laboratory plasmas.

What carries the argument

The expanding magnetic bubble produced by a rising current, whose front velocity is set by the Alfvén speed formed from the inner-edge magnetic field and the outer-edge plasma density.

Load-bearing premise

The velocity of the expansion front is fixed exclusively by the Alfvén speed from the inner magnetic field and outer plasma density, with no other forces or effects altering the scaling.

What would settle it

A simulation or experiment in which the measured front velocity departs from the predicted Alfvén scaling when the inner magnetic field strength or outer plasma density is varied independently while holding other parameters fixed.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Impulsive current drive generates directed plasma flows inside laboratory devices.
  • Particles gain energy at the expanding bubble front under the same conditions.
  • The identified scaling supplies a quantitative relation between current rise rate and resulting flow speed.
  • The mechanism operates in both the simulated kinetic regime and the laboratory capacitor-coil setup.

Where Pith is reading between the lines

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

  • The same current-driven bubble expansion could be examined in other laboratory configurations such as pulsed-power facilities to test the scaling's robustness.
  • If the scaling persists at higher densities or stronger fields, it may offer a route to controlled plasma jet formation without additional hardware.
  • Astrophysical contexts with sudden current sheets might exhibit analogous bubble-driven flows, though the paper does not explore that mapping.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 2 minor

Summary. The manuscript uses fully kinetic PIC simulations and laser-driven capacitor-coil experiments to show that a rising current expels plasma and forms an expanding magnetic bubble that accelerates particles. The central result is that the expansion front velocity scales with the Alfvén speed constructed from the magnetic field at the inner edge of the bubble and the plasma density at its outer edge. This is presented as establishing impulsive current drive as a fundamental mechanism for plasma flows and particle acceleration in laboratory plasmas with potential astrophysical relevance.

Significance. If the reported scaling is robust, the work identifies a concrete, experimentally accessible mechanism linking current rise to plasma expulsion and acceleration. The dual use of fully kinetic simulations and laser-driven experiments is a strength, as is the focus on a scaling relation that could be tested in other impulsive-current configurations.

major comments (2)
  1. [Abstract (and §3–4, where the scaling is presented)] The abstract and central claim assert that the front velocity equals the Alfvén speed formed from B_inner and ρ_outer, yet no section derives this combination from the integrated momentum equation or demonstrates that J×B, magnetic tension, inertia, and electrostatic terms yield precisely this non-local expression while resistivity and electron inertia remain sub-dominant.
  2. [§4 (simulation diagnostics) and §5 (experimental comparison)] Without an explicit force-balance analysis or diagnostic that isolates why the mixed (inner-B, outer-ρ) construction governs the front rather than the local v_A at the current sheet, the scaling risks being setup-specific rather than fundamental; the manuscript should supply the relevant momentum-equation diagnostics or analytic model.
minor comments (2)
  1. Figure captions should explicitly state the time at which inner-edge B and outer-edge density are sampled for the scaling comparison.
  2. Add a table listing the key simulation and experimental parameters (current rise rate, initial density, coil geometry) to facilitate reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The two major comments both concern the absence of an explicit derivation or force-balance analysis supporting the reported non-local Alfvén-speed scaling. We address each point below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [Abstract (and §3–4, where the scaling is presented)] The abstract and central claim assert that the front velocity equals the Alfvén speed formed from B_inner and ρ_outer, yet no section derives this combination from the integrated momentum equation or demonstrates that J×B, magnetic tension, inertia, and electrostatic terms yield precisely this non-local expression while resistivity and electron inertia remain sub-dominant.

    Authors: We agree that the manuscript would be strengthened by an explicit derivation. The scaling was identified empirically from the suite of kinetic simulations and confirmed in the experiments; no integrated momentum-equation analysis was presented in the original text. In the revised manuscript we will add a new subsection (or appendix) that starts from the ion momentum equation, identifies the dominant terms at the expansion front, and shows under what ordering the non-local combination v_A(B_inner, ρ_outer) emerges while resistivity and electron inertia remain negligible. revision: yes

  2. Referee: [§4 (simulation diagnostics) and §5 (experimental comparison)] Without an explicit force-balance analysis or diagnostic that isolates why the mixed (inner-B, outer-ρ) construction governs the front rather than the local v_A at the current sheet, the scaling risks being setup-specific rather than fundamental; the manuscript should supply the relevant momentum-equation diagnostics or analytic model.

    Authors: We accept the criticism. The original submission relied on the observed consistency of the scaling across parameter scans rather than on direct momentum diagnostics. We will incorporate additional simulation diagnostics that evaluate the individual terms of the momentum equation at the front location, together with a brief analytic argument showing why the local Alfvén speed evaluated at the current sheet does not govern the front speed in this geometry. These additions will appear in the revised §4 and will be referenced in the experimental comparison of §5. revision: yes

Circularity Check

0 steps flagged

No circularity; result reported from external simulations and experiments

full rationale

The paper establishes its central scaling claim via fully kinetic PIC simulations and laser-driven capacitor-coil experiments rather than an analytic derivation. No load-bearing step reduces by construction to a fitted parameter, self-definition, or self-citation chain. The non-local Alfvén speed construction is presented as an observed outcome, not as a quantity defined in terms of the result itself. This is the normal case of an empirical finding that remains self-contained against its external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review performed on abstract only; no explicit free parameters, invented entities, or non-standard axioms are stated. Standard plasma-physics assumptions (collisionless kinetics, ideal MHD limits for Alfvén speed) are implicitly used but not detailed.

axioms (1)
  • domain assumption Standard assumptions of fully kinetic plasma physics and the definition of the Alfvén speed apply without modification at the bubble edge.
    The scaling relation presupposes that the Alfvén speed constructed from inner B and outer density is the relevant characteristic speed.

pith-pipeline@v0.9.1-grok · 5672 in / 1344 out tokens · 28296 ms · 2026-06-26T11:31:39.617433+00:00 · methodology

0 comments
read the original abstract

Impulsive plasma dynamics in the laboratory are often driven by rising electric currents, yet their quantitative plasma response has not been well established. By means of fully kinetic particle-in-cell simulations and laser-driven capacitor-coil experiments, we show that a rising current expels plasma, forming an expanding magnetic bubble and accelerating particles. The expansion front velocity scales with the Alfv\'en speed determined by the magnetic field at its inner edge and the plasma density at its outer edge. This mechanism establishes impulsive current drive as a fundamental way that generates plasma flows and accelerates particles in laboratory plasmas, with potential relevance to astrophysics.

Figures

Figures reproduced from arXiv: 2606.21853 by Adam Stainer, Brandon K. Russell, Chuanfei Dong, Geoffrey Pomraning, Hantao Ji, Kian Orr, Lan Gao, Liang Wang, Peiyun Shi, William Daughton, Xiaocan Li, Yang Zhang.

Figure 1
Figure 1. Figure 1: FIG. 1. Plasma response to a rising wire current. (a) Normalized axial current density at [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Time-evolving particle energy spectra. (a) Ion distribu [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Experimental validation of plasma dynamics driven by an increasing current. (a) Proton radiography setup for the laser-driven [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Reverse current and magnetic-field structure. (a) Integrated current showing that the reverse current cancels the coil current, leaving [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Particle tracing illustrating ion acceleration through interaction with the expanding front. (a) Trajectory of a representative traced [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

58 extracted references · 2 canonical work pages

  1. [1]

    Fujioka, Z

    S. Fujioka, Z. Zhang, K. Ishihara, K. Shigemori, Y . Hironaka, T. Johzaki, A. Sunahara, N. Yamamoto, H. Nakashima, T. Watanabe, et al., Kilotesla magnetic field due to a capacitor-coil target driven by high power laser, Sci. Rep. 3, 1170 (2013). 023317-7 Y ANG ZHANGet al. PHYSICAL REVIEW RESEARCH 8, 023317 (2026)

    2013

  2. [2]

    L. Gao, H. Ji, G. Fiksel, W. Fox, M. Evans, and N. Alfonso, Ultrafast proton radiography of the magnetic fields generated by a laser-driven coil current,Phys. Plasmas 23, 043106 (2016)

    2016

  3. [3]

    Haines, A review of the dense Z-pinch, Plasma Phys

    M. Haines, A review of the dense Z-pinch, Plasma Phys. Controlled Fusion 53, 093001 (2011)

    2011

  4. [4]

    Zhang, P

    Y . Zhang, P. Wongwaitayakornkul, and P. M. Bellan, Magnetic Rayleigh–Taylor instability in an experiment simulating a solar loop, Astrophys. J. Lett. 889, L32 (2020)

    2020

  5. [5]

    Schwarz, B

    J. Schwarz, B. Hutsel, T. Awe, B. Bauer, J. Banasek, E. Breden, J. Chen, M. Cuneo, K. Chandler, K. DeZetter, et al., Mykonos: A pulsed power driver for science and innovation,High Energy Density Phys. 53, 101144 (2024)

    2024

  6. [6]

    Lavine, D

    E. Lavine, D. Lund, E. Freeman, W. Potter, C. Seyler, and B. Kusse, An experimental platform for investigating astrophysi- cally relevant magnetized plasma jets on the COBRA facility, Phys. Plasmas 32, 012902 (2025)

    2025

  7. [7]

    Forest, K

    C. Forest, K. Flanagan, M. Brookhart, M. Clark, C. Cooper, V . Désangles, J. Egedal, D. Endrizzi, I. Khalzov, H. Li, et al.,T h e Wisconsin plasma astrophysics laboratory, J. Plasma Phys. 81, 345810501 (2015)

    2015

  8. [8]

    D. B. Schaeffer, W. Fox, D. Haberberger, G. Fiksel, A. Bhattacharjee, D. H. Barnak, S. X. Hu, and K. Germaschewski, Generation and evolution of high-Mach-number laser-driven magnetized collisionless shocks in the laboratory, Phys. Rev. Lett. 119, 025001 (2017)

    2017

  9. [9]

    S. You, J. von der Linden, E. S. Lavine, E. G. Carroll, A. Card, M. Quinley, and M. Azuara-Rosales, The Mochi LabJet experiment for measurements of canonical helicity injection in a laboratory astrophysical jet, Astrophys. J. Suppl. Ser. 236,2 9 (2018)

    2018

  10. [10]

    Bellan, Experiments relevant to astrophysical jets, J

    P. Bellan, Experiments relevant to astrophysical jets, J. Plasma Phys. 84, 755840501 (2018)

    2018

  11. [11]

    B. Seo, M. Avila, T. Clevenger, C. Castleberry, C. Lamb, X. Ma, K. Nykyri, A. Barjatya, and D.-W. Kim, A new single flux rope experiment for studying the dynamics of a magnetized plasma jet, Rev. Sci. Instrum. 96, 053505 (2025)

    2025

  12. [12]

    Yamada, H

    M. Yamada, H. Ji, S. Hsu, T. Carter, R. Kulsrud, N. Bretz, F. Jobes, Y . Ono, and F. Perkins, Study of driven magnetic reconnection in a laboratory plasma, Phys. Plasmas 4, 1936 (1997)

    1936

  13. [13]

    M. R. Brown, Experimental studies of magnetic reconnection, Phys. Plasmas 6, 1717 (1999)

    1999

  14. [14]

    Egedal, W

    J. Egedal, W. Fox, N. Katz, M. Porkolab, K. Reim, and E. Zhang, Laboratory observations of spontaneous magnetic re- connection, Phys. Rev. Lett. 98, 015003 (2007)

    2007

  15. [15]

    P. Shi, P. Srivastav, M. H. Barbhuiya, P. A. Cassak, E. E. Scime, and M. Swisdak, Laboratory observations of electron heating and non-Maxwellian distributions at the kinetic scale during electron-only magnetic reconnection, Phys. Rev. Lett. 128, 025002 (2022)

    2022

  16. [16]

    Zhang, S

    Y . Zhang, S. Pree, and P. M. Bellan, Generation of laboratory nanoflares from multiple braided plasma loops, Nat. Astron. 7, 655 (2023)

    2023

  17. [17]

    H. Ji, L. Gao, G. Pomraning, K. Sakai, F. Guo, X. Li, A. Stanier, A. Milder, R. Follett, G. Fiksel, et al. , Study of magnetic re- connection at low-β using laser-powered capacitor coils, Phys. Plasmas 31, 102112 (2024)

    2024

  18. [18]

    J. Y . Park, Y . D. Yoon, and Y . S. Hwang, Kinetic turbulence drives MHD equilibrium change via 3D reconnection, Nature (London) 644, 59 (2025)

    2025

  19. [19]

    K. J. Bowers, B. J. Albright, L. Yin, B. Bergen, and T. J. Kwan, Ultrahigh performance three-dimensional electromagnetic rel- ativistic kinetic plasma simulation, Phys. Plasmas 15, 055703 (2008)

    2008

  20. [20]

    Chien, L

    A. Chien, L. Gao, H. Ji, X. Yuan, E. G. Blackman, H. Chen, P. C. Efthimion, G. Fiksel, D. H. Froula, K. W. Hill,et al., Study of a magnetically driven reconnection platform using ultrafast proton radiography, Phys. Plasmas 26, 062113 (2019)

    2019

  21. [21]

    L. Gao, Y . Zhang, H. Ji, B. K. Russell, G. Pomraning, J. Griff- McMahon, S. Klein, C. Kuranz, and M. Wei, Record magnetic field generation by short-pulse laser-driven capacitor-coil tar- gets, Appl. Phys. Lett. 127, 094101 (2025)

    2025

  22. [22]

    Zhang, R

    Y . Zhang, R. Omura, R. Akematsu, K. F. F. Law, B. K. Russell, G. Pomraning, K. Orr, K. Kimura, M. F. Syahbana, Y . Karaki, et al. , Time-resolved interferometric measurements of plasma density evolution in laser-driven capacitor-coil targets, Appl. Phys. Lett. 128, 234102 (2026)

    2026

  23. [23]

    F. C. Jones and D. C. Ellison, The plasma physics of shock acceleration, Space Sci. Rev. 58, 259 (1991)

    1991

  24. [24]

    F. Guo, O. French, Q. Zhang, X. Li, and J. Seo, Particle injection problem in magnetic reconnection and turbulence, Space Sci Rev. 221, 103 (2025)

    2025

  25. [25]

    Daido, F

    H. Daido, F. Miki, K. Mima, M. Fujita, K. Sawai, H. Fujita, Y . Kitagawa, S. Nakai, and C. Yamanaka, Generation of a strong magnetic field by an intense CO 2 laser pulse, Phys. Rev. Lett. 56, 846 (1986)

    1986

  26. [26]

    Morita and S

    H. Morita and S. Fujioka, Generation, measurement, and mod- eling of strong magnetic fields generated by laser-driven micro coils, Rev. Mod. Plasma Phys. 7, 13 (2023)

    2023

  27. [27]

    D. B. Schaeffer, A. F. A. Bott, M. Borghesi, K. A. Flippo, W. Fox, J. Fuchs, C. Li, F. H. Séguin, H.-S. Park, P. Tzeferacos, and L. Willingale, Proton imaging of high-energy-density labo- ratory plasmas, Rev. Mod. Phys. 95, 045007 (2023)

    2023

  28. [28]

    PlasmaPy (2024.7.0),

    PlasmaPy Community, “PlasmaPy (2024.7.0),” Zenodo, 2024, https://doi.org/10.5281/zenodo.12788848

    work page doi:10.5281/zenodo.12788848 2024

  29. [29]

    Zhang, L

    Y . Zhang, L. Gao, H. Ji, B. K. Russell, G. Pomraning, J. Griff- McMahon, S. R. Klein, C. C. Kuranz, and M. Wei, Diagnosing electric and magnetic fields in laser-driven coil targets, Plasma Phys. Controlled Fusion 67, 085039 (2025)

    2025

  30. [30]

    Chien, L

    A. Chien, L. Gao, S. Zhang, H. Ji, E. G. Blackman, W. Daughton, A. Stanier, A. Le, F. Guo, R. Follett, et al. , Non-thermal electron acceleration from magnetically driven reconnection in a laboratory plasma, Nat. Phys. 19, 254 (2023)

    2023

  31. [31]

    Bradford, M

    P. Bradford, M. Read, M. Ehret, L. Antonelli, M. Khan, N. Booth, K. Glize, D. Carroll, R. Clarke, R. Heathcote, et al. , Proton deflectometry of a capacitor coil target along two axes, High Power Laser Sci. Eng. 8, e11 (2020)

    2020

  32. [32]

    Bradford, A

    P. Bradford, A. Dearling, M. Ehret, L. Antonelli, N. Booth, D. Carroll, R. Clarke, K. Glize, R. Heathcote, M. Khan, et al. , Measuring magnetic fields in laser-driven coils with dual- axis proton deflectometry, Plasma Phys. Controlled Fusion 63, 084008 (2021)

    2021

  33. [33]

    Ciardi, S

    A. Ciardi, S. V . Lebedev, A. Frank, E. G. Blackman, J. P. Chittenden, C. Jennings, D. J. Ampleford, S. Bland, S. C. Bott, J. Rapley, et al. , The evolution of magnetic tower jets in the laboratory, Phys. Plasmas 14, 056501 (2007)

    2007

  34. [34]

    M. A. Haw, P. Wongwaitayakornkul, H. Li, and P. M. Bellan, Reverse current model for coronal mass ejection cavity forma- tion, Astrophys. J. Lett. 862, L15 (2018). 023317-8 PLASMA FLOW GENERATION AND PARTICLE … PHYSICAL REVIEW RESEARCH 8, 023317 (2026)

    2018

  35. [35]

    Kugland, D

    N. Kugland, D. Ryutov, P. Chang, R. Drake, G. Fiksel, D. Froula, S. Glenzer, G. Gregori, M. Grosskopf, M. Koenig, et al. , Self-organized electromagnetic field structures in laser- produced counter-streaming plasmas, Nat. Phys. 8, 809 (2012)

    2012

  36. [36]

    Huntington, F

    C. Huntington, F. Fiuza, J. Ross, A. Zylstra, R. Drake, D. Froula, G. Gregori, N. Kugland, C. Kuranz, M. Levy,et al.,O b - servation of magnetic field generation via the Weibel instability in interpenetrating plasma flows, Nat. Phys. 11, 173 (2015)

    2015

  37. [37]

    Schaeffer, F

    D. Schaeffer, F. Cruz, R. Dorst, F. Cruz, P. Heuer, C. Constantin, P. Pribyl, C. Niemann, L. Silva, and A. Bhattacharjee, Laser- driven, ion-scale magnetospheres in laboratory plasmas. I. Experimental platform and first results, Phys. Plasmas 29, 042901 (2022)

    2022

  38. [38]

    D. Yuan, Z. Lei, H. Wei, Z. Zhang, J. Zhong, Y . Li, Y . Ping, Y . Zhang, Y . Li, F. Wang,et al., Electron stochastic acceleration in laboratory-produced kinetic turbulent plasmas, Nat. Commun. 15, 5897 (2024)

    2024

  39. [39]

    Haberberger, S

    D. Haberberger, S. Tochitsky, F. Fiuza, C. Gong, R. A. Fonseca, L. O. Silva, W. B. Mori, and C. Joshi, Collisionless shocks in laser-produced plasma generate monoenergetic high-energy proton beams, Nat. Phys. 8, 95 (2012)

    2012

  40. [40]

    Meinecke, H

    J. Meinecke, H. Doyle, F. Miniati, A. R. Bell, R. Bingham, R. Crowston, R. Drake, M. Fatenejad, M. Koenig, Y . Kuramitsu, et al., Turbulent amplification of magnetic fields in laboratory laser-produced shock waves, Nat. Phys. 10, 520 (2014)

    2014

  41. [41]

    Fiuza, G

    F. Fiuza, G. Swadling, A. Grassi, H. Rinderknecht, D. Higginson, D. Ryutov, C. Bruulsema, R. Drake, S. Funk, S. Glenzer, et al. , Electron acceleration in laboratory-produced turbulent collisionless shocks, Nat. Phys. 16, 916 (2020)

    2020

  42. [42]

    W. Yao, A. Fazzini, S. Chen, K. Burdonov, P. Antici, J. Béard, S. Bolaños, A. Ciardi, R. Diab, E. Filippov, et al., Laboratory evidence for proton energization by collisionless shock surfing, Nat. Phys. 17, 1177 (2021)

    2021

  43. [43]

    Y . Bai, D. Zhang, Y . Zeng, J. Mao, L. Song, Y . Tian, and R. Li, Observation of sub-relativistic collisionless shock generation and breakout dynamics, Nat. Commun. 16, 3770 (2025)

    2025

  44. [44]

    H. Ji, J. Yoo, W. Fox, M. Yamada, M. Argall, J. Egedal, Y .-H. Liu, R. Wilder, S. Eriksson, W. Daughton, et al. , Laboratory study of collisionless magnetic reconnection, Space Sci. Rev. 219, 76 (2023)

    2023

  45. [45]

    Alfvén, Electric currents in cosmic plasmas, Rev

    H. Alfvén, Electric currents in cosmic plasmas, Rev. Geophys. 15, 271 (1977)

    1977

  46. [46]

    Raouafi, S

    N. Raouafi, S. Patsourakos, E. Pariat, P. R. Young, A. C. Sterling, A. Savcheva, M. Shimojo, F. Moreno-Insertis, C. DeV ore, V . Archontis,et al. , Solar coronal jets: Observations, theory, and modeling, Space Sci. Rev. 201, 1 (2016)

    2016

  47. [47]

    Sharykin, I

    I. Sharykin, I. Zimovets, and I. Myshyakov, Flare energy release at the magnetic field polarity inversion line during the M1.2 solar flare of 2015 March 15. II. Investigation of photospheric electric current and magnetic field variations using HMI 135 s vector magnetograms, Astrophys. J. 893, 159 (2020)

    2015

  48. [48]

    P. P. Kronberg, R. V . Lovelace, G. Lapenta, and S. A. Colgate, Measurement of the electric current in a kpc-scale jet, Astrophys. J. Lett. 741, L15 (2011)

    2011

  49. [49]

    Bell, Turbulent amplification of magnetic field and diffusive shock acceleration of cosmic rays, Mon

    A. Bell, Turbulent amplification of magnetic field and diffusive shock acceleration of cosmic rays, Mon. Not. R. Astron. Soc. 353, 550 (2004)

    2004

  50. [50]

    E. G. Zweibel, The microphysics and macrophysics of cosmic rays, Phys. Plasmas 20, 055501 (2013)

    2013

  51. [51]

    A. M. Beloborodov, Untwisting magnetospheres of neutron stars, Astrophys. J. 703, 1044 (2009)

    2009

  52. [52]

    Knight and P

    J. Knight and P. Sturrock, Reverse current in solar flares, Astrophys. J. 218, 306 (1977)

    1977

  53. [53]

    Battaglia and A

    M. Battaglia and A. O. Benz, Observational evidence for re- turn currents in solar flare loops, Astron. Astrophys. 487, 337 (2008)

    2008

  54. [54]

    G. D. Holman, M. J. Aschwanden, H. Aurass, M. Battaglia, P. C. Grigis, E. P. Kontar, W. Liu, P. Saint-Hilaire, and V . V . Zharkova, Implications of X-ray observations for electron ac- celeration and propagation in solar flares, Space Sci. Rev. 159, 107 (2011)

    2011

  55. [55]

    Schure, A

    K. Schure, A. Bell, L. O’C Drury, and A. Bykov, Diffusive shock acceleration and magnetic field amplification, Space Sci. Rev. 173, 491 (2012)

    2012

  56. [56]

    Lynden-Bell, Magnetic collimation by accretion discs of quasars and stars, Mon

    D. Lynden-Bell, Magnetic collimation by accretion discs of quasars and stars, Mon. Not. R. Astron. Soc. 279, 389 (1996)

    1996

  57. [57]

    Nakamura, H

    M. Nakamura, H. Li, and S. Li, Structure of magnetic tower jets in stratified atmospheres, Astrophys. J. 652, 1059 (2006)

    2006

  58. [58]

    023317-9

    See Supplemental Material at http://link.aps.org/supplemental/ 10.1103/yw76-d6kh for more details. 023317-9

    work page doi:10.1103/yw76-d6kh