arxiv: 2604.12000 · v1 · submitted 2026-04-13 · ⚛️ physics.space-ph · astro-ph.SR· physics.plasm-ph

Recognition: unknown

MMS Insights into CME Driven Sub-Alfv\'enic Solar Wind at 1 AU

Harsha Gurram , Li-Jen Chen , Matthew R. Argall , Subash Adhikari , Lynn B. Wilson , Jason R. Shuster , Victoria D. Wilder

Authors on Pith no claims yet

Pith reviewed 2026-05-10 16:06 UTC · model grok-4.3

classification ⚛️ physics.space-ph astro-ph.SRphysics.plasm-ph

keywords solar windCMEmagnetic cloudsub-AlfvénicMHD turbulenceelectron distributionsintermittencycross helicity

0 comments

The pith

Sub-Alfvénic solar wind inside a CME magnetic cloud shows hotter electrons and weak MHD turbulence with steeper spectral slopes.

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

The paper reports on measurements taken by the MMS spacecraft during a coronal mass ejection event in April 2023. Inside the magnetic cloud portion of the CME, the solar wind speed dropped below the Alfvén speed for about two hours. In this sub-Alfvénic region, electrons reached higher temperatures and their energy distributions showed excess high-energy particles along with a shortage in the 15 to 50 electron-volt range. The magnetic field variations there had no preferred direction of propagation, followed a power law steeper than the usual Kolmogorov spectrum without a break point, and displayed lower levels of intermittent bursts at ion scales. These traits together suggest that the turbulence is weak and magnetohydrodynamic in nature, similar to what is seen inside the magnetospheres of planets like Jupiter.

Core claim

Within the sub-Alfvénic interval of the magnetic cloud, electron temperatures are higher, with one-dimensional distributions revealing super-thermal tails and depletion between 15-50 eV; isolated electron heating occurs in the sheath. Magnetic field fluctuations exhibit negligible cross helicity, steeper-than-Kolmogorov scaling in the inertial range with no spectral break, reduced intermittency at ion and sub-ion scales, emerging intermittency at electron scales, and weak magnetic compressibility. These features indicate the presence of weak magnetohydrodynamic turbulence in the sub-Alfvénic magnetic cloud, resembling conditions in planetary magnetospheres.

What carries the argument

Comparison of electron velocity distributions and magnetic field fluctuation spectra between the two-hour sub-Alfvénic interval inside the magnetic cloud and the surrounding super-Alfvénic MC and sheath regions.

Load-bearing premise

That the two-hour sub-Alfvénic interval and chosen comparison regions are representative enough to attribute the electron and turbulence differences specifically to the sub-Alfvénic regime rather than other CME-specific or instrumental factors.

What would settle it

Detection of a different sub-Alfvénic magnetic cloud interval that displays strong cross-helicity and Kolmogorov-like spectral scaling in magnetic fluctuations would challenge the link between these properties and sub-Alfvénic conditions.

Figures

Figures reproduced from arXiv: 2604.12000 by Harsha Gurram, Jason R. Shuster, Li-Jen Chen, Lynn B. Wilson, Matthew R. Argall, Subash Adhikari, Victoria D. Wilder.

**Figure 1.** Figure 1: MMS 2 observations of sheath, super-Alv´enic MC (marked MC-super) and sub-Alfv´enic MC (marked MC-sub) driven by the CME on 2023-04-23. a) Magnetic field, b) ion velocity, c) omni-directional ion energy flux, d) electron density, e) electron temperature, f) Alfv´en Mach number (from OMNI) and g) omni-directional electron energy flux. The black dotted line in panel f) indicates MA = 1. approximately 0.5 cm−… view at source ↗

**Figure 2.** Figure 2: (a) Magnetic field components, (b) omni-directional ion energy flux, (c) electron density, (d) parallel and (e) anti-parallel electron energy fluxes highlighting the sub-Alfv´enic MC (MC-sub). Panels (f1) and (g1) show electron energy velocity distribution functions (VDFs) inside the super-Alfv´enic (MC-super) and sub-Alfv´enic (MC-sub) MCs, respectively. Dashed circles in the eVDFs mark the energy levels … view at source ↗

**Figure 3.** Figure 3: a) Magnetic field, b) omni-directional ion energy flux, c) electron density, e) parallel and f) anti-parallel electron energy fluxes inside CME sheath and super-Alfv´enic MC. Solar wind electrons VDFs inside f1) CME sheath, f2) CME sheath with localized energetic electrons and f3) super-Alfv´enic MC. Wave activity within the CME sheath: g) magnetic field power spectral density (PSD) with the electron cyclo… view at source ↗

**Figure 4.** Figure 4: Omnidirectional power spectrum of the magnetic field magnitude B within (a) the sub-Alfv´enic (MC-sub) and (b) super-Alfv´enic (MC-super) magnetic cloud intervals, whose plasma parameters are listed in [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

read the original abstract

We report the properties of electron distributions and turbulence during a Coronal Mass Ejection (CME) in April 2023 observed by Magnetospheric Multiscale (MMS). The CME exhibits a clear sheath and magnetic cloud (MC), and within the MC, the solar wind becomes sub-Alfv\'enic for two hours. We investigate plasma and turbulence properties of the sub-Alfv\'enic CME wind and compare them with those in the super-Alfv\'enic solar wind in the MC and CME sheath. Electrons within the sub-Alfv\'enic MC show significantly higher temperatures than those in the CME sheath and the super-Alfv\'enic MC, with their one-dimensional distributions revealing super-thermal tail and a depletion in electron populations between 15-50 eV. Within the CME sheath, isolated regions of electron heating are observed, where parallel energy flux is enhanced up to ~1 keV. Magnetic field fluctuations within the sub-Alfv\'enic MC interval exhibit negligible cross helicity and steeper-than-Kolmogorov scaling in the inertial range, with no clear spectral break. These fluctuations also show reduced intermittency at ion and sub-ion scales, emerging intermittency at electron scales, and weak magnetic compressibility. Together, these observations point to the presence of weak magnetohydrodynamic (MHD) turbulence within the sub-Alfv\'enic MC, resembling conditions commonly observed in planetary magnetospheres such as Jupiter's.

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.

Desk Editor's Note private letter to a colleague

The paper supplies useful MMS case-study data on electron distributions and turbulence inside one two-hour sub-Alfvénic interval of a 2023 CME magnetic cloud, but the attribution of those features specifically to the sub-Alfvénic regime rests on limited intra-event comparisons.

read the letter

The main thing to know is that this work documents concrete plasma and turbulence properties during a rare sub-Alfvénic solar wind stretch at 1 AU. Electrons appear hotter with superthermal tails and a clear depletion between 15-50 eV, while magnetic fluctuations show negligible cross-helicity, steeper-than-Kolmogorov inertial-range slopes, no spectral break, reduced ion-scale intermittency, and weak compressibility. The authors contrast these with the super-Alfvénic MC and sheath portions of the same CME event using MMS measurements. That combination of details is new relative to earlier reports on sub-Alfvénic intervals. The paper does a straightforward job of presenting the observational contrasts and linking them to weak MHD turbulence conditions that echo some planetary magnetosphere regimes. For modelers who need in-situ anchors for CME-driven solar wind or space-weather coupling, these numbers and spectral shapes are worth having on record. The central limitation is the single two-hour interval and the fact that all three regions sit inside the same CME structure. Differences could trace to flux-rope geometry, expansion, or trajectory effects rather than the local Alfvén Mach number crossing unity. The stress-test concern holds up: without multi-event statistics or control intervals outside CMEs, the claim that these signatures indicate a distinct weak-turbulence state stays tied to this event's particulars. Interval selection criteria and error handling are not visible in the abstract, so the full text needs to demonstrate they are robust. This is for solar-wind turbulence and space-plasma researchers who work with case studies of unusual regimes. A reader who wants specific electron and spectral features from sub-Alfvénic flow will extract value from the reported measurements. It deserves peer review because the data come from a high-resolution mission and fill a genuine observational gap, even if revisions will be needed to address the single-event scope and strengthen the attribution.

Referee Report

3 major / 2 minor

Summary. The manuscript presents in-situ MMS observations of electron distributions and magnetic field turbulence during a CME event in April 2023. It identifies a two-hour sub-Alfvénic interval inside the magnetic cloud and contrasts its properties with the super-Alfvénic portion of the MC and the CME sheath, concluding that the sub-Alfvénic region hosts weak MHD turbulence with characteristics similar to those in planetary magnetospheres.

Significance. The observations provide direct measurements of plasma conditions in an uncommon sub-Alfvénic solar wind environment at 1 AU using high-resolution MMS instrumentation. This could be significant for understanding turbulence transitions across the Alfvén critical surface and analogies to magnetospheric plasmas, though the single-event scope restricts its immediate impact on broader theory.

major comments (3)

[Abstract and Results] The turbulence diagnostics (negligible cross helicity, steeper-than-Kolmogorov scaling, no spectral break, scale-dependent intermittency, weak compressibility) are presented for only one 2-hour interval. Without quantitative spectral index values, error bars, or details on how the inertial range was identified, the distinction from Kolmogorov scaling and the 'weak turbulence' interpretation cannot be fully assessed.
[Methods or Data Selection] No information is provided on the criteria for selecting the sub-Alfvénic interval, the comparison intervals, or any statistical tests used to establish differences in electron temperatures or turbulence properties between regions.
[Discussion] The inference that these features indicate 'weak MHD turbulence within the sub-Alfvénic MC, resembling conditions commonly observed in planetary magnetospheres' is weakened by the lack of multi-event analysis; all data come from the same CME, so CME-specific effects cannot be ruled out as the source of the observed differences.

minor comments (2)

[Abstract] The abstract states 'significantly higher temperatures' without providing the actual temperature values or the basis for significance.
[Figure captions] Ensure figure captions explicitly describe what each panel shows regarding the different solar wind regions (sub-Alfvénic, super-Alfvénic, sheath).

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for their constructive comments on our manuscript. We have prepared point-by-point responses below and will revise the manuscript to address the concerns where possible, improving clarity on methods, quantitative results, and limitations.

read point-by-point responses

Referee: [Abstract and Results] The turbulence diagnostics (negligible cross helicity, steeper-than-Kolmogorov scaling, no spectral break, scale-dependent intermittency, weak compressibility) are presented for only one 2-hour interval. Without quantitative spectral index values, error bars, or details on how the inertial range was identified, the distinction from Kolmogorov scaling and the 'weak turbulence' interpretation cannot be fully assessed.

Authors: We agree that quantitative details are needed for full assessment. The full manuscript contains the underlying spectral analysis; in revision we will explicitly report the fitted spectral indices with uncertainties (e.g., for the inertial-range power-law fits), describe the precise frequency/wavenumber bounds used to identify the inertial range, and note the fitting procedure. These additions will allow readers to evaluate the steeper-than-Kolmogorov claim and the weak-turbulence interpretation directly. revision: yes
Referee: [Methods or Data Selection] No information is provided on the criteria for selecting the sub-Alfvénic interval, the comparison intervals, or any statistical tests used to establish differences in electron temperatures or turbulence properties between regions.

Authors: We will expand the Methods section to detail the selection criteria: the sub-Alfvénic interval is defined where the Alfvén Mach number remains below 1 for the full two-hour period inside the magnetic cloud, with explicit start/end times and the plasma parameters used to compute M_A. The super-Alfvénic MC and sheath comparison intervals will be defined by their temporal boundaries relative to the MC leading edge. We will also report the quantitative temperature differences (means and standard deviations) and any statistical comparisons performed. revision: yes
Referee: [Discussion] The inference that these features indicate 'weak MHD turbulence within the sub-Alfvénic MC, resembling conditions commonly observed in planetary magnetospheres' is weakened by the lack of multi-event analysis; all data come from the same CME, so CME-specific effects cannot be ruled out as the source of the observed differences.

Authors: We acknowledge this is a single-event case study, which inherently limits the ability to separate CME-specific effects from general sub-Alfvénic behavior. In revision we will explicitly frame the conclusions as applying to this rare observed interval, add a statement that additional events would be required to test generality, and soften the analogy to magnetospheric turbulence to reflect the single-CME scope. No further events are available in the present MMS dataset for this CME. revision: partial

standing simulated objections not resolved

The single-event nature of the study prevents multi-event statistical analysis or ruling out CME-specific effects without additional data.

Circularity Check

0 steps flagged

No significant circularity: purely observational data analysis

full rationale

The paper reports direct MMS observations of electron distributions and magnetic field fluctuations during one April 2023 CME event, comparing a 2-hour sub-Alfvénic MC interval against super-Alfvénic MC and sheath regions from the same event. No derivations, equations, fitted parameters, or predictions are present; all reported properties (temperatures, spectral slopes, cross-helicity, intermittency, compressibility) are measured quantities. The analysis contains no self-referential definitions, load-bearing self-citations, or reductions of results to inputs by construction, rendering the derivation chain empty and the findings self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work is observational and relies on standard interpretations of MMS particle and field data; no free parameters, ad-hoc axioms, or new entities are introduced in the abstract.

axioms (1)

standard math Standard plasma physics assumptions for interpreting electron velocity distributions and magnetic fluctuation spectra from spacecraft data
Used to classify turbulence regimes and electron heating without additional justification in the abstract.

pith-pipeline@v0.9.0 · 5592 in / 1403 out tokens · 76128 ms · 2026-05-10T16:06:09.334247+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

68 extracted references · 67 canonical work pages

[1]

1991, Journal of Geophysical Research: Space Physics, 96, 5847, doi: https://doi.org/10.1029/91JA00087

work page doi:10.1029/91ja00087 1991
[2]

2026, The Astrophysical Journal, 997, 259, doi: 10.3847/1538-4357/ae2c78

Adhikari, S., Bandyopadhyay, R., Goodwill, J., et al. 2026, The Astrophysical Journal, 997, 259, doi: 10.3847/1538-4357/ae2c78

work page doi:10.3847/1538-4357/ae2c78 2026
[3]

2022, Universe, 8, 338, doi: 10.3390/universe8070338

Alberti, T., Benella, S., Carbone, V., et al. 2022, Universe, 8, 338, doi: 10.3390/universe8070338

work page doi:10.3390/universe8070338 2022
[4]

2009, Physical Review Letters, 103, doi: 10.1103/physrevlett.103.165003

Alexandrova, O., Saur, J., Lacombe, C., et al. 2009, Physical Review Letters, 103, doi: 10.1103/physrevlett.103.165003

work page doi:10.1103/physrevlett.103.165003 2009
[5]

R., Chen, L.-J., Lugaz, N., et al

Argall, M. R., Chen, L.-J., Lugaz, N., et al. 2025, https://arxiv.org/abs/2505.13645

work page arXiv 2025
[6]

T., Stevens, M

Badman, S. T., Stevens, M. L., Bale, S. D., et al. 2025, arXiv e-prints. https://arxiv.org/abs/2509.17149

work page arXiv 2025
[7]

J., Szalay, J

Bandyopadhyay, R., McComas, D. J., Szalay, J. R., et al. 2021, Geophysical Research Letters, 48, e2021GL095006, doi: https://doi.org/10.1029/2021GL095006

work page doi:10.1029/2021gl095006 2021
[8]

H., McComas, D

Bandyopadhyay, R., Matthaeus, W. H., McComas, D. J., et al. 2022, ApJL, 926, L1, doi: 10.3847/2041-8213/ac4a5c Berˇ ciˇ c, L., Larson, D., Whittlesey, P., et al. 2020, The Astrophysical Journal, 892, 88, doi: 10.3847/1538-4357/ab7b7a

work page doi:10.3847/2041-8213/ac4a5c 2022
[9]

2006, PhRvL, 96, 115002, doi: 10.1103/PhysRevLett.96.115002

Boldyrev, S. 2006, Phys. Rev. Lett., 96, 115002, doi: 10.1103/PhysRevLett.96.115002

work page doi:10.1103/physrevlett.96.115002 2006
[10]

Borovsky, J. E. 2021, Frontiers in Astronomy and Space Sciences, 8, doi: 10.3389/fspas.2021.646443

work page doi:10.3389/fspas.2021.646443 2021
[11]

A., Bale, S

Bowen, T. A., Bale, S. D., Bonnell, J. W., et al. 2018, The Astrophysical Journal. https://arxiv.org/abs/1805.02739

work page arXiv 2018
[12]

F., Jackman, C

Bowers, C. F., Jackman, C. M., Jia, X., et al. 2025, Journal of Geophysical Research: Space Physics, doi: 10.1029/2024JA033619

work page doi:10.1029/2024ja033619 2025
[13]

2017, MNRAS, 472, 1052, doi: 10.1093/mnras/stx2008

Bruno, R., Telloni, D., DeIure, D., & Pietropaolo, E. 2017, MNRAS, 472, 1052, doi: 10.1093/mnras/stx2008

work page doi:10.1093/mnras/stx2008 2017
[14]

L., Torbert, R

Burch, J. L., Torbert, R. B., Phan, T. D., et al. 2016, Science, 352, aaf2939, doi: 10.1126/science.aaf2939

work page doi:10.1126/science.aaf2939 2016
[15]

L., Chen, L.-J., Sarantos, M., et al

Burkholder, B. L., Chen, L.-J., Sarantos, M., et al. 2024, Geophysical Research Letters, 51, e2024GL108311, doi: 10.1029/2024GL108311

work page doi:10.1029/2024gl108311 2024
[16]

F., Sittler, E., Mariani, F., & Schwenn, R

Burlaga, L. F., Sittler, E., Mariani, F., & Schwenn, R. 1981, Journal of Geophysical Research: Space Physics, 86, 6673, doi: 10.1029/JA086iA08p06673

work page doi:10.1029/ja086ia08p06673 1981
[17]

2024, Geophysical Research Letters, 51, e2024GL108894, doi: https://doi.org/10.1029/2024GL108894

Chen, L.-J., Gershman, D., Burkholder, B., et al. 2024, Geophysical Research Letters, 51, e2024GL108894, doi: https://doi.org/10.1029/2024GL108894

work page doi:10.1029/2024gl108894 2024
[18]

Burkholder, B. L. 2025, Geophysical Research Letters, 52, e2024GL113416, doi: https://doi.org/10.1029/2024GL113416

work page doi:10.1029/2024gl113416 2025
[19]

2025, The Astrophysical Journal Letters, 992, L11, doi: 10.3847/2041-8213/ae0b56

Ervin, T., Mallet, A., Eriksson, S., et al. 2025, The Astrophysical Journal Letters, 992, L11, doi: 10.3847/2041-8213/ae0b56

work page doi:10.3847/2041-8213/ae0b56 2025
[20]

2021, Monthly Notices of the Royal Astronomical Society, 502, 5821, doi: 10.1093/mnras/stab387

Grasso, D. 2021, Monthly Notices of the Royal Astronomical Society, 502, 5821, doi: 10.1093/mnras/stab387

work page doi:10.1093/mnras/stab387 2021
[21]

V., Newell, A

Galtier, S., Nazarenko, S. V., Newell, A. C., & Pouquet, A. 2000, Journal of Plasma Physics, 63, 447, doi: 10.1017/S0022377899008284

work page doi:10.1017/s0022377899008284 2000
[22]

J., Pfaff, R

Gershman, D. J., Pfaff, R. F., Khotyaintsev, Y. V., Burch, J. L., et al. 2019, Journal of Geophysical Research: Space Physics, 124, e2019JA026980, doi: 10.1029/2019JA026980

work page doi:10.1029/2019ja026980 2019
[23]

J., Avanov, L

Gershman, D. J., Avanov, L. A., Boardsen, S. A., et al. 2017, Journal of Geophysical Research: Space Physics, 122, 11,548, doi: https://doi.org/10.1002/2017JA024518

work page doi:10.1002/2017ja024518 2017
[24]

2: Strong alfvenic turbulence

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

work page doi:10.1086/175121 1995
[25]

1997, The Astrophysical Journal, 485, 680, doi: 10.1086/304442

Goldreich, P., & Sridhar, S. 1997, The Astrophysical Journal, 485, 680, doi: 10.1086/304442

work page doi:10.1086/304442 1997
[26]

W., Ala-Lahti, M., Palmerio, E., Kilpua, E

Good, S. W., Ala-Lahti, M., Palmerio, E., Kilpua, E. K. J., & Osmane, A. 2020, The Astrophysical Journal, 893, 110, doi: 10.3847/1538-4357/ab7fa2

work page doi:10.3847/1538-4357/ab7fa2 2020
[27]

Gosling, J. T. 1993, J. Geophys. Res., 98, 18937, doi: 10.1029/93JA01896

work page doi:10.1029/93ja01896 1993
[28]

R., Chen, L.-J., et al

Gurram, H., Shuster, J. R., Chen, L.-J., et al. 2025, Geophysical Research Letters, 52, e2024GL111931, doi: https://doi.org/10.1029/2024GL111931

work page doi:10.1029/2024gl111931 2025
[29]

Hajra, R., & Tsurutani, B. T. 2022, The Astrophysical Journal, 926, 186, doi: 10.3847/1538-4357/ac4471

work page doi:10.3847/1538-4357/ac4471 2022
[30]

S., Forman, M., & Oughton, S

Horbury, T. S., Forman, M., & Oughton, S. 2008, PhRvL, 101, 175005, doi: 10.1103/PhysRevLett.101.175005

work page doi:10.1103/physrevlett.101.175005 2008
[31]

2025, The Astrophysical Journal, 989, 133, doi: 10.3847/1538-4357/ada3d3

Vourlidas, A. 2025, The Astrophysical Journal, 989, 133, doi: 10.3847/1538-4357/ada3d3

work page doi:10.3847/1538-4357/ada3d3 2025
[32]

H., & Szalay, J

Janser, S., Saur, J., Clark, G., Sulaiman, A. H., & Szalay, J. R. 2022, Journal of Geophysical Research: Space Physics, 127, e2022JA030675, doi: https://doi.org/10.1029/2022JA030675

work page doi:10.1029/2022ja030675 2022
[33]

D., Ran, H., & Cheng, W

Jiao, Y., Liu, Y. D., Ran, H., & Cheng, W. 2023, The Astrophysical Journal, 960, 42, doi: 10.3847/1538-4357/ad0dfe

work page doi:10.3847/1538-4357/ad0dfe 2023
[34]

Jokipii, J. R. 1973, ARA&A, 11, 1, doi: 10.1146/annurev.aa.11.090173.000245

work page doi:10.1146/annurev.aa.11.090173.000245 1973
[35]

Kilpua, E. K. J., Good, S. W., Ala-Lahti, M., et al. 2021, Frontiers in Astronomy and Space Sciences, 7, 109, doi: 10.3389/fspas.2020.610278 12

work page doi:10.3389/fspas.2020.610278 2021
[36]

Kilpua, E. K. J., Koskinen, H. E. J., & Pulkkinen, T. I. 2017, Living Reviews in Solar Physics, 14, 5, doi: 10.1007/s41116-017-0009-6

work page doi:10.1007/s41116-017-0009-6 2017
[37]

Kilpua, E. K. J., Fontaine, D., Good, S. W., et al. 2020, Annales Geophysicae, 38, 999, doi: 10.5194/angeo-38-999-2020

work page doi:10.5194/angeo-38-999-2020 2020
[38]

W., & Burlaga, L

Klein, L. W., & Burlaga, L. F. 1982, Journal of Geophysical Research: Space Physics, 87, 613, doi: 10.1029/JA087iA02p00613

work page doi:10.1029/ja087ia02p00613 1982
[39]

2003, The Astrophysical Journal, 582, 1220, doi: 10.1086/344676

Lithwick, Y., & Goldreich, P. 2003, The Astrophysical Journal, 582, 1220, doi: 10.1086/344676

work page doi:10.1086/344676 2003
[40]

Marsch, E., & Tu, C. Y. 1994, Annales Geophysicae, 12, 1127, doi: 10.1007/s00585-994-1127-8

work page doi:10.1007/s00585-994-1127-8 1994
[41]

H., & Goldstein, M

Matthaeus, W. H., & Goldstein, M. L. 1982, Journal of Geophysical Research: Space Physics, 87, 6011, doi: https://doi.org/10.1029/JA087iA08p06011

work page doi:10.1029/ja087ia08p06011 1982
[42]

1996, The Astrophysical Journal, 465, 845, doi: 10.1086/177472

Ng, C.-S., & Bhattacharjee, A. 1996, The Astrophysical Journal, 465, 845, doi: 10.1086/177472

work page doi:10.1086/177472 1996
[43]

2002, Journal of Geophysical Research: Space Physics, 107, SSH 6, doi: https://doi.org/10.1029/2002JA009331

Pagel, C., & Balogh, A. 2002, Journal of Geophysical Research: Space Physics, 107, SSH 6, doi: https://doi.org/10.1029/2002JA009331

work page doi:10.1029/2002ja009331 2002
[44]

N., Chasapis, A., Bandyopadhyay, R., et al

Parashar, T. N., Chasapis, A., Bandyopadhyay, R., et al. 2018, PhRvL, 121, 265101, doi: 10.1103/PhysRevLett.121.265101

work page doi:10.1103/physrevlett.121.265101 2018
[45]

C., & Boldyrev, S

Perez, J. C., & Boldyrev, S. 2009, Phys. Rev. Lett., 102, 025003, doi: 10.1103/PhysRevLett.102.025003

work page doi:10.1103/physrevlett.102.025003 2009
[46]

C., Bourouaine, S., Chen, C

Perez, J. C., Bourouaine, S., Chen, C. H. K., & Raouafi, N. E. 2021, A&A, 650, A22, doi: 10.1051/0004-6361/202039879

work page doi:10.1051/0004-6361/202039879 2021
[47]

2010, ApJ, 714, 937, doi: 10.1088/0004-637X/714/1/937

Perri, S., & Balogh, A. 2010, ApJ, 714, 937, doi: 10.1088/0004-637X/714/1/937

work page doi:10.1088/0004-637x/714/1/937 2010
[48]

Podesta, J. J. 2009, The Astrophysical Journal, 698, 986, doi: 10.1088/0004-637X/698/2/986

work page doi:10.1088/0004-637x/698/2/986 2009
[49]

J., & Borovsky, J

Podesta, J. J., & Borovsky, J. E. 2010, Physics of Plasmas, 17, 112905, doi: 10.1063/1.3505092

work page doi:10.1063/1.3505092 2010
[50]

2016, Space Science Reviews, 199, 331, doi: 10.1007/s11214-016-0245-4

Pollock, C., Moore, T., Jacques, A., et al. 2016, Space Science Reviews, 199, 331, doi: 10.1007/s11214-016-0245-4

work page doi:10.1007/s11214-016-0245-4 2016
[51]

T., Anderson, B

Russell, C. T., Anderson, B. J., Baumjohann, W., et al. 2016, SSRv, 199, 189, doi: 10.1007/s11214-014-0057-3

work page doi:10.1007/s11214-014-0057-3 2016
[52]

C., & Olson, J

Samson, J. C., & Olson, J. V. 1980, Geophysical Journal of the Royal Astronomical Society, 61, 115, doi: 10.1111/j.1365-246X.1980.tb04308.x

work page doi:10.1111/j.1365-246x.1980.tb04308.x 1980
[53]

2021, Frontiers in Astronomy and Space Sciences, 8, 56, doi: 10.3389/fspas.2021.624602

Saur, J. 2021, Frontiers in Astronomy and Space Sciences, 8, 56, doi: 10.3389/fspas.2021.624602

work page doi:10.3389/fspas.2021.624602 2021
[54]

Saur, J., Politano, H., Pouquet, A., & Matthaeus, W. H. 2002, A&A, 386, 699, doi: 10.1051/0004-6361:20020305

work page doi:10.1051/0004-6361:20020305 2002
[55]

H., & Dmitruk, P

Servidio, S., Matthaeus, W. H., & Dmitruk, P. 2008, Physical Review Letters, 100, 095005, doi: 10.1103/PhysRevLett.100.095005

work page doi:10.1103/physrevlett.100.095005 2008
[56]

W., Stawarz, J

Smith, C. W., Stawarz, J. E., Vasquez, B. J., Forman, M. A., & MacBride, B. T. 2009, Phys. Rev. Lett., 103, 201101, doi: 10.1103/PhysRevLett.103.201101

work page doi:10.1103/physrevlett.103.201101 2009
[57]

1: Weak Alfvenic turbulence

Sridhar, S., & Goldreich, P. 1994, ApJ, 432, 612, doi: 10.1086/174600

work page doi:10.1086/174600 1994
[58]

Stix, T. H. 1992, Waves in plasmas

1992
[59]

Taylor, G. I. 1938, Proceedings of the Royal Society of London Series A, 164, 476, doi: 10.1098/rspa.1938.0032

work page doi:10.1098/rspa.1938.0032 1938
[60]

J., Forman, M

Vasquez, B. J., Forman, M. A., Coburn, J. T., Smith, C. W., & Stawarz, J. E. 2018, The Astrophysical Journal, 867, 156, doi: 10.3847/1538-4357/aae6c6

work page doi:10.3847/1538-4357/aae6c6 2018
[61]

2021, in Astrophysics and Space Science Library, Vol

Vocks, C. 2021, in Astrophysics and Space Science Library, Vol. 464, Kappa Distributions; From Observational Evidences via Controversial Predictions to a Consistent Theory of Nonequilibrium Plasmas, ed. M. Lazar & H. Fichtner, 125–143, doi: 10.1007/978-3-030-82623-9 7

work page doi:10.1007/978-3-030-82623-9 2021
[62]

2003, ApJ, 593, 1134, doi: 10.1086/376682

Vocks, C., & Mann, G. 2003, ApJ, 593, 1134, doi: 10.1086/376682

work page doi:10.1086/376682 2003
[63]

2008, A&A, 480, 527, doi: 10.1051/0004-6361:20078826 ˇStver´ ak,ˇS., Maksimovic, M., Tr´ avn´ ıˇ cek, P

Vocks, C., Mann, G., & Rausche, G. 2008, A&A, 480, 527, doi: 10.1051/0004-6361:20078826 ˇStver´ ak,ˇS., Maksimovic, M., Tr´ avn´ ıˇ cek, P. M., et al. 2009, Journal of Geophysical Research (Space Physics), 114, A05104, doi: 10.1029/2008JA013883

work page doi:10.1051/0004-6361:20078826 2008
[64]

F., & Howard, T

Webb, D. F., & Howard, T. A. 2012, Living Reviews in Solar Physics, 9, 3, doi: 10.12942/lrsp-2012-3

work page doi:10.12942/lrsp-2012-3 2012
[65]

2009, Journal of Geophysical Research: Space Physics, 114, doi: https://doi.org/10.1029/2009JA014067

Yordanova, E., Balogh, A., Noullez, A., & von Steiger, R. 2009, Journal of Geophysical Research: Space Physics, 114, doi: https://doi.org/10.1029/2009JA014067

work page doi:10.1029/2009ja014067 2009
[66]

P., Zhao, L

Zank, G. P., Zhao, L. L., Adhikari, L., et al. 2022, ApJL, 926, L16, doi: 10.3847/2041-8213/ac51da

work page doi:10.3847/2041-8213/ac51da 2022
[67]

Y., Yuan, Z

Zhang, J., Huang, S. Y., Yuan, Z. G., et al. 2022, ApJ, 937, 70, doi: 10.3847/1538-4357/ac8c34

work page doi:10.3847/1538-4357/ac8c34 2022
[68]

L., Zank, G

Zhao, L. L., Zank, G. P., Adhikari, L., et al. 2022, ApJL, 934, L36, doi: 10.3847/2041-8213/ac8353

work page doi:10.3847/2041-8213/ac8353 2022