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Polarization ratios of turbulent Langmuir/$\mathcal{Z}$-mode waves generated by electron beams in magnetized solar wind plasmas

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read The paper's central claim is that random density fluctuations, not slow electrostatic decay, drive near-total perpendicular polarization of beam-driven solar wind Langmuir/Z-mode waves.

desk verdict Density fluctuations, not electrostatic decay, drive large polarization ratios via LMC in 2D/3V PIC; the main caveat is missing 3D validation. read the letter →

arxiv 2506.18429 v1 pith:FPLOGJEV submitted 2025-06-23 physics.plasm-ph

Francisco Javier Polanco-Rodríguez , Catherine Krafft , Philippe Savoini This is my paper · ORCID
classification physics.plasm-ph
keywords polarizationratioLangmuirwavesZ-modelinearmodeconversiondensityfluctuationstypeIIIsolarradioburstsparticle-in-cellsimulationswind
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 argues that the large perpendicular polarization ratios of beam-generated Langmuir/Z-mode waves in type III solar radio bursts are produced chiefly by linear mode conversion at constant frequency: wave packets scattering on random density fluctuations convert, within a few thousand plasma periods, into electromagnetic slow extraordinary Z-mode waves whose perpendicular field dominates. Using long 2D/3V particle-in-cell simulations in which virtual satellites record thousands of waveforms the way spacecraft do, the paper shows polarization ratios reaching $F\simeq 1$ when the average density-fluctuation level satisfies $\Delta N \gtrsim 3(v_T/v_b)^2$, and much lower, slower growth otherwise. The sharp jump at this threshold reproduces the observed break near $v_b\simeq 0.08c$ and yields a practical diagnostic: at the beam speed where $F$ jumps, $\Delta N\simeq 3(v_T/v_b)^2$. A sympathetic reading is that a fast, efficient linear route from electrostatic turbulence to electromagnetic radiation explains high $F$ events better than the much slower nonlinear electrostatic decay.

What carries the argument

The load-bearing object is the polarization ratio $F=|E_\perp|^2/|E|^2$ sampled at frequencies near $\omega_p$, together with the threshold condition $\Delta N\gtrsim 3(v_T/v_b)^2$ that separates the scattering-dominated regime from the decay-dominated regime. The process carrying the argument is linear mode conversion at constant frequency (LMC): when $LZ$ waves scatter on random density fluctuations $\delta n$, their energy is transferred to electromagnetic slow extraordinary $Z$-mode waves whose frequencies lie below $\omega_p$ down to the $Z$-mode cutoff; near that cutoff the electric field is almost entirely perpendicular, so $F$ approaches 1. Virtual satellites moving through the simulation box supply the thousands of waveforms whose distributions connect $F$ to beam velocity, magnetization, temperature, and density-fluctuation level.

What would settle it

A three-dimensional particle-in-cell run with the same parameters ($\Delta N=0.05$, $\omega_c/\omega_p=0.07$, $v_b=12.7v_T$) that fails to show the sharp rise in mean polarization ratio at $\Delta N\simeq 3(v_T/v_b)^2$, or that does not reach values near 0.45 within about $2000\,\omega_p^{-1}$, would show the claimed LMC dominance and the threshold diagnostic depend on the two-dimensional geometry. In observations, a spacecraft survey finding no jump in $F$ near $v_b\simeq 0.08c$ in regions with $\Delta N\simeq 0.01$ would contradict the inferred relation.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that random density fluctuations $\delta n$ are the key factor controlling the polarization ratio $F=|E_\perp|^2/|E|^2$ of turbulent Langmuir/Z-mode ($LZ$) waves and of the electromagnetic emissions they radiate at the plasma frequency. In a homogeneous weakly magnetized plasma, $F$ grows slowly, from about 0.1 to 0.25--0.3, as electrostatic decay cascades $LZ$ energy to smaller and more oblique wavevectors over tens of thousands of $\omega_p^{-1}$. In a randomly inhomogeneous plasma with $\Delta N\gtrsim 3(v_T/v_b)^2$, the same ratio rises within roughly $2000\,\omega_p^{-1}$ to time-averaged values near 0.45, with distributions extending to $F\simeq 1$, because $LZ$ waves trapped in density wells are linearly converted at constant frequency into electromagnetic $Z$-mode waves near their cutoff, where the field is nearly perpendicular and circularly polarized. The paper therefore presents linear mode conversion (LMC) as the fastest and most efficient producer of large polarization ratios, and electrostatic decay as a secondary process that matters mainly below the threshold. It also finds that increasing magnetization $\omega_c/\omega_p\gtrsim 0.2$ suppresses large $F$, in part because the $Z$-mode cutoff moves farther below $\omega_p$ and the condition $\Delta N\gtrsim \omega_c/2\omega_p$ becomes harder to satisfy.

Load-bearing premise

The simulations are two-dimensional, and the paper assumes, without testing in three dimensions, that the same wave conversion efficiency and polarization statistics hold in the real solar wind.

Editorial extensions

If this is right

  • In randomly inhomogeneous solar wind regions with $\Delta N\gtrsim 3(v_T/v_b)^2$, wave packets with $F$ up to about 1 should be common, appearing within a few thousand $\omega_p^{-1}$, and their distributions should stay nearly steady over time.
  • In weakly fluctuating plasma ($\Delta N\lesssim 3(v_T/v_b)^2$), polarization ratios should grow slowly through electrostatic decay and saturate near 0.25--0.3 after tens of thousands of $\omega_p^{-1}$, below the LMC-dominated values.
  • At the beam velocity where observed $F$ rises sharply, the estimate $\Delta N\simeq 3(v_T/v_b)^2$ gives the average density-fluctuation level; using $v_b\simeq 0.08c$ and $T_e\simeq 10$ eV near 1 au yields $\Delta N\simeq 0.01$.
  • Detecting circularly polarized $Z$-mode waves near their cutoff implies $\Delta N\gtrsim \omega_c/(2\omega_p)$, a lower bound on density fluctuations once the local magnetization is known.
  • For $\omega_c/\omega_p\gtrsim 0.2$, large polarization ratios become rarer, so the shape of the $F$ distribution can also serve as a magnetization diagnostic.

Reading between the lines

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

  • An extension left implicit in the paper: the threshold relation is a calibration curve that could be inverted against spacecraft data along type III beam paths to map $\Delta N$ as a function of heliocentric distance, not just at 1 au.
  • Since the simulations are 2D/3V, a natural test is a three-dimensional run with identical parameters; if three-dimensional wavevector distributions change the linear-mode-conversion rate, the numerical constant 3 in the threshold and the quantitative $F$ values could shift without changing the qualitative mechanism.
  • The same constant-frequency conversion route may apply to other beam-driven plasma emissions, making near-cutoff $Z$-mode detections a generic marker of stochastic density inhomogeneity.
  • The virtual-satellite PDFs could be used for parameter inversion: with density-fluctuation levels known independently, observed $F$ distributions could be matched to simulation PDFs to constrain electron temperature, beam velocity, or local magnetization.
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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 2D/3V Particle-In-Cell simulations, analyzed through thousands of 'virtual satellite' waveforms, to study the polarization ratio F=|E_perp|^2/|E|^2 of beam-generated Langmuir/Z-mode (LZ) waves and near-omega_p electromagnetic emissions in weakly magnetized, randomly inhomogeneous plasmas. In homogeneous plasmas, F grows slowly as electrostatic decay cascades LZ energy to small wavenumbers; in plasmas with density fluctuations Delta_N >= 3(v_T/v_b)^2, F rises rapidly toward values near 1. The authors attribute this fast growth to linear mode conversion (LMC) at constant frequency of LZ waves scattering on density fluctuations, converting them into Z-mode waves near cutoff. They show F_{k,omega} maps with large F near the Z-mode cutoff, correlate the growth of F with Z-mode electromagnetic energy, and propose using the sharp rise at Delta_N ~ 3(v_T/v_b)^2 as a diagnostic of solar-wind density fluctuation levels.

Significance. If the proposed mechanism is correct, the paper addresses a long-standing puzzle concerning the origin of large polarization ratios in type III solar radio burst source regions, and it provides a falsifiable diagnostic relation (Delta_N ~ 3(v_T/v_b)^2 at the beam speed where F jumps) that connects simulation to spacecraft observations. The work has clear strengths: the use of a large number (N_w=1000) of virtual-satellite waveforms, direct Fourier-space polarization maps in Figure 3g-i, and the time-correlation analysis between F and Z-mode energy in Figure 4c-d. These features make the qualitative conclusion that LMC is faster than electrostatic decay reasonably well supported within the 2D simulation geometry. The main significance is, however, contingent on the extrapolation from 2D/3V simulations to the three-dimensional solar wind, which is not validated in the manuscript.

major comments (3)
  1. [§2.1, §5] The central generalization from the simulated 2D/3V geometry to the solar wind is not supported by any 3D validation. In the simulations, wavevectors are confined to the (x,y) plane and density fluctuations are invariant along z; both the intrinsic statistics of F for a given wavevector distribution and the efficiency of LMC depend on the full 3D angular structure of k and on the orientation of density gradients relative to k. The abstract and §5 state that LMC is 'the most efficient and fast process' in randomly inhomogeneous plasmas and propose Delta_N ~ 3(v_T/v_b)^2 as a solar-wind diagnostic (Figure 3f), but no 3D run or quantitative estimate of the 2D-to-3D error is provided. The companion paper (Krafft et al. 2025) treats LMC in 2D/3D analytically, but it does not supply 3D beam-driven turbulent statistics or virtual-satellite PDFs. Please add at least one representative 3D PIC validation run, or explicitly restrict the quantitative claims, including the threshold and the diagnostic, to 2D geometry and give an estimate of the expected 3D error.
  2. [§4.1, Figure 3f] The x-axis of Figure 3f is Delta_N v_b^2/(3 v_T^2), which normalizes by the very condition being tested. With only two values of Delta_N (0.025 and 0.05) and five beam speeds, the visual jump near x=1 does not by itself establish the sharp threshold as strongly as the text claims. The threshold condition is independently motivated by Ryutov (1969) and Krafft et al. (2013), but the diagnostic claim requires showing the raw dependence of <F>_{w,t} on Delta_N and v_b/v_T separately, and ideally checking whether an alternative scaling collapses the data equally well. This is load-bearing because the inferred relationship Delta_N ~ 3(v_T/v_b)^2 is a central deliverable of the paper.
  3. [§4.3] The correlation analysis in Figure 4c-d uses the quantities W_Z and W_{<Z+LZ} defined as in companion papers (Krafft et al. 2025; Polanco-Rodriguez et al. 2025), but the manuscript does not specify how these energies are computed (mode filters, k/omega windows, or field-component combinations). Since the identification of LMC as the mechanism behind large F is the key claim, the mode-selection criteria should be stated in the text or an appendix. Without these definitions, the statement in §5 that the paper 'demonstrate[s] unambiguously' that LMC is the dominant process is not fully self-contained.
minor comments (5)
  1. [§3.2] In the text describing Figure 2, 'averaged over 0 <= omega_p <= 10,000' should read '0 <= omega_p t <= 10,000'.
  2. [Figure 3 caption] The caption contains a typo: 'The theoretical dispersion curve*s' should be 'curves'.
  3. [Figure 3d] The fit of <F>_{w,t} to alpha + beta cosh^{-2}(gamma omega_c/omega_p) is reported only through R^2 > 0.99; please list the best-fit values of alpha, beta, and gamma together with their uncertainties, and state the number of points used.
  4. [§5] The phrase 'demonstrate unambiguously' is stronger than the evidence supports, given that the identification of LMC relies on correlations with quantities defined in companion papers and on 2D simulations; 'indicate' or 'support' would be more measured.
  5. [§2.2] Please specify the initial positions and trajectories of the virtual satellites and justify the statistical independence of the N_w=1000 waveforms; if the satellites repeatedly sample the same turbulent structures, the standard deviations in Figure 3f may be underestimated.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: LMC-dominance and ΔN-threshold claims rest on in-paper PIC simulations and direct F/Z-mode correlations, with self-citations used only as context.

full rationale

The paper's central claim that linear mode conversion (LMC) at constant frequency is the fastest and most efficient route to large polarization ratios F is supported by in-paper diagnostics rather than by construction. The threshold ΔN ≈ 3(v_T/v_b)^2 is introduced from prior work (Ryutov 1969; Krafft et al. 2013), but the paper does not use that threshold as a fitted output; instead it scans beam velocities and density fluctuation levels and finds an empirical jump near ΔN v_b^2/(3 v_T^2) = 1 in Figure 3f. The LMC-dominance comparison is carried by in-paper time histories (Figures 4a-b) showing rapid growth of ⟨F(t)⟩ for ΔN = 0.05 versus slow growth for ΔN = 0, and by in-paper spectral maps (Figures 2d-e, 3g-i) showing Z-mode emission and F_{k,ω} ≈ 1 near the Z-mode cutoff. The companion-paper energy curves W_Z and W_{Z+LZ} overlaid in Figures 4c-d are self-citations, but they are corroborated by the same simulations' magnetic spectra and are not the sole evidence for the correlation; the paper's own F(t) curves are the primary comparison. The diagnostic application to solar wind observations uses externally measured jumps of F and does not rename a fitted parameter as a prediction. The 2D/3V geometry is a modeling limitation that could affect quantitative extrapolation, but it is not a circularity: no equation is equivalent to its own input by construction, and no fitted input is presented as an independent prediction.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claims rest on the SMILEI PIC model, prior threshold and LMC results by the same group, the assumed representativeness of the imposed density fluctuations, and the wavelet filtering choices. No new physical entities are introduced; the virtual satellite is a measurement technique, not a postulated entity.

free parameters (4)
  • Fit parameters alpha, beta, gamma for <F>_{w,t} vs omega_c/omega_p (cosh^-2 fit) = not stated (R^2 > 0.99)
    Empirical fit to simulation points in Figure 3d; used to describe the decrease of mean polarization with magnetization, but not derived from theory.
  • Empirical curve fitting <F>_{w,t} vs Delta_N v_b^2/(3 v_T^2) in Figure 3f = not stated
    Black dashed curve is fit to the color points to show the sharp rise near the threshold; the coefficient 3 in the x-axis is taken from prior theory, not fitted.
  • Wavepacket selection thresholds = |E|^2_max/1000 (Figures 3) and |E|^2_max/100 (Figure 5)
    Chosen by hand to suppress noise; these thresholds affect the tails of the F PDFs and therefore the reported distributions.
  • Virtual satellite speed and sampling rate = v_s = 0.3 v_T; sampling rate 0.06-0.18 omega_p
    Chosen for convenience and Doppler separation; affects the resolved frequency bands and the F estimates.
assumptions (5)
  • domain assumption SMILEI PIC code accurately simulates the Vlasov-Maxwell beam-plasma system
    Section 2.1 assumes the numerical model with 5400 particles per cell and m_e/m_i=1/1836 captures the relevant wave dynamics; energy error ~1e-4 is given as justification.
  • domain assumption Linear mode conversion at constant frequency of LZ waves scattering on delta_n produces Z-mode emission (Krafft et al. 2025)
    The interpretation of the simulation signatures and the central claim rely on this companion in-press paper from the same group; it is not re-derived here.
  • domain assumption Threshold condition Delta_N approximately 3(v_T/v_b)^2 separates the LMC-dominant and decay-dominant regimes
    Borrowed from Ryutov (1969) and Krafft et al. (2013); used throughout Section 4 to interpret PDFs and to estimate Delta_N from observed beam speeds.
  • domain assumption Random density fluctuations with Delta_N up to 0.05 in the simulations represent solar wind density turbulence
    Section 2.1 imposes delta_n; solar wind levels up to 0.07 are cited from Celnikier et al. (1987), but the simulated fluctuation spectrum is not shown to match solar wind statistics.
  • domain assumption Filtering waveforms to [0.9,1.1] omega_p captures all relevant LZ and fundamental electromagnetic wave energy
    Section 4.1 states this for weakly magnetized plasmas with Delta_N <= 0.05; it is an assumption used to define the computed F at frequency omega approximately omega_p.

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Cite this review

Pith. "Pith review of Polarization ratios of turbulent Langmuir/$\mathcal{Z}$-mode waves generated by electron beams in magnetized solar wind plasmas." pith.science (2026). https://pith.science/paper/FPLOGJEV

@misc{pith2026250618429,
  author       = {Pith},
  title        = {Pith review of: Polarization ratios of turbulent Langmuir/$\mathcalZ$-mode waves generated by electron beams in magnetized solar wind plasmas},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FPLOGJEV}},
  note         = {Machine review of arXiv:2506.18429}
}
abstract

The polarization ratios $F=|E_\perp|^2/|E|^2$ of beam-generated turbulent Langmuir/$\mathcal{Z}$-mode ($\mathcal{LZ}$) waves and electromagnetic emissions radiated at plasma frequency $\omega_p$ by such sources are studied in weakly magnetized and randomly inhomogeneous plasmas owing to large-scale and long-term 2D/3V Particle-In-Cell simulations with parameters relevant to type III solar radio bursts. Statistical studies using waveforms recorded by virtual satellites are performed to determine the distributions of polarization ratios as a function of beam and plasma parameters. This efficient method, which mimics waveform recording by spacecraft in the solar wind, leads to results consistent with observations. Moreover, plasma random density fluctuations $\delta n$ turn out to be the key factor responsible for the increase in polarization ratios up to $F\simeq 1$. Indeed, it is demonstrated that linear mode conversion at constant frequency of $\mathcal{LZ}$ waves scattering on $\delta n$ is the most efficient and fast process to produce large polarization ratios in randomly inhomogeneous plasmas, due to electromagnetic slow extraordinary $\mathcal Z$-mode wave emission by $\mathcal{LZ}$ wave turbulence. Results provide guidance to theoretical studies and useful support to estimate the average level of density fluctuations $\Delta N$ in solar wind plasmas.

Figures

Figures reproduced from arXiv: 2506.18429 by the authors.

Figure 1
Figure 1. Typical example of waveform, together with hodograms, polarization ratios and wave energies, in a weakly magnetized homogeneous plasma with ωc/ωp = 0.07 and ∆N = 0, for 0 ≤ ωpt ≤ 30, 000. (a) Waveform of electric fields E∥(t) = Ex(t) (gray), E⊥1(t) = Ey(t) (red), and E⊥2(t) = Ez(t) (blue), filtered in the frequency interval [0.9, 1.1]ωp. (b) Hodograms E∥(E⊥1) calculated in equidistant time windows of 60ω −1 p . (c) … view at source ↗
Figure 2
Figure 2. Typical example of waveform, together with hodograms, polarization ratios and wave energies, in a ran￾domly inhomogeneous and weakly magnetized plasma with ∆N = 0.05 and ωc/ωp = 0.07, for 0 ≤ ωpt ≤ 10, 000. (a) Waveform of electric fields E∥(t) (gray), E⊥1(t) (red), and E⊥2(t) (blue), filtered in the frequency interval [0.9, 1.1]ωp; the applied density fluctuations δn/n0 are superimposed (green lines); a reflection … view at source ↗
Figure 3
Figure 3. Distributions of polarization ratios as a function of beam and plasma parameters. (a-c) Distributions ⟨f⟩w calculated using Nw = 1000 waveforms with frequencies filtered in the range [0.9, 1.1]ωp, in magnetized plasmas with 0 ≤ ωc/ωp ≤ 0.5, in the time intervals 3000 ≤ ωpt ≤ 6000 (a and c) and 12, 000 ≤ ωpt ≤ 15, 000 (b), for ∆N = 0 (a-b) and ∆N = 0.05 (c). (d) Variations of ⟨F⟩w,t with ωc/ωp, for ∆N = 0 (triangles)… view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: (a-b) Variations with time of ⟨F(t)⟩w (2) averaged over Nw = 1000 waveforms filtered in the frequency range [0.9, 1.1]ωp, in plasmas with various ∆N and ωc/ωp. (a) Homogeneous (∆N = 0, solid lines) and randomly inhomogeneous (∆N = 0.05, dashed lines) plasmas with diffe…
Figure 5
Figure 5. Figure 5: c shows the distribution ⟨f(F, δni/n0)⟩w as a function of F and the ion density perturbation δni/n0 = (ni −n0)/n0, in a plasma with ∆N = 0.05 and ωc/ωp = 0.07. The distribution peaks at −0.05 ≲ δni/n0 < 0, with most of polarization ratios satisfying 0.2 ≲ F ≲ 0.7, and …

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Works this paper leans on

32 extracted references · 15 canonical work pages

  1. [1]

    D., Burgess, D., Kellogg, P

    Bale, S. D., Burgess, D., Kellogg, P. J., et al. 1996, Geophys. Res. Lett., 23, 109, doi: 10.1029/95GL03595

    doi:10.1029/95gl03595 1996

  2. [2]

    D., Kellogg, P

    Bale, S. D., Kellogg, P. J., Goetz, K., & Monson, S. J. 1998, Geophys. Res. Lett., 25, 9, doi: 10.1029/97GL03493

    work page doi:10.1029/97gl03493 1998

  3. [3]

    M., Muschietti, L., & Goldman, M

    Celnikier, L. M., Muschietti, L., & Goldman, M. V. 1987, A&A, 181, 138

    1987

  4. [4]

    2018, Computer Physics Communications, 222, 351, doi: 10.1016/j.cpc.2017.09.024

    Derouillat, J., Beck, A., P´ erez, F., et al. 2018, Computer Physics Communications, 222, 351, doi: 10.1016/j.cpc.2017.09.024

    doi:10.1016/j.cpc.2017.09.024 2018

  5. [5]

    E., Malaspina, D

    Ergun, R. E., Malaspina, D. M., Cairns, I. H., et al. 2008, Phys. Rev. Lett., 101, 051101, doi: 10.1103/PhysRevLett.101.051101

    work page doi:10.1103/physrevlett.101.051101 2008

  6. [6]

    J., Velli, M

    Fox, N. J., Velli, M. C., Bale, S. D., et al. 2016, SSRv, 204, 7, doi: 10.1007/s11214-015-0211-6

    doi:10.1007/s11214-015-0211-6 2016

  7. [7]

    B., & Cairns, I

    Graham, D. B., & Cairns, I. H. 2013, J. Geophys. Res., 118, 3968, doi: 10.1002/jgra.50402 —. 2014, Journal of Geophysical Research: Space Physics, 119, 2430, doi: 10.1002/2013JA019425

    doi:10.1002/jgra.50402 2013

  8. [8]

    B., Cairns, I

    Graham, D. B., Cairns, I. H., Prabhakar, D. R., et al. 2012, Journal of Geophysical Research (Space Physics), 117, A09107, doi: 10.1029/2012JA018033

    work page doi:10.1029/2012ja018033 2012

Show all 32 references
  1. [9]

    B., Khotyaintsev, Y

    Graham, D. B., Khotyaintsev, Y. V., Vaivads, A., et al. 2021, A&A, 656, A23, doi: 10.1051/0004-6361/202140943

    2021 doi

  2. [10]

    E., Fried, B

    Hinkel-Lipsker, D. E., Fried, B. D., & Morales, G. J. 1989, PhRvL, 62, 2680, doi: 10.1103/PhysRevLett.62.2680 12 Polanco-Rodr´ıguez, Krafft & Savoini

    1989 doi

  3. [11]

    B., & Gurnett, D

    Hospodarsky, G. B., & Gurnett, D. A. 1995, Geophys. Res. Lett., 22, 1161, doi: 10.1029/95GL00303

    1995 doi

  4. [12]

    J., Goetz, K., Monson, S

    Kellogg, P. J., Goetz, K., Monson, S. J., & Bale, S. D. 1999, J. Geophys. Res., 104, 17069, doi: 10.1029/1999JA900163

    1999 doi

  5. [13]

    J., Goetz, K., Monson, S

    Kellogg, P. J., Goetz, K., Monson, S. J., & Opitz, A. 2013, J. Geophys. Res., 118, 4766, doi: 10.1002/jgra.50443

    2013 doi

  6. [14]

    2021, ApJL, 917, L23, doi: 10.3847/2041-8213/ac1795 —

    Krafft, C., & Savoini, P. 2021, ApJL, 917, L23, doi: 10.3847/2041-8213/ac1795 —. 2022a, ApJL, 924, L24, doi: 10.3847/2041-8213/ac46a7 —. 2022b, ApJL, 934, L28, doi: 10.3847/2041-8213/ac7f28 —. 2023, ApJ, 949, 24, doi: 10.3847/1538-4357/acc1e4 —. 2024, ApJL, 964, L30, doi: 10.3...

    2021 doi

  7. [15]

    Krafft, C., Savoini, P., & Polanco-Rodr´ ıguez, F. J. 2024, ApJL, 967, L20, doi: 10.3847/2041-8213/ad47b5

    2024 doi

  8. [16]

    Krafft, C., & Volokitin, A. S. 2021, ApJ, 923, 103, doi: 10.3847/1538-4357/ac2153

    2021 doi

  9. [17]

    S., & Krasnoselskikh, V

    Krafft, C., Volokitin, A. S., & Krasnoselskikh, V. V. 2013, ApJ, 778, 111, doi: 10.1088/0004-637X/778/2/111

    2013 doi

  10. [18]

    S., Krasnoselskikh, V

    Krafft, C., Volokitin, A. S., Krasnoselskikh, V. V., & de Wit, T. D. 2014, Journal of Geophysical Research: Space Physics, 119, 9369, doi: https://doi.org/10.1002/2014JA020329

    2014 doi

  11. [19]

    2025, Nature Astronomy, in press

    Savoini, P. 2025, Nature Astronomy, in press. https://arxiv.org/abs/2506.16816

    2025 arXiv

  12. [20]

    2019, ApJ, 879, 51, doi: 10.3847/1538-4357/ab22bf

    Krasnoselskikh, V., Voshchepynets, A., & Maksimovic, M. 2019, ApJ, 879, 51, doi: 10.3847/1538-4357/ab22bf

    2019 doi

  13. [21]

    V., Dudok de Wit, T., & Bale, S

    Krasnoselskikh, V. V., Dudok de Wit, T., & Bale, S. D. 2011, Annales Geophysicae, 29, 613, doi: 10.5194/angeo-29-613-2011

    2011 doi

  14. [22]

    Krauss-Varban, D. 1989, J. Geophys. Res., 94, 3527, doi: 10.1029/JA094iA04p03527

    1989 doi

  15. [23]

    2020, ApJS, 246, 57, doi: 10.3847/1538-4365/ab65bd

    Krupar, V., Szabo, A., Maksimovic, M., et al. 2020, ApJS, 246, 57, doi: 10.3847/1538-4365/ab65bd

    2020 doi

  16. [24]

    D., Krasnoselskikh, V., et al

    Larosa, A., de Wit, T. D., Krasnoselskikh, V., et al. 2022, The Astrophysical Journal, 927, 95, doi: 10.3847/1538-4357/ac4e85

    2022 doi

  17. [25]

    H., Li, B., & Robinson, P

    Layden, A., Cairns, I. H., Li, B., & Robinson, P. A. 2013, PhRvL, 110, 185001, doi: 10.1103/PhysRevLett.110.185001

    2013 doi

  18. [26]

    Y., Reid, H

    Lorfing, C. Y., Reid, H. A. S., G´ omez-Herrero, R., et al. 2023, ApJ, 959, 128, doi: 10.3847/1538-4357/ad0be3

    2023 doi

  19. [27]

    M., Cairns, I

    Malaspina, D. M., Cairns, I. H., & Ergun, R. E. 2011, Geophysical Research Letters, 38, doi: 10.1029/2011GL047642

    2011 doi

  20. [28]

    M., & Ergun, R

    Malaspina, D. M., & Ergun, R. E. 2008, Journal of Geophysical Research (Space Physics), 113, A12108, doi: 10.1029/2008JA013656 M¨ uller, D., St. Cyr, O. C., Zouganelis, I., et al. 2020, A&A, 642, A1, doi: 10.1051/0004-6361/202038467 P´ ıˇ sa, D., Souˇ cek, J., Santol´ ık, O., ...

    2008 doi

  21. [29]

    E., Matteini, L., Squire, J., et al

    Raouafi, N. E., Matteini, L., Squire, J., et al. 2023, SSRv, 219, 8, doi: 10.1007/s11214-023-00952-4

    2023 doi

  22. [30]

    Ryutov, D. D. 1969, Soviet Journal of Experimental and Theoretical Physics, 30, 131

    1969

  23. [31]

    2021, A&A, 656, A26, doi: 10.1051/0004-6361/202140948

    Soucek, J., P´ ıˇ sa, D., Kolmasova, I., et al. 2021, A&A, 656, A26, doi: 10.1051/0004-6361/202140948

    2021 doi

  24. [32]

    J., & Cairns, I

    Willes, A. J., & Cairns, I. H. 2000, Physics of Plasmas, 7, 3167, doi: 10.1063/1.874180

    2000 doi

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