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Linear mode conversion theory of radio emission from turbulent solar wind plasmas

T0 review · 5 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper argues that linear mode conversion of upper-hybrid wave turbulence on quasi-static random density fluctuations generates O-, X-, and Z-mode radio emission at the plasma frequency, with rates scaling as $(v_T/c)^2$ and linearly…

desk verdict A useful extension of the group's LMC framework to weakly magnetized plasmas, but the headline (v_T/c)^2 scaling for Z-mode rests on a five-point scan whose fitted exponent is 2.3, and the analytic 'confirmation' is not independent. read the letter →

arxiv 2507.13856 v1 pith:YT6JAKVC submitted 2025-07-18 physics.plasm-ph

Catherine Krafft , Alexandr Volokitin This is my paper · ORCID
classification physics.plasm-ph
keywords solarwindtypeIIIradioburstsupper-hybridwaveslinearmodeconversiondensityfluctuationsweakturbulenceZakharovequationsplasma-frequencyradiation
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

Solar wind plasmas are full of random density ripples, and this paper builds a case that those ripples alone—without nonlinear wave decay—can convert upper-hybrid wave turbulence into the radio emission that type III solar bursts show at the plasma frequency. The authors set up a two-dimensional weakly magnetized plasma with a prescribed, quasi-static fluctuation spectrum and solve envelope equations for the three electromagnetic modes that can radiate near $\omega_p$: the ordinary O-mode and the extraordinary X- and Z-modes, with the radiated current computed from upper-hybrid waves moving across the density ripples. Their numerical solutions, backed by a weak-turbulence analytic calculation, give radiation rates that grow linearly with the fluctuation level $\Delta_N$ and as a power of $v_T/c$: essentially $(v_T/c)^2$ for the O-mode in an unmagnetized plasma and for the Z-mode in the magnetized case, with the Z-mode about ten times stronger than the O-mode. If correct, this means observed radio flux at the plasma frequency is a direct probe of the density-fluctuation level and magnetization of the source, and the decades-old problem of type III radio bursts gains a mechanism that does not depend on three-wave interactions.

What carries the argument

The load-bearing object is the fluctuating current $\delta \mathbf{j} = -e\,\delta n\,\mathbf{v}_e$ produced when upper-hybrid wave electric fields drive electron motion across the density modulation $\delta n$. Its slow envelope acts as the source term in envelope equations for each radiated mode: the O-mode is followed through the magnetic-field amplitude $B_{zk}$ obeying $(i\partial_t - \Delta\omega_k) b_k = - (c_L/2)\omega_p^2/(\omega_p^2-\omega_c^2) \hat{G}_{zk}$, and the X- and Z-modes through rotated fields $E^\pm_k = E_{zk}\pm iE_{yk}$ obeying $(i\partial_t-\Delta\omega^\pm) E^\pm_k = iq^\pm_k$. The upper-hybrid potential that feeds these currents evolves by a modified Zakharov equation including weak magnetic terms, with density fluctuations following linear ion-acoustic dynamics. The rate calculation then uses the weak-turbulence apparatus of random phases: density fluctuations are statistically independent, $\langle \rho_{k_1}\rho^*_{k_3}\rangle = \delta_{k_1k_3}|\rho_{k_1}|^2$, wave correlations decay exponentially, and at large times the double time integral collapses to a delta function $\delta(\omega^t_k-\omega_{k_2})$ enforcing frequency matching between the radiated transverse wave and the electrostatic wave. This reduces the radiation rate to an integral over the density and wave spectra weighted by mode-specific polarization factors, from which the scaling laws follow.

What would settle it

A decisive test would be a two-dimensional particle-in-cell simulation (or a laboratory plasma experiment) with an electron beam driving upper-hybrid turbulence through imposed or self-consistent density fluctuations, measuring the escaping O- and Z-mode radiation while varying the thermal velocity and fluctuation level. If the rates do not grow approximately as $(v_T/c)^2$ and linearly in $\Delta_N$, or if Z-mode does not exceed O-mode by about an order of magnitude whenever the modes are separated in frequency, the linear mode conversion mechanism as modeled is not the dominant source of plasma-frequency radio emission.

Watch

Extended reading notes

Core claim

The central claim is that linear mode conversion at constant frequency, in which upper-hybrid waves scatter on quasi-static random density fluctuations, is sufficient to explain electromagnetic emission at the plasma frequency in weakly magnetized solar wind plasmas. In an unmagnetized plasma the O-mode radiation rate obeys $\dot{\eta}_O \propto \Delta_N (v_T/c)^\sigma$ with $\sigma \simeq 2$ (the numerically measured indices cluster around $2.02$); in a weakly magnetized plasma the O-mode index drops into the range $1<\sigma<2$ in 2D because two analytic contributions, one proportional to $(v_T/c)^2$ and one to $(v_T/c)^3$ in 3D, compete. The Z-mode rate scales as $\dot{\eta}_Z \propto \Delta_N (v_T/c)^2$ and exceeds the O-mode rate by roughly a factor of ten, while X-mode radiation is weak or absent when $\omega_c/\omega_p \gtrsim \Delta_N$ and can appear when density fluctuations dominate the magnetization. The paper further claims that these scalings hold for anisotropic as well as isotropic initial wave and density spectra, with the absolute rates sensitive to the spectra but the exponents stable.

Load-bearing premise

The model treats the density fluctuations as a frozen, externally prescribed random landscape that the waves do not alter; if wave feedback reshapes $\delta n$ on the timescale of the upper-hybrid oscillations, the predicted power laws and the ten-to-one Z/O ratio could change.

Editorial extensions

If this is right

  • Radio emission near $\omega_p$ in the solar wind can be computed from local values of $\Delta_N$ and $v_T/c$ alone, without invoking nonlinear three-wave decay or coalescence.
  • Z-mode radiation should dominate the escaping spectrum by about an order of magnitude, so high-frequency radio observations near the plasma frequency should look for the Z-mode signature as the main carrier.
  • The near-absence or presence of X-mode radiation is a diagnostic: it is suppressed when $\omega_c/\omega_p \gtrsim \Delta_N$ and switched on when density fluctuations dominate, giving an observational handle on the ratio of magnetization to density-turbulence level.
  • The scaling $\dot{\eta}\propto \Delta_N (v_T/c)^2$ means measurements of absolute radio emissivity from a source volume can be inverted to estimate either the electron temperature or the mean density-fluctuation level, once the other is known.

Reading between the lines

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

  • A natural stress test is to let the waves react back on the density fluctuations: at higher $W_{UH}$, ponderomotive forces could modify $\delta n$ and break the linear growth in $\Delta_N$, so the predicted scaling marks an upper limit in fluctuation level for which the mechanism operates as described.
  • Because the frequency-matching delta function links each radiated wavenumber to a particular upper-hybrid wavenumber through the density spectrum, the bandwidth and angular distribution of the emitted Z- and O-mode radiation should carry a retrievable image of the source's density-fluctuation spectrum; spacecraft observations of burst fine structure could test this.
  • In 3D geometry the analytic O-mode rate contains both $(v_T/c)^2$ and $(v_T/c)^3$ terms, so the effective scaling index should interpolate between 2 and 3; an observed index outside that range would suggest either strong anisotropy or that another radiation mechanism contributes.
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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

5 major / 5 minor

Summary. This paper develops a two-dimensional model of upper-hybrid wave turbulence in a weakly magnetized, randomly inhomogeneous plasma, where density fluctuations are prescribed as quasi-static and the waves evolve under modified Zakharov equations. The authors derive envelope equations for radiated O, X, and Z electromagnetic modes (Eqs. 14-16 and 30-31), integrate them numerically for a range of parameters, and complement the numerics with a weak-turbulence analytic calculation of radiation rates (Eqs. 40-41, 52-59). The central claims are scaling laws: in unmagnetized plasmas the O-mode radiation rate scales as (v_T/c)^2 with exponent near 2 and linearly with Δ_N; in weakly magnetized plasmas the Z-mode rate scales as (v_T/c)^2, the O-mode rate scales as (v_T/c)^σ with 1<σ<2 in 2D, and Z-mode radiation is about ten times stronger than O-mode.

Significance. If the scaling laws hold, this work provides a quantitative framework for interpreting solar wind radio emission at the plasma frequency, and the compact equations for the three electromagnetic modes are a useful new tool. The numerical implementation is sufficiently described to be reproducible, and the analytic derivation is internally coherent up to its stated assumptions. The paper's strengths—the physically motivated model, the derivation of mode-specific evolution equations, and the explicit analytic expressions—are genuine. However, the quantitative claim about the scaling exponents is not yet supported by the evidence: the magnetized exponents are obtained from a single five-point scan without error bars, and the analytic calculation relies on assumptions validated only by the same simulations, making it a consistency check rather than an independent confirmation.

major comments (5)
  1. [Section 3.2, Eq. (59), Fig. 10] The fitted exponents for the magnetized O-mode (σ=1.53) and Z-mode (σ=2.3) do not equal the analytic prediction σ=2 stated in Eq. (59), yet the text claims agreement 'with our simulation results.' The five-point scan in Fig. 10 has no error bars, no multiple realizations, and no stated fitting uncertainty, so these exponents are underdetermined; σ_Z=2.3 is equally compatible with 2.0 and 2.5 at the displayed precision. To support the central scaling claim, the authors should provide error estimates, a wider range of c_L values, and ideally independent realizations, and they should quantitatively address the discrepancy between the fitted exponents and the predicted value.
  2. [Section 3.2, Eq. (59), and Sec. 2.2.2] Equation (59) is proportional to the integral of |ρ_{-k2}|^2 |E_{k2}|^2 over k2. Given the definition of Δ_N in Eq. (1) as the root-mean-square fluctuation level, Parseval's theorem implies that the integrated density spectral power is proportional to Δ_N^2, so Eq. (59) predicts a Δ_N^2 dependence, not the linear '∝ Δ_N' stated in the text and used in the comparison with Figs. 4 and 14. The paper must either correct the scaling claim or clarify the normalization of ρ_k that would make the dependence linear; as written, the analytic formula and the stated Δ_N scaling are inconsistent.
  3. [Section 3.1, Fig. 10] For the magnetized O-mode, the paper explains the observed 1<σ<2 by a 3D analytic argument (Eqs. 52-55) that yields an exponent between 2 and 3 in 3D, and then asserts that this 'explains' the 2D simulation exponents. No 2D O-mode analytic calculation is presented, so the comparison between the 2D numerical exponents and the analytic prediction is indirect. The authors should either supply the 2D O-mode derivation or present the 3D-to-2D mapping more rigorously; otherwise the claim that the simulation result is 'in agreement' with theory is not established.
  4. [Section 3, Eqs. (36)-(38)] The analytic derivation introduces several assumptions—exponential decay of wave correlations (Eq. 36), small ν leading to the Dirac-delta replacement in Eq. (38), and quasi-static random density fluctuations—and states that their validity is 'based on the results presented above,' i.e., on the same numerical simulations that the analytic calculation is meant to confirm. This is a circular validation. To make the analytic result an independent test of the scaling laws, the authors should validate these assumptions using diagnostics that are separate from the radiation-rate measurement, such as directly computed correlation functions and spectral widths, or at least explicitly acknowledge that the analytic calculation is a post-hoc consistency check rather than a predictive confirmation.
  5. [Section 2.2.2, Eqs. (21)-(24)] The scalar function Ψ is introduced in Eq. (21) and then set to c^2 ∇·E based on 'general heuristic considerations' of linearity and dimensionality. This choice directly enters the X/Z-mode equations (23)-(24) and hence the central analytic result (59), but no derivation or independent verification is provided. The authors should justify Ψ more rigorously—for instance, by deriving it from the vector identity used to integrate Eq. (20)—or test the sensitivity of the predicted scaling to alternative choices of Ψ.
minor comments (5)
  1. [Sec. 2.2.1, Fig. 3] The inset reports fitted exponents σ≃2.14 and σ≃1.78 for η and μ, yet the text states that the power law 1/c_L^2 is satisfied 'with good accuracy'; the discrepancy should be quantified rather than attributed only to numerical features.
  2. [Fig. 10 and throughout] The horizontal axis is labeled '1/c_L' whereas the scaling variable is v_T/c; using the explicitly physical variable v_T/c in the figures and text would improve clarity.
  3. [Sec. 2.1] There is a typo: 'λD id the electron Debye length' should read 'λD is the electron Debye length.'
  4. [Appendix B] The statement that the O-mode dispersion approximations (B17)-(B18) have 'relative errors ranging from 1 to 10%, depending on k, θ and ω_c' is too vague; a figure or table showing the error over the relevant parameter range would allow the reader to assess the impact on the scaling-law calculation.
  5. [References] The citation 'Krafft et al. (2025), Nature Astronomy, in press' should be updated to the published version if available, and the relation between that paper and the present one should be stated explicitly to clarify the incremental contribution.

Circularity Check

2 steps flagged · score 4.0 of 10

Partial circularity: the magnetized O-mode 2D scaling range is inferred from the numerical fit, and the analytic/numerical agreement is an internal same-model consistency check rather than an independent confirmation.

  1. fitted input called prediction [Sec. 3.1 (after Eq. 55) and Sec. 2.2.2 (after Fig. 10)]
    "The resulting expression ˙µO = ˙µO,1 + ˙µO,2 shows that the total radiation rate does not scale as (v_T/c)^3; indeed, it exhibits two terms, containing (v_T/c)^3 (46) and (v_T/c)^2 (52), respectively; the actual scaling index is then between 2 and 3 in 3D geometry. This explains why, in 2D geometry, we observe O-mode radiation rates in a magnetized plasma with scaling indices between 1 and 2 (see Fig. 10)."

    The analytic calculation of Sec. 3.1 is performed in 3D and yields a scaling index between 2 and 3. The claimed 2D prediction, 1 < σ < 2, is not derived from a 2D analytic calculation; it is taken from the numerically fitted value σ = 1.53 in Fig. 10. The paper then presents this observed range as an analytic prediction in Sec. 2.2.2 ('analytic calculations ... predict, in 2D geometry, the scaling laws ˙ηZ ∝ (v_T/c)^2 and ˙ηO ∝ (v_T/c)^σ, with 1 < σ < 2'). The predicted range is therefore calibrated to the same simulation data it is said to agree with, making this part of the central scaling-law claim a fitted input renamed as a prediction.

  2. other [Abstract; Sec. 3 intro; Sec. 2.2.2 (Eqs. 30-31) vs Sec. 3.2 (Eqs. 56-59)]
    "Jointly, on the basis of these numerical results that validate theoretical hypotheses, analytical calculations are conducted in the framework of weak turbulence theory extended to randomly inhomogeneous plasmas, that recover the main physical conclusions stated using the new model."

    The abstract explicitly states that the numerical results validate the theoretical hypotheses and that the analytical calculations then recover the numerical conclusions. The analytic derivation starts from the same model equations that the simulations integrate: Sec. 3.2 says 'let us start here from equations (30)-(31), obtained in our model', while Sec. 2.2.2 says the simulations 'numerically integrate equations (30)-(31)'. The additional analytic assumptions, including the exponential correlation decay, are described as having 'validity ... based on the results presented above'. Thus the agreement reported in Eq. 59 ('in agreement with our simulation results') is a consistency check within a single model rather than an independent confirmation.

full rationale

The paper contains genuine analytic content: the Z-mode scaling ∝ (v_T/c)^2 is derived in Eq. (59) from the stated dispersion and current expressions, and the unmagnetized O-mode scaling near (v_T/c)^2 is obtained by taking the ω_c → 0 limit of the analytic formulas. These parts do not reduce to the numerical fits. The circularity is partial and concentrated in the magnetized O-mode 2D claim: the range 1 < σ < 2 is not an independent predictor but is inferred from the observed σ = 1.53 and then restated as a prediction. A second, milder loop is that the analytic calculation starts from the same equations as the numerics and uses the numerics to justify its additional assumptions, so the 'recovery' of the simulation scalings is internal consistency rather than external validation. Self-citations to prior work are present but not load-bearing for the derivations. The lack of error bars on the fitted exponents (σ = 1.53, 2.3 in Fig. 10) is a correctness/evidence concern, not a circularity concern.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

The model rests on standard plasma physics (Maxwell equations, Zakharov equations, dielectric tensor) plus domain assumptions about the solar wind environment (weak magnetization, quasi-static random density fluctuations, optically thin source) and several ad hoc approximations for analytic tractability (exponential correlation decay, Psi ansatz, two-branch O-mode dispersion). No free parameters are fitted to data; the scaling exponents are outputs of simulation and analytic derivation.

assumptions (6)
  • domain assumption Density fluctuations are quasi-static and follow linear ion-acoustic dynamics, with ponderomotive back-reaction neglected.
    Section 2.1, Eq. (2) and text: 'we neglect ponderomotive effects and thus do not take into account nonlinear wave-wave interactions'.
  • domain assumption The plasma is weakly magnetized (omega_c/omega_p <= 0.2) and the radio source is optically thin, so local radiation rates represent escaping flux.
    Introduction and Section 2.1: 'in many cases of practical interest, such as in the solar wind, the radiating source is optically thin'.
  • ad hoc to paper The wave correlation function decays exponentially with rate nu_k2, and nu is small enough to replace the Lorentzian by a Dirac delta in Eq. (38).
    Section 3, Eq. (36) and subsequent text; this is an assumption about turbulence statistics not derived from the model.
  • ad hoc to paper The scalar function Psi introduced in the X/Z mode equations is set to c^2 div E based on heuristic dimensional and linearity considerations.
    Section 2.2.2, near Eqs. (21)-(23): 'general heuristic considerations ... allows us to assume Psi = c^2(div E)'.
  • ad hoc to paper O-mode dispersion is approximated by two branches (B17) and (B18) with matching at k^2 c^2 sin^2 theta = omega_p omega_c, with relative errors of 1 to 10 percent.
    Appendix B, Eqs. (B17)-(B18) and text: 'These approximations result in relative errors ranging from 1 to 10 percent'.
  • domain assumption X and Z modes are frequency-separated and can be treated independently, valid when omega_c/omega_p is not too small, e.g., omega_c/omega_p >= Delta_N.
    Section 2.2.2: 'if omega_c/omega_p is not too small as, for example, if omega_c/omega_p >= Delta_N, these modes turn out to be separated in frequency'.

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Pith. "Pith review of Linear mode conversion theory of radio emission from turbulent solar wind plasmas." pith.science (2026). https://pith.science/paper/YT6JAKVC

@misc{pith2026250713856,
  author       = {Pith},
  title        = {Pith review of: Linear mode conversion theory of radio emission from turbulent solar wind plasmas},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YT6JAKVC}},
  note         = {Machine review of arXiv:2507.13856}
}
abstract

This work presents a new theoretical and numerical model describing all possible linear interactions between upper-hybrid wave turbulence and random density fluctuations in a solar wind plasma; not only linear processes as wave reflection, refraction, scattering, tunneling, trapping, or mode conversion at constant frequency are taken into account, but also linear wave coupling, interferences between scattered waves, etc. Compact equations describing the time evolution of electromagnetic fields radiated in the $\mathcal{O}$, $\mathcal{X}$ and $\mathcal{Z}$ modes by the current due to transformations of upper-hybrid waves on density fluctuations, as well as the dispersion and polarization properties of the modes, are determined analytically and solved numerically, providing the time variations of electromagnetic energies and corresponding radiation rates. Jointly, on the basis of these numerical results that validate theoretical hypotheses, analytical calculations are conducted in the framework of weak turbulence theory extended to randomly inhomogeneous plasmas, that recover the main physical conclusions stated using the new model. The dependencies of radiation rates on plasma parameters as the magnetization, the electron thermal velocity and the average level of random density fluctuations are determined in the form of scaling laws. This work opens a new way to analyze the efficiency of electromagnetic emissions at plasma frequency by realistic wave and density turbulence spectra interacting in solar wind plasmas.

Figures

Figures reproduced from arXiv: 2507.13856 by the authors.

Figure 1
Figure 1. Example of distributions of upper-hybrid waves and density fluctuations in the plasma source, at initial time t = 0, for ωc/ωp = 0.1. (a) Density fluctuations’ spectrum |ρk| = |δnk/n0| in the map (kxλD, kyλD); δnk is the Fourier component of δn. (b) Corresponding spatial distribution ρ(x, y) = δn(x, y)/n0 in the 2D map (x/λD, y/λD), with ∆N = 0.05. (c) Electric field energy spectrum |Ek| 2 in the map (kxλD, kyλD), w… view at source ↗
Figure 2
Figure 2. Wave and density turbulence at ωpt ≃ 7600. (a) Spatial distribution of the upper-hybrid wave energy |E| 2 in the map (x/λD, y/λD); the red square delimits the region where a zoom is shown in (d). (b) Spatial distribution of δn(x, y)/n0 in the map (x/λD, y/λD); the red square is the same as in (a). (c) Upper-hybrid wave spectrum |Ek| 2 in the map (kxλD, kyλD). (d) Zoom of the domain delimited by a red square in (a); … view at source ↗
Figure 3
Figure 3. Time variations of the electric (a) and magnetic (b) wave energies η(t) and µ(t), respectively, in an unmagnetized plasma (ωc = 0), for ∆N = 0.03 and four values of cL (see legend in (a)). The insets show, in logarithmic scales, the variations of the corresponding radiation rates ˙η and ˙µ as a function of 1/cL, which exhibit scaling indices σ ≃ 2.14 (a) and σ ≃ 1.78 (b), respectively, to be compared with the value … view at source ↗
Figures from the paper (13 more)
Figure 4
Figure 4. Figure 4: Electromagnetic O-mode in an unmagnetized plasma. (a) Variations of the radiation rate ˙η as a function of 1/cL, for different values of ∆N, corresponding to the scaling indices σ listed in the legend. (b) Variations of ˙η(cL/70)2 as a function of ∆N, for different val…
Figure 5
Figure 5. Figure 5: Electromagnetic O-mode in an unmagnetized plasma. (a) Variations of the radiation rate ˙η as a function of 1/cL, for different values of ∆N, corresponding to the scaling indices σ listed in the legend. (b) Variations of ˙η(cL/70)2 as a function of ∆N, for different val…
Figure 6
Figure 6. Figure 6: Electromagnetic O-mode in an unmagnetized plasma. (a) Variations of the radiation rate ˙η as a function of 1/cL, for different values of ∆N, corresponding to the scaling indices σ listed in the legend. (b) Variations of ˙η(cL/70)2 as a function of ∆N, for different val…
Figure 7
Figure 7. Figure 7: Time variations of the magnetic wave energy µ(t) in an unmagnetized plasma (ωc = 0), for ∆N = 0.03 and cL = 30, 40, 50 and 60. The dashed black and solid pink lines correspond to simulations performed with the time steps ωp∆t = 1 and ωp∆t = 5.4, respectively. The inset…
Figure 8
Figure 8. Figure 8: Energy spectra of the modes O (Wk = |E 2 k| + |B 2 k|, left column), X (|E 2 k, middle column) and Z (|E 2 k|, right column), in the map (kxλD, kyλD), at times ωpt = 100 (upper row), 200 (middle row) and 400 (bottom row), for ωc/ωp = 0.15 and ∆N = 0.03. The circles rep…
Figure 9
Figure 9. Figure 9: Time variations of the electromagnetic wave energy η(t) in a weakly magnetized plasma, for ∆N = 0.03, ωc/ωp = 0.15, and 5 values of cL (see legend in the left panel), for the O-mode (left), the X -mode (middle), and the Z-mode (right). The superimposed thick yellow str…
Figure 10
Figure 10. Figure 10: Variations of the electromagnetic radiation rate ˙η as a function of 1/cL (in logarithmic scales), for O-mode (left) and Z-mode (right) waves, at plasma conditions of [PITH_FULL_IMAGE:figures/full_fig_p012_10.png]
Figure 11
Figure 11. Figure 11: Variations with ωc/ωp of the electromagnetic radiation rate ˙η(cL/30)2 of O-mode (left) and Z-mode (right) waves, for ∆N = 0.02 and different cL (see the legend in the left panel). All variables are normalized [PITH_FULL_IMAGE:figures/full_fig_p013_11.png]
Figure 12
Figure 12. Figure 12: Variations with ωc/ωp of the electromagnetic radiation rate ˙η(cL/30)2 of O-mode (left) and Z-mode (right) waves, for ∆N = 0.05 and different cL (see the legend in the left panel). All variables are normalized [PITH_FULL_IMAGE:figures/full_fig_p013_12.png]
Figure 13
Figure 13. Figure 13: Variations with ωc/ωp of the electromagnetic radiation rate ˙η(cL/30)2 of O-mode (left) and Z-mode (right) waves, for ∆N = 0.06 and different cL (see the legend in the left panel). All variables are normalized [PITH_FULL_IMAGE:figures/full_fig_p013_13.png]
Figure 14
Figure 14. Figure 14: Variations with the average level of density fluctuations ∆N of the electromagnetic radiation rates ˙η(cL/30)2 of O-mode (left) and Z-mode (right) waves, for ωc/ωp = 0.05 (upper row) and ωc/ωp = 0.15 (bottom row), for different cL (see the legend in the upper-left pan…
Figure 15
Figure 15. Figure 15: Electromagnetic O-mode waves : dispersion curves in the map (ck∥/ωp, ck⊥/ωp), for ωc/ωp = 0.2 and the frequencies ω/ωp = 1.005, 1.0125, 1.025 (see legend) [PITH_FULL_IMAGE:figures/full_fig_p021_15.png]
Figure 16
Figure 16. Figure 16: Dispersion of electromagnetic modes near the frequency ωp, for ωc/ωp = 0.1 and θ = 10◦ : variation of c 2 k 2 /ω2 p as a function of ω/ωp. Green (blue) lines represent the Z-mode waves and the curve ω = ωp (the O-mode waves). Black dashed and solid lines represent the…

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Works this paper leans on

55 extracted references · 45 canonical work pages

  1. [1]

    1989, Physics of Fluids B, 1, 1998, doi: 10.1063/1.859063

    Akimoto, K. 1989, Physics of Fluids B, 1, 1998, doi: 10.1063/1.859063

    work page doi:10.1063/1.859063 1989

  2. [2]

    T., Carley, E., Ca˜ nizares, L

    Badman, S. T., Carley, E., Ca˜ nizares, L. A., et al. 2022, ApJ, 938, 95, doi: 10.3847/1538-4357/ac90c2 24 Krafft and Volokitin

    work page doi:10.3847/1538-4357/ac90c2 2022

  3. [3]

    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

    work page doi:10.1029/95gl03595 1996

  4. [4]

    H., & Layden, A

    Cairns, I. H., & Layden, A. 2018, Physics of Plasmas, 25, 082309, doi: 10.1063/1.5037300

    work page doi:10.1063/1.5037300 2018

  5. [5]

    H., & Willes, A

    Cairns, I. H., & Willes, A. J. 2005, Physics of Plasmas, 12, 052315, doi: 10.1063/1.1889123

    work page doi:10.1063/1.1889123 2005

  6. [6]

    2021, ApJL, 915, L22, doi: 10.3847/2041-8213/ac0b43

    Chen, L., Ma, B., Wu, D., et al. 2021, ApJL, 915, L22, doi: 10.3847/2041-8213/ac0b43

    doi:10.3847/2041-8213/ac0b43 2021

  7. [7]

    Dulk, G. A. 1985, ARA&A, 23, 169, doi: 10.1146/annurev.aa.23.090185.001125

    work page arXiv 1985

  8. [8]

    T., & Nishikawa, K

    Dum, C. T., & Nishikawa, K. I. 1994, Physics of Plasmas, 1, 1821, doi: 10.1063/1.870636

    work page doi:10.1063/1.870636 1994

Show all 55 references
  1. [9]

    D., & Robinson, P

    Edney, S. D., & Robinson, P. A. 1999, Phys. Plasmas, 6, 3799, doi: 10.1063/1.873644

    1999 doi

  2. [10]

    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

    2016 doi

  3. [11]

    L., & Zhelezniakov, V

    Ginzburg, V. L., & Zhelezniakov, V. V. 1958, Soviet Ast., 2, 653

    1958

  4. [12]

    S., & Ryzhik, I

    Gradshteyn, I. S., & Ryzhik, I. M. 2007, Table of integrals, series, and products, seventh edn. (Elsevier/Academic

    2007

  5. [13]

    B., & Cairns, I

    Graham, D. B., & Cairns, I. H. 2013, J. Geophys. Res., 118, 3968, doi: 10.1002/jgra.50402

    2013 doi

  6. [14]

    E., Fried, B

    Hinkel-Lipsker, D. E., Fried, B. D., & Morales, G. J. 1989, PhRvL, 62, 2680, doi: 10.1103/PhysRevLett.62.2680 —. 1991, PhRvL, 66, 1862, doi: 10.1103/PhysRevLett.66.1862

    1989 doi

  7. [15]

    C., Krasnoselskikh, V., Pulupa, M., Magdalenic, J., & Bale, S

    Jebaraj, I. C., Krasnoselskikh, V., Pulupa, M., Magdalenic, J., & Bale, S. D. 2023, ApJL, 955, L20, doi: 10.3847/2041-8213/acf857

    2023 doi

  8. [16]

    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

  9. [17]

    H., & Robinson, P

    Kim, E.-H., Cairns, I. H., & Robinson, P. A. 2007, PhRvL, 99, 015003, doi: 10.1103/PhysRevLett.99.015003 —. 2008, Phys. Plasmas, 15, 102110, doi: 10.1063/1.2994719

    2007 doi

  10. [18]

    2022, ApJL, 924, L24, doi: 10.3847/2041-8213/ac46a7 —

    Krafft, C., & Savoini, P. 2022, ApJL, 924, L24, doi: 10.3847/2041-8213/ac46a7 —. 2024, ApJL, 964, L30, doi: 10.3847/2041-8213/ad3449

    2022 doi

  11. [19]

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

    2024 doi

  12. [20]

    Krafft, C., & Volokitin, A. S. 2021, ApJ, 923, 103, doi: 10.3847/1538-4357/ac2153 —. 2024, ApJ, 964, 65, doi: 10.3847/1538-4357/ad20ee

    2021 doi

  13. [21]

    S., & Gauthier, G

    Krafft, C., Volokitin, A. S., & Gauthier, G. 2019, Fluids, 4, doi: 10.3390/fluids4020069

    2019 doi

  14. [22]

    2025, Nature Astronomy, in press

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

    2025 arXiv

  15. [23]

    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

  16. [24]

    V., & Sotnikov, V

    Krasnoselskikh, V. V., & Sotnikov, V. I. 1977, Fizika Plazmy, 3, 872

    1977

  17. [25]

    P., Soucek, J., et al

    Krupar, V., Kontar, E. P., Soucek, J., et al. 2015, A&A, 580, A137, doi: 10.1051/0004-6361/201425308

    2015 doi

  18. [26]

    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

  19. [27]

    2024a, ApJ, 961, 88, doi: 10.3847/1538-4357/ad12ba —

    Krupar, V., Kruparova, O., Szabo, A., et al. 2024a, ApJ, 961, 88, doi: 10.3847/1538-4357/ad12ba —. 2024b, ApJL, 967, L32, doi: 10.3847/2041-8213/ad4be7

    doi

  20. [28]

    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

  21. [29]

    H., Lee, E., & Tu, W

    Lee, S.-Y., Yoon, P. H., Lee, E., & Tu, W. 2022, The Astrophysical Journal, 924, 36, doi: 10.3847/1538-4357/ac32bb

    2022 doi

  22. [30]

    F., Yoon, P

    Lee, S.-Y., Ziebell, L. F., Yoon, P. H., Gaelzer, R., & Lee, E. S. 2019, ApJ, 871, 74, doi: 10.3847/1538-4357/aaf476

    2019 doi

  23. [31]

    H., & Robinson, P

    Li, B., Cairns, I. H., & Robinson, P. A. 2008a, J. Geophys. Res.Space Physics, 113, 1, doi: 10.1029/2007JA012958

    doi

  24. [32]

    A., & Cairns, I

    Li, B., Robinson, P. A., & Cairns, I. H. 2008b, J. Geophys. Res.Space Physics, 113, 1, doi: 10.1029/2008JA013255

    doi

  25. [33]

    J., Robinson, P

    Li, B., Willes, A. J., Robinson, P. A., & Cairns, I. H. 2005, Phys. Plasmas, 12, 052324, doi: 10.1063/1.1906214

    2005 doi

  26. [34]

    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

  27. [35]

    M., Cairns, I

    Malaspina, D. M., Cairns, I. H., & Ergun, R. E. 2012, ApJ, 755, 45, doi: 10.1088/0004-637X/755/1/45

    2012 doi

  28. [36]

    Melrose, D. B. 1980, SSRv, 26, 3, doi: 10.1007/BF00212597

    1980 doi

  29. [37]

    B., & Sy, W

    Melrose, D. B., & Sy, W. N. 1972, Australian Journal of Physics, 25, 387, doi: 10.1071/PH720387 M¨ uller, D., St. Cyr, O. C., Zouganelis, I., et al. 2020, A&A, 642, A1, doi: 10.1051/0004-6361/202038467

    1972 doi

  30. [38]

    V., & Newman, D

    Muschietti, L., Goldman, M. V., & Newman, D. 1985, SoPh, 96, 181, doi: 10.1007/BF00239800

    1985 doi

  31. [39]

    Nishikawa, K., & Ryutov, D. D. 1976, Journal of the Physical Society of Japan, 41, 1757, doi: 10.1143/JPSJ.41.1757

    1976 doi

  32. [40]

    L., & Smith, R

    Papadopoulos, K., Goldstein, M. L., & Smith, R. A. 1974, ApJ, 190, 175, doi: 10.1086/152862 Polanco-Rodr ´ ıguez, F. J., Krafft, C., & Savoini, P. 2025, The Astrophysical Journal Letters, 982, L24, doi: 10.3847/2041-8213/adba64

    1974 doi

  33. [41]

    P., & Reid, H

    Ratcliffe, H., Kontar, E. P., & Reid, H. A. S. 2014, A&A, 572, A111, doi: 10.1051/0004-6361/201423731

    2014 doi

  34. [42]

    Reid, H. A. S., & Kontar, E. P. 2021, Nature Astronomy, 5, 796, doi: 10.1038/s41550-021-01370-8 Linear mode conversion theory 25

    2021 doi

  35. [43]

    Reid, H. A. S., & Ratcliffe, H. 2014, Res. Astron. Astrophys., 14, 773, doi: 10.1088/1674-4527/14/7/003

    2014 doi

  36. [44]

    2009, ApJ, 694, 618, doi: 10.1088/0004-637X/694/1/618

    Rhee, T., Ryu, C.-M., Woo, M., et al. 2009, ApJ, 694, 618, doi: 10.1088/0004-637X/694/1/618

    2009 doi

  37. [45]

    H., & Kim, E

    Schleyer, F., Cairns, I. H., & Kim, E. H. 2013, Physics of Plasmas, 20, 032101, doi: 10.1063/1.4793726

    2013 doi

  38. [46]

    H., & Kim, E.-H

    Schleyer, F., Cairns, I. H., & Kim, E.-H. 2014, Journal of Geophysical Research (Space Physics), 119, 3392, doi: 10.1002/2013JA019364

    2014 doi

  39. [47]

    Shafranov, V. D. 1967, Reviews of Plasma Physics, 3, 1, doi: 10.1007/978-1-4615-7799-7

    1967 doi

  40. [48]

    Thejappa, G., & MacDowall, R. J. 2021, ApJ, 912, 61, doi: 10.3847/1538-4357/abee74

    2021 doi

  41. [49]

    Tsytovich, V. N. 1970, Nonlinear Effects in Plasma (Plenum Press, New-York-London) van Haarlem, M. P., Wise, M. W., Gunst, A. W., et al. 2013, A&A, 556, A2, doi: 10.1051/0004-6361/201220873

    1970 doi

  42. [50]

    S., & Krafft, C

    Volokitin, A. S., & Krafft, C. 2018, ApJ, 868, 104, doi: 10.3847/1538-4357/aae7cc —. 2020, ApJL, 893, L47, doi: 10.3847/2041-8213/ab74de

    2018 doi

  43. [51]

    J., & Cairns, I

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

    2000 doi

  44. [52]

    M., & Bougeret, J

    Yin, L., Ashour-Abdalla, M., El-Alaoui, M., Bosqued, J. M., & Bougeret, J. L. 1998, Geophys. Res. Lett., 25, 2609, doi: 10.1029/98GL01989

    1998 doi

  45. [53]

    A., B¨ uchner, J., & Liu, S

    Zhou, X., Mu˜ noz, P. A., B¨ uchner, J., & Liu, S. 2020, The Astrophysical Journal, 891, 92, doi: 10.3847/1538-4357/ab6a0d

    2020 doi

  46. [54]

    F., Yoon, P

    Ziebell, L. F., Yoon, P. H., Petruzzellis, L. T., Gaelzer, R., & Pavan, J. 2015, ApJ, 806, 237, doi: 10.1088/0004-637X/806/2/237

    2015 doi

  47. [55]

    Zlotnik, E. I. 1981, A&A, 101, 250

    1981

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