Pith. sign in

REVIEW 4 major objections 5 minor 36 references

Implication of Kinetic Alfven Waves to Magnetic Field Turbulence Spectra: Earth's Magnetosheath

T0 review · 4 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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

Pith's one-line read Kinetic Alfvén waves may explain steepened magnetosheath spectra

desk verdict The observational statistics on 337 magnetosheath intervals are a solid confirmation of known steepening, but the KAW simulation comparison is too loose to carry the theoretical claim. read the letter →

arxiv 1908.02533 v1 pith:5XWGX7LS submitted 2019-08-07 physics.space-ph astro-ph.EPastro-ph.SR

N. K. Dwivedi , S. Kumar , P. Kovacs , E. Yordanova , M. Echim , R. P. Sharma , M. L. Khodachenko , Y. Sasunov This is my paper · ORCID
classification physics.space-phastro-ph.EPastro-ph.SR PACS 52.35.Bj94.30.cq
keywords magneticfieldturbulencemagnetosheathkineticAlfvénwavesspectralslopeClusterspacecraftplasmanonlinearityiongyroradius
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

The paper asks why magnetic-field fluctuation spectra in Earth's magnetosheath steepen sharply at kinetic scales. Using 337 Cluster magnetosheath intervals, it shows that spectra remain shallow (slopes between $-1.5$ and $0$) down to about 20 ion gyroradii, then break near $k\rho_i \approx 0.05$ and steepen to slopes between $-2.6$ and $-1.8$, with the most probable value near $-2.4$. The authors conjecture that the high-frequency part is produced by kinetic Alfvén waves: there the propagation angles become oblique and the compressibility stays modest. A two-fluid model of kinetic Alfvén wave turbulence, evolved numerically, yields a magnetic-field power spectrum with slope about $-2.8$, close to the observed steep range. The match is offered as evidence that perpendicular kinetic Alfvén waves contribute to the small-scale magnetosheath cascade.

What carries the argument

The central object is the dimensionless two-fluid envelope equation for a kinetic Alfvén wave (Eq. (6)), in which nonlinearity enters through density fluctuations that adiabatically follow the wave amplitude and shift the wave frequency. The equation is evolved with a $128 \times 128$ de-aliased pseudo-spectral scheme from a slightly perturbed plane wave, and the resulting magnetic-field spectrum is compared with the observed one. On the data side, the machinery is the statistical slope-identification algorithm applied to Welch power spectra, together with minimum-variance analysis of the spectral matrix to obtain propagation angle $\theta_{kB}$ and compressibility $R$; Taylor's frozen-in hypothesis maps spacecraft frequencies to wavenumbers.

What would settle it

Determine the wavenumber spectrum of the same magnetosheath intervals directly from multi-point spacecraft measurements (Cluster tetrahedron or MMS) without invoking Taylor's hypothesis; if the break does not appear near $k\rho_i \simeq 0.05$ and the high-frequency slope does not fall between $-2.6$ and $-1.8$, the KAW explanation loses its observational basis. A direct measurement showing near-zero compressibility and parallel propagation for the high-frequency fluctuations would also contradict the KAW picture.

Watch

Extended reading notes

Core claim

On its own terms, the paper establishes a statistical phenomenology and a candidate mechanism. The Cluster data show a clear transition: for $f_{sc}/f_{ci} < 0.5$ the spectral index $\alpha$ is broadly distributed between $-1.5$ and $0$, while for $f_{sc}/f_{ci} > 0.5$ the distribution peaks near $\alpha \approx -2.4$, with a persistent second power law between $-2.6$ and $-1.8$. In wavenumber units the break sits at $k\rho_i \simeq 0.05$. Propagation-angle and compressibility statistics indicate that low-frequency fluctuations are mostly perpendicular and mixed compressive/transverse, whereas above about $10 f_{ci}$ the angles spread over $30^\circ$-$90^\circ$ and the compressibility falls to $0.2 \lesssim R \lesssim 0.5$. The theoretical result is that the nonlinear evolution of kinetic Alfvén waves, simulated from a two-fluid envelope equation, produces a magnetic-field spectrum with slope near $-2.8$, close to the observed steep range. The paper therefore claims kinetic Alfvén waves are a plausible partial cause of the observed steepening, not that they are the only or definitively identified mechanism.

Load-bearing premise

The analysis assumes that each spacecraft-measured frequency can be converted to a spatial wavenumber by the bulk flow speed (Taylor's frozen-in hypothesis); if wave propagation speeds are not negligible, the reported spectral break and slopes in wavenumber space would change.

Editorial extensions

If this is right

  • If kinetic Alfvén waves drive the steep range, the observed break near $k\rho_i \sim 0.05$ marks the scale at which KAW dynamics begins to dominate over larger-scale fluctuations.
  • The near-absence of a Kolmogorov inertial range in most magnetosheath intervals would be a natural consequence of wave-dominated dynamics and finite shock-processing time, rather than a sign that no cascade exists.
  • Magnetic spectra in other planetary magnetosheaths with similar plasma $\beta$ and temperature ratios should show the same break location and steep slopes if KAW turbulence is a general feature.
  • The simulated slope near $-2.8$ gives a quantitative prediction that can be tested with higher-cadence or multi-spacecraft spectra without relying on Taylor's hypothesis.

Reading between the lines

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

  • An extension implied by the paper is that the steepened range should carry KAW polarization signatures—magnetic fluctuations mostly perpendicular to $\mathbf{B}_0$ with a modest compressive component—which MMS data can check directly.
  • The model's slope likely depends on $T_e/T_i$ and plasma $\beta$; sorting magnetosheath events by these parameters should reveal systematic shifts in the break scale and steepening rate.
  • Because the simulation omits electron Landau damping, the observed steepening may combine KAW nonlinear transfer with kinetic dissipation; adding collisionless damping would predict whether the spectrum steepens further at electron scales.
  • If KAW turbulence feeds the kinetic cascade, the energy should be deposited preferentially in electrons, so simultaneous electron temperature measurements could test the interpretation.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. This paper analyzes 337 Cluster-1 magnetosheath intervals from 2007–2008, computes total magnetic field power spectra in spacecraft frequency and wavenumber domains, and uses a sliding-window fitting algorithm to extract spectral slopes, propagation angles from minimum variance analysis, and compressibility. The authors report low-frequency slopes between -1.5 and 0, a transition near 0.5 f_ci, steepened high-frequency slopes between -2.6 and -1.8 with a break at k rho_i ≈ 0.05, and broad propagation angles with moderate compressibility at high frequencies. They conjecture that kinetic Alfvén waves contribute to the small-scale steepening and support this with a two-fluid KAW model and a 2D pseudo-spectral simulation whose magnetic field spectrum has a slope near -2.8. The paper concludes that the simulated and observed spectra are analogous.

Significance. If the KAW interpretation were quantitatively established, the paper would provide a useful link between statistical magnetosheath observations and kinetic turbulence modeling, complementing earlier work by Zimbardo et al. and Tao et al. The observational statistical analysis covers a large event set and combines slope statistics with wave diagnostics, which is a strength; the data selection and spectral procedures are described in enough detail to be reproduced. The main limitation is that the quantitative comparison between simulation and observation is not yet convincing: the simulated spectrum is a different observable than the measured one and its slope is outside the quoted observed range. Thus the paper is better seen as presenting a plausible conjecture rather than a demonstrated implication.

major comments (4)
  1. [Section 4.2 (Fig. 7) versus Section 2.2 (Figs. 2 and 4)] The simulated spectrum plotted in Fig. 7 is |B_y(k_z)|^2 on the cut k_x=0 for a single transverse component, whereas the observed spectra in Figs. 2 and 4 are total-|B| spectra mapped along the spacecraft flow direction using the Taylor hypothesis. Because the flow direction is generally not parallel to the mean magnetic field, and because the observed high-frequency fluctuations have propagation angles broadly distributed between about 30 and 90 degrees (Fig. 5) with compressibility 0.2–0.5 (Fig. 6), the slope of a one-dimensional component cut along the parallel direction need not equal the slope of the observed trace spectrum. Please demonstrate that the simulated quantity is the same observable as the measured one, for example by computing an angle-averaged or flow-directed total-|B| spectrum from the model, or restrict the claim accordingly.
  2. [Section 4.2 and Section 5] The simulated spectral slope of about -2.8 lies outside the observed range -2.6 to -1.8 quoted in the abstract, Section 4.1, and Fig. 4, and it also differs from the most probable value of -2.4. Calling this 'close' is not quantitatively justified. Please provide a statistical comparison, such as the distribution of simulated slopes over an ensemble of realizations or a sensitivity study over the model parameters, and state explicitly whether the model reproduces the observed range or only a nearby value.
  3. [Section 5] The Taylor-hypothesis conditional analysis is described in the text but the results are not shown: the authors state that the basic statistical results remain unchanged for events with V_flow < 150 km/s (111 events) and V_flow > 219 km/s (112 events), but no figure or table is provided. Since the wavenumber-domain results and the break at k rho_i ≈ 0.05 (Fig. 4) rely directly on the Taylor mapping, please include the conditional results so that the reader can verify the claimed insensitivity to the flow speed.
  4. [Section 4.1 (Figs. 3 and 4)] The spectral slope distributions are reported without error bars or confidence intervals, and the scaling-range definition depends on an adjustable window length L and the sliding-fit procedure. Please quantify the uncertainty of the slope values (for example, with bootstrap resampling or interquartile ranges) to establish that the high-frequency range -2.6 to -1.8 and the break at k rho_i ≈ 0.05 are robust features rather than artifacts of the fitting algorithm.
minor comments (5)
  1. [Section 3.1 (Eq. 6)] The definitions of the dimensionless parameters Gamma_1 and Gamma_2 following Eq. (6) are unclear as printed, appearing to contain i and i^2 factors; please fix the notation and provide the intermediate algebra from Eq. (5) to Eq. (6) in an appendix or on request.
  2. [Abstract and Section 4.1] The expression '0.1 < R > 0.9' appears to be a typographical error for 0.1 ≤ R ≤ 0.9; please correct it.
  3. [Section 5] The sentence 'The conditional analyses prove that our results reliably characterise the spectral behaviour' is too strong given that the results are not shown; please soften the wording or include the analysis.
  4. [Throughout] The name 'Alfvèn' should be 'Alfvén', and the reference 'Kairmabadi' should be 'Karimabadi'; there are also several garbled mathematical expressions, for example '2.8k−' in Section 4.2, which should read '≈ -2.8'.
  5. [Section 2.2] The sentence 'the first three data pairs of the Welch spectra are skipped' is ambiguous; please clarify what is being skipped and why.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity; the simulated KAW spectrum is not fitted to the observed slopes, though self-cited model setup and quantity mismatches weaken the comparison.

full rationale

The paper's claimed derivation chain is: Cluster observations produce independent spectral-slope statistics; the authors conjecture KAWs as a possible cause; a two-fluid KAW equation (Eq. 6) with stated plasma parameters and initial condition (Eq. 7) is simulated; the simulated spectrum is then compared with the observed slopes. The simulation output is not obtained by fitting the observed spectral indices: the slope of about -2.8 in Fig. 7 emerges from the dynamical equation and the chosen initial perturbation, not from the observed -2.6 to -1.8 range. Thus there is no self-definitional or fitted-input-called-prediction circularity. The governing equation and initial condition are attributed partly to the authors' prior work (Dwivedi et al. 2012, 2013; Dwivedi & Sharma 2013), but these self-citations are not load-bearing in the circular sense: the equation is also traced to Shukla and Stenflo (1999, 2000), and the cited prior works do not assert the observational result. The comparison is weakened by legitimate scientific concerns -- the simulated quantity |B_y(k_z)|^2 at k_x=0 differs from the observed total-field spectrum along the flow, and -2.8 is outside the quoted observed range -- but these are correctness/evidence limitations, not circular reductions. The Taylor-hypothesis conditional analysis is described but not shown, which is an evidence gap rather than a construction of the result. Overall, the observational and theoretical parts remain independent, so the circularity score is low.

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

No new physical entities are introduced. The model relies on standard two-fluid assumptions and on hand-picked simulation parameters (pump frequency, wavenumber, initial perturbation). The observational analysis relies on Taylor's hypothesis and a plane-wave interpretation of minimum variance analysis. These assumptions are load-bearing for the k-space spectrum and the comparison to the simulation.

free parameters (5)
  • pump KAW frequency omega0 = 0.01 omega_ci
    Chosen in the simulation, not measured; controls the nonlinear timescale and the spectral shape of the evolving turbulence.
  • pump perpendicular wavenumber k_x0 rho_i = 0.01
    Chosen in the simulation, not measured; sets the perpendicular scale of the initial KAW and affects the nonlinear cascade.
  • initial perturbation amplitude and scale = amplitude 0.1, kappa_x = kappa_z = 0.1
    Initial condition for the simulation, taken as a small modulation of the pump wave; not constrained by the observed fluctuation amplitudes.
  • spectral slope window L = 0.3 times the range of alpha(f)
    Defined dynamically in the automated power-law finder; an arbitrary threshold that determines which frequency ranges are called scaling ranges.
  • signal-to-noise truncation threshold = 2
    Spectra are truncated where S/N falls below 2; a reasonable but arbitrary choice that sets the high-frequency extent of the analysis.
assumptions (5)
  • domain assumption Taylor's frozen-in flow hypothesis applies to all magnetosheath intervals.
    Invoked in Section 2.2 to convert spacecraft-frame frequencies to wavenumbers; the validity is checked only qualitatively through unreported conditional analyses.
  • domain assumption The minimum variance eigenvector gives the wave propagation direction.
    Assumed in Section 2.2 to estimate theta_kB and compressibility; this is only valid for a single plane-wave superposition, which is questionable in strong turbulence.
  • domain assumption Two-fluid drift approximation with isothermal electrons and ions and adiabatic density response.
    Used in Section 3.1 to derive the KAW governing equation; valid only for low-frequency, weakly nonlinear kinetic Alfven waves in a homogeneous plasma.
  • domain assumption Weak nonlinearity and a plane-wave envelope ordering with d_x >> d_z.
    Used in Section 3.1 to reduce Eq. (2) to the envelope equation Eq. (6); restricts the model to a specific parameter regime.
  • ad hoc to paper The pump KAW frequency and perpendicular wavenumber are small (0.01 omega_ci and 0.01 rho_i).
    Chosen for the simulation without observational justification; the resulting spectrum depends on this choice.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Implication of Kinetic Alfven Waves to Magnetic Field Turbulence Spectra: Earth's Magnetosheath." pith.science (2026). https://pith.science/paper/5XWGX7LS

@misc{pith2026190802533,
  author       = {Pith},
  title        = {Pith review of: Implication of Kinetic Alfven Waves to Magnetic Field Turbulence Spectra: Earth's Magnetosheath},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5XWGX7LS}},
  note         = {Machine review of arXiv:1908.02533}
}
read the original abstract

In the present paper, we investigate the power-law behaviour of the magnetic field spectra in the Earths magnetosheath region using Cluster spacecraft data under solar minimum condition. The power spectral density of the magnetic field data and spectral slopes at various frequencies are analysed. Propagation angle and compressibility are used to test the nature of turbulent fluctuations. The magnetic field spectra have the spectral slopes between -1.5 to 0 down to spatial scales of 20 ion gyroradius and show clear evidence of a transition to steeper spectra for small scales with a second power-law, having slopes between -2.6 to -1.8. At low frequencies, f_sc<0.3f_ci(where f_ci is ion gyro-frequency), propagation angle approximately 90 degrees to the mean magnetic field, B_0, and compressibility shows a broad distribution, 0.1 < R > 0.9. On the other hand at f_sc>10f_ci, the propagation angle exhibits a broad range between 30-90 degree while 'R' has a small variation: 0.2 < R > 0.5. We conjecture that at high frequencies, the perpendicularly propagating Alfven waves could partly explain the statistical analysis of spectra. To support our prediction of kinetic Alfven wave-dominated spectral slope behaviour at high frequency, we also present a theoretical model and simulate the magnetic field turbulence spectra due to the nonlinear evolution of kinetic Alfven waves. The present study also shows the analogy between the observational and simulated spectra.

Figures

Figures reproduced from arXiv: 1908.02533 by the authors.

Figure 1
Figure 1. Normalised superposed power spectral density of the magnetic field time-series (337 events) inside the magnetosheath. The frequency in the spacecraft frame, sc f , normalised to the ion gyrofrequency ci f is shown on the x-axis, and the magnetic field power spectral density, normalised to the square of the mean magnetic field amplitude, 0 2 B , is shown on the y-axis. The sensitivities of spacecraft fluxgate magneto… view at source ↗
Figure 2
Figure 2. Normalised superposed power spectral density of the magnetic field time-series (337 events) inside the magnetosheath. The spatial coordinate spanning the streamline component of the wave number, 2 sc flow f k V   , in the unit of ion gyroradius 2 Ti i ci V f    is depicted on the x-axis, and the magnetic field power spectral density, normalised to 0 2 B , is shown on the y-axis [PITH_FULL_IMAGE:figures/full_fi… view at source ↗
Figure 3
Figure 3. Two-dimensional histogram for the spectral slope analysis of the magnetic field fluctuations, frequency, sc f , normalised to ion gyrofrequency, ci f , is presented on the x-axis, different slope values are depicted on the y-axis, and colours show the cumulative number of occurrence of different slopes at logarithmically equal frequency bins. The right histogram shows the cumulative number of occurrence of different… view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Two-dimensional histogram for the spectral slope analysis of the magnetic field fluctuations is shown in the spatial spanning of wave number, k , in the unit of ion gyroradius, i , and the cumulative number of occurrence of different slopes at logarithmically equal wa…
Figure 5
Figure 5. Figure 5: Two-dimensional histogram of the distribution of the angle of propagation (  kB ) concerning frequency ( sc ci ff ). For frequencies above 10 ci f , the distribution becomes broader and the peak at 90 vanishes gradually at higher frequencies. The thick red line shows …
Figure 6
Figure 6. Figure 6: Two-dimensional histogram of the distribution of compressibility ( R ‖ ) concerning frequency ( sc ci ff ). Ion cyclotron mode is incompressible, circularly or elliptically (left-hand) polarised, and the direction of the wave vectors can change from parallel to quasi-p…
Figure 7
Figure 7. Figure 7: The magnetic field spectra obtained by the simulation. The variation of 2 Byk against k is depicted on the y-axis. The thick red line represents the spectral slope value. Unlike many of other simulation studies (Karimabadi et al. 2013; Boldyrev et al. 2013; Franci et a…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

36 extracted references · 36 canonical work pages

  1. [1]

    M., Acuna, M

    Balogh, A., Carr, C. M., Acuna, M. H., Dunlop, M. W., Beek, T. J., Brown, P. et al.: Annales Geophys. 19, 1207 (2001). Bavassano Cattaneo, M. B., Moreno, G., Russo, G., Richardson, J. D.: J. Geophys. Res. 105, 23141-23152 (2000)

    work page 2001

  2. [2]

    C.: Astrophys

    Boldyrev, S., Horaites, K., Xia, Q., Perez, J. C.: Astrophys. J. 777, 41 (2013)

    work page 2013

  3. [3]

    R., Sahraoui, F, Andriopoulou, M., Le Contel, O

    Breuillard, H., Matteini, L., Argall, M. R., Sahraoui, F, Andriopoulou, M., Le Contel, O. et al.: Astrophys. J. 859, 127 (2018)

    work page 2018

  4. [4]

    in Solar Phys

    Bruno, R., Carbone, V: Living Rev. in Solar Phys. 2, 4 (2005)

    work page 2005

  5. [5]

    Carr, C., Brown, P., Alconcel, L. -N. et al.: User guide to the FGM measurements in the Cluster Active Archive, (2014)

    work page 2014

  6. [6]

    Chen, C.H.K., Leung, L., Boldyrev, S., Maruca, B.A., Ba le, S.D.: Geophys. Res. Lett. 28 , 41 (2014)

    work page 2014

  7. [7]

    N., Matthaeus, W

    Chhiber, R., Chasapis, A., Bandyopadhyay, R., Parashar, T. N., Matthaeus, W. H., Maruca, B. A., Moore, T. E., Burch, J. L., Torbert, R. B., Russelll, C. T., Le Contel, O. et al: J. Geophys. Res.: Space Phys. 123, 12 (2018). Décréau, P. M. E., Fergeau, P., Krannosels’kikh, V. et al.: Space Sci. Rev. 79, 157– 193 (1997). 24 | P a g e

    work page 2018

  8. [8]

    K., Schmid, D., Narita, Y

    Dwivedi, N. K., Schmid, D., Narita, Y. et al.: Earth, Planets and Space 67, 137 (2015)

    work page 2015

Show all 36 references
  1. [9]

    K., Sharma, R

    Dwivedi, N. K., Sharma, R. P.: Phys. of Plasmas 20, 042308 (2013)

    2013

  2. [10]

    K., Batra, K., Sharma, R

    Dwivedi, N. K., Batra, K., Sharma, R. P.: J. Geophys. Res. 117, A07201 (2012)

    2012

  3. [11]

    K., Sharma, R

    Dwivedi, N. K., Sharma, R. P., Batra, K.: Astrophys. Space Sci. 343: 19-26 (2013)

    2013

  4. [12]

    Franci, L., Landi, S., Matteini, L., Verdini, A., Hellinger, P.: Astrophys. J. 833, 91 (2016)

    2016

  5. [13]

    Franci, L., Landi, S., Verdini, A., Matteini, L., Hellinger, P.: Astrophys. J. 853, 26 (2018)

    2018

  6. [14]

    T., Thomsen, M

    Gosling, J. T., Thomsen, M. F., Bame, S. J.: Geophys. Res. 94, 10011-10025 (1989)

    1989

  7. [15]

    F., Jenko, F.: Phys

    Groselj, D., Mallet, A., Loureiro, N. F., Jenko, F.: Phys. Rev. Lett. 120, 105101 (2018)

    2018

  8. [16]

    K.: Astrophys

    Dougherty, M. K.: Astrophys. J. Lett. 813, L29 (2015)

    2015

  9. [17]

    Y., Sahraoui, F., Deng, X

    Huang, S. Y., Sahraoui, F., Deng, X. H., He, J. S., Yuan, Z. G., Zhou, M., Pang, Y., Fu, H. S.: Astrophys. J. Lett. 836, L10 (2017)

    2017

  10. [18]

    Y., Hadid, L

    Huang, S. Y., Hadid, L. Z., Sahraoui, F., Yuan, Z. G., Deng, X. H.: Astrophys. J. Lett. 836, L10 (2017)

    2017

  11. [19]

    et al.: Phys

    Kairmabadi, H., Roytershteyn, V., Wan, M. et al.: Phys. of Plasmas 20, 012303 (2013)

    2013

  12. [20]

    P., Singh, H

    Kumar, S., Sharma, R. P., Singh, H. D.: Phys. of Plasmas 16, 072903 (2009)

    2009

  13. [21]

    Kovacs, P., Facsko, G., Dandouras, I.: Planetary and Space Science 92, 24 (2014)

    2014

  14. [22]

    J., Smith, C

    Leamon, R. J., Smith, C. W., Ness, N. F. et al.: J. Geophys. Res. 104, 22331 (1999)

    1999

  15. [23]

    Matteini, L., Alexandrova, O., Chen, C. H. K., Lacombe, C: MNRAS 466, 945-951 (2016)

    2016

  16. [24]

    L., Russel, C

    McPherron, R. L., Russel, C. T., Coleman, P. J.: Space Sci. Rev. 13, 411 (1972). Remé, H., Aoustin, C., Bosqued, J. M., Dandouras, I. et al.: Ann. Geophys. 19, 1303 (2001)

    1972

  17. [25]

    P., Modi, K

    Sharma, R. P., Modi, K. V.: Phys. of Plasmas 20, 08230 (2013)

    2013

  18. [26]

    P., Malik, M.: Astron

    Sharma, R. P., Malik, M.: Astron. Astrophys. 457, 675 (2006)

    2006

  19. [27]

    P., Singh, H

    Sharma, R. P., Singh, H. D.: J. Astrophys. Astr. 29, 239 (2008)

    2008

  20. [28]

    K., Stenflo, L.: Phys

    Shukla, P. K., Stenflo, L.: Phys. Plasmas 6, 4120–4122 (1999). 25 | P a g e

    1999

  21. [29]

    K., Stenflo, L.: Phys

    Shukla, P. K., Stenflo, L.: Phys. Plasmas 7, 2738–2739 (2000)

    2000

  22. [30]

    de, Chust, T., Kasahara, S., Retinò, A.: J

    Tao, C., Sahraoui, F., Fontaine, D., Patoul, J. de, Chust, T., Kasahara, S., Retinò, A.: J. Geophys. Res. 120, 2477-2493 (2015)

    2015

  23. [31]

    I.: Proc

    Taylor, G. I.: Proc. Roy. Soc. London A 164, 476 (1938)

    1938

  24. [32]

    M., Slavin, J

    Uritsky, V. M., Slavin, J. A., Khazanov, G. V., Donovan, E. F., Boardsen, S. A., Anderson, von Papen, M. V., Saur, J., Alexandrova, O.: J. Geophys. Res. 119, 2797 (2013). Vörös, Z., Zhang, T. L., Leubner, M. P. et al.: J. Geophys. Res. 113, E00B21 (2008)

    2013

  25. [33]

    D.: IEEE Transactions on Audio and Electroacoustics 15, 7073 (1967)

    Welch, P. D.: IEEE Transactions on Audio and Electroacoustics 15, 7073 (1967)

    1967

  26. [34]

    V., Khodachenko, M

    Zaqarashvili, T. V., Khodachenko, M. L., Rucker, H. O.: Astron. Astrophys. 529, A82 (2011)

    2011

  27. [35]

    V., Khodachenko, M

    Zaqarashvili, T. V., Khodachenko, M. L., Soler, R.: Astron. Astrophys. 549, A113 (2013)

    2013

  28. [36]

    Zimbardo, G., Greco, A., Sorriso-Valvo, L., Perri, S., et al.: Space Sci. Rev. 156, 89 (2010)

    2010

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.