Resonant excitation of whistler waves by a helical electron beam

Bart Van Compernolle; Jacob Bortnik; Lunjin Chen; Richard M. Thorne; Wen Li; Xin An

REVIEW 3 major objections 5 minor 40 references

Resonant excitation of whistler waves by a helical electron beam

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A helical electron beam in a cold magnetized plasma spontaneously excites whistler waves through three distinct resonances at once, and linear growth theory reproduces their frequency and propagation angle.

desk verdict Solid experimental identification of three simultaneous whistler resonances, with a linear-theory comparison that is plausible but rests on an unmeasured beam distribution. read the letter →

arxiv 1908.06952 v1 pith:HEH7THBQ submitted 2019-08-19 physics.plasm-ph astro-ph.SRphysics.space-ph

Xin An , Bart Van Compernolle , Jacob Bortnik , Richard M. Thorne , Lunjin Chen , Wen Li This is my paper · ORCID

classification physics.plasm-phastro-ph.SRphysics.space-ph

keywords whistlerwaveschorushelicalelectronbeamcyclotronresonanceLandauanomalouslineargrowthratewavenormalangle

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 reports a laboratory experiment in which a beam of electrons, injected at an angle to a magnetic field in a cold plasma, spontaneously generates chorus-like whistler waves with no imposed wave frequency. A phase-correlation technique reconstructs the full three-dimensional wave field and identifies three simultaneous resonance branches corresponding to $n=1$, $n=0$, and $n=-1$ in the resonance condition $\omega - k_z v_d = n\Omega_e$ — normal cyclotron, Landau, and anomalous cyclotron resonance — each occupying a distinct frequency and propagation-angle region. The authors argue that linear hot-plasma growth-rate calculations, using a beam-ring electron distribution inferred from physical arguments, reproduce the location and wave-normal angles of all three branches. If correct, this is the first experimental resolution of the resonance structure of spontaneously excited whistler waves, and it supports the idea that very oblique chorus waves in the Earth's radiation belts can be generated by low-energy electron beams through combined cyclotron and Landau resonances.

What carries the argument

The experimental machinery is a phase-correlation technique: a moving magnetic probe paired with a fixed reference probe measures the phase delay $\Delta\varphi(\rho,z,\omega)$ over many identical plasma shots, and a linear fit to $\Delta\varphi = k_z(\omega)z + k_\perp(\omega)\rho$ yields the parallel and perpendicular wave numbers at every frequency. This converts a broadband spectrogram into a $k_z-\omega$ diagram color-coded by wave-normal angle. The theoretical machinery is a beam-ring electron distribution function, a drifting Maxwellian in the parallel direction with a hollow perpendicular distribution, inserted into the hot-plasma dispersion relation; its free parameters are inferred from how the beam slows by generating plasma oscillations, and from beam geometry, rather than measured directly. Together, these pieces place the observed wave power on the resonance lines $\omega - k_z v_d = n\Omega_e$, which is the paper's evidence that three resonance branches coexist.

What would settle it

Directly probe the electron velocity distribution near the wave excitation region. The inferred beam-ring distribution predicts a positive slope of the distribution at Landau-resonant velocities and a negative slope at cyclotron-resonant velocities; if the measured distribution lacks these slopes at those velocities, or the wave numbers do not satisfy $\omega - k_z v_z = n\Omega_e$ for the measured resonant velocities, the three-branch resonance assignment is falsified.

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Extended reading notes

Core claim

The central discovery is that a helical electron beam in a cold, magnetized afterglow plasma excites broadband whistler waves whose frequency spectrum has the same two-band shape as magnetospheric chorus, with a gap near half the electron gyrofrequency. Reconstructing the wave field with a phase-correlation technique, the experiment resolves wave energy in wavenumber space organized along the resonance conditions $\omega - k_z v_d = n\Omega_e$ for $n = 1, 0, -1$, which the paper interprets as normal cyclotron, Landau, and anomalous cyclotron resonances acting simultaneously. The normal cyclotron mode is the dominant, quasi-parallel, counter-streaming wave and carries the largest amplitude; the Landau and anomalous cyclotron modes are oblique, with wave-normal angles near the resonance cone. Linear hot-plasma dispersion calculations using a beam-ring distribution reproduce all three branches in approximately the correct locations with consistent wave-normal angles, and parameter scans show that spectral peaks shift with plasma density and beam energy exactly as the resonance condition predicts.

Load-bearing premise

The growth-rate calculations depend on an assumed shape for the electron beam's velocity distribution, inferred from how the beam relaxes and from geometry rather than from direct measurement; if that assumed shape is wrong, the match with observations does not independently confirm the resonance mechanism.

Editorial extensions

If this is right

A two-band chorus spectrum with a gap at $0.5\Omega_e$ can be produced by a single unmodulated beam-ring electron distribution, simply because the three resonance branches populate different frequency ranges.
Linear growth-rate theory can predict the dominant frequency and wave-normal angle of beam-excited whistler waves without invoking nonlinear mechanisms, at least for the parameter range tested.
Very oblique lower-band chorus waves in the magnetosphere may be explained by low-energy electron beams generating waves through simultaneous cyclotron and Landau resonances, a mechanism the experiment reproduces in scaled laboratory conditions.
The spectral peak frequency of whistler waves should shift upward when the background plasma density or the beam energy decreases, because the cyclotron resonance condition must remain satisfied.
The dominant, most intense modes will be quasi-parallel and counter-streaming relative to the beam, consistent with the primarily parallel propagation of lower-band chorus.

Reading between the lines

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

If direct velocity-space measurements of the beam electrons were added, the inferred beam-ring parameters could be checked rather than assumed; the paper itself lists beam-distribution diagnostics as a future need.
The experiment uses a beam-ring distribution, whereas magnetospheric chorus is usually attributed to a bi-Maxwellian anisotropic distribution; if the same three-branch resonance structure appears for both, resonance-branch analysis could unify different chorus generation theories.
The inverse correlation between saturated wave power and linear growth rate at low plasma density suggests nonlinear processes take over control of wave amplitude there; a dedicated scan at even smaller $n_b/n_0$ could identify where linear growth stops predicting saturation.
The phase-correlation mapping technique could be applied to other unmodulated beam-plasma experiments to test whether $n = \pm1$ and $n=0$ resonance branches appear near other plasma boundaries.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague,

Read the An et al. LAPD paper on whistler excitation by a helical beam. The core result is the phase-correlation kz-omega diagram in Fig. 3a,b: in a single unmodulated beam experiment, the wave data aggregate onto three distinct resonance lines, n=1 (normal cyclotron), n=0 (Landau), and n=-1 (anomalous cyclotron). That is a genuine first, as far as I know. Previous beam experiments used density-modulated beams or looked at one resonance at a time; here the broadband spontaneous emission is resolved into all three branches simultaneously. The mode-structure extraction from phase delay looks careful, and the wave normal angles are consistent with the expected resonance-cone behavior.

What I would push back on is not the experiment but the evidential weight of the linear-theory comparison. The HOTRAY runs use Eq. 2, a four-parameter beam-ring distribution (vd, alpha_par, alpha_perp, beta). The paper is upfront that the distribution is not measured; the parameters are inferred from Langmuir-relaxation scaling and beam geometry. That is reasonable, and the authors do not overclaim—they say 'approximate' and note the Landau branch above 0.4Ωe is not captured. But with four free shape parameters and no sensitivity analysis, the agreement in Fig. 3c,d is not an independent confirmation of the mechanism. A serious referee should ask for a sensitivity scan, e.g., vary beta or alpha_perp by a factor of two and show the branch locations still appear. I doubt that would overturn the paper's conclusion, because the experimental resonance-line assignment already stands on its own; the theory is corroborative, not load-bearing for the basic claim. Still, the text says the growth-rate calculation 'captures the major observations' without quantifying how much the result depends on the assumed distribution.

Minor points: the spectral peak comparisons in Fig. 5 would benefit from error bars or at least scatter estimates, and the inverse correlation between saturated power and linear growth rate at low density is noted but left somewhat open. The citation pattern is appropriate; the prior lab and space literature is covered, and the self-citations are to the instrument and related LAPD work.

This paper deserves a serious referee. It is a careful experimental contribution that advances lab studies of chorus-like whistler excitation, and the simultaneous three-branch identification is new. With a sensitivity analysis and a slightly more modest claim about the theory comparison, it would be a solid letter.

Recommendation: send to peer review.

Referee Report

3 major / 5 minor

Summary. This letter reports laboratory observations on the Large Plasma Device of whistler-mode waves excited by a helical electron beam injected into a cold helium plasma. The authors use a phase-correlation technique with moving and fixed magnetic probes to reconstruct the three-dimensional mode structure, from which they extract parallel and perpendicular wavenumbers as functions of frequency. The resulting k_z-omega diagram shows the measured waves aggregating onto three resonance lines corresponding to omega - k_z u = n Omega_e with n = 1, 0, -1, which they identify as normal cyclotron, Landau, and anomalous cyclotron resonance branches. They compare these observations with linear growth rate calculations from the HOTRAY code, using a beam-ring distribution function described by Eq. (2), and report qualitative and quantitative agreement in branch locations, wave normal angles, and parametric dependencies for scans of plasma density, beam energy, and beam density. The main claim is that this experiment demonstrates simultaneous excitation of whistler waves through three resonance mechanisms and that linear theory reproduces the major observed features.

Significance. If the results hold, this is a valuable laboratory demonstration that a helical electron beam in a cold plasma can spontaneously excite whistler-mode waves through three simultaneous resonance branches, and that the experimentally measured mode structure can be organized onto the corresponding resonance conditions. The phase-correlation technique used to extract the k_z-omega dispersion is a strength and provides the first, to my knowledge, direct experimental measurement of the resonance structure of beam-driven whistler waves in a laboratory plasma. The parameter scans in Section 4, especially the peak-frequency dependencies, lend support to the cyclotron-resonance interpretation. However, the comparison to linear theory depends on a four-parameter model beam distribution that is not directly measured, and the manuscript contains no sensitivity analysis for those parameters. In addition, two acknowledged discrepancies -- the poorly captured Landau branch above 0.4 Omega_e and the inverse intensity correlation in the low-density scan limit the strength of the 'linear theory captures the observations' claim.

major comments (3)

[Section 3, Eq. (2), Fig. 3(c,d)] The HOTRAY calculations rely on four unmeasured beam distribution parameters (vd, alpha_parallel, alpha_perp, beta) that are inferred from Langmuir-relaxation scaling and beam geometry arguments. Since no direct measurement of the beam distribution is available, the agreement between the computed resonance branches and the observed kz-omega structure is not an independent confirmation of the excitation mechanism. I request a systematic sensitivity analysis in which each parameter is varied over a physically plausible range while the others are held fixed, with the resulting changes in linear growth rates, branch locations, and wave normal angles shown. If the qualitative agreement is robust to such variations, the claim is substantially strengthened; if it is not, the inference procedure must be made explicit and justified.
[Section 3, final paragraph] The manuscript states that waves in Landau resonance with the beam in the frequency range omega/Omega_e > 0.4 are 'not well captured by the linear growth rate calculations.' This is an explicit discrepancy in one of the three claimed resonance branches, and it appears to be at odds with the Abstract's statement that 'linear wave growth rates captures the major observations.' Please either quantify the discrepancy (e.g., by comparing the computed growth rates and observed power for that branch) or provide a more complete model that incorporates the spatial growth geometry described in the same paragraph. At minimum, the Abstract and Summary should be qualified so that the reader is not left with the impression that all three resonance branches are equally well reproduced by the linear calculation.
[Section 4, Fig. 5(b)] The claim that linear theory shows 'consistent behavior in both intensity and wave normal angle' is only partially supported by the parameter scans. While the spectral peak frequencies agree well, the saturated wave power and the maximum linear growth rate are inversely correlated in the low plasma density regime, as shown in Fig. 5(b). The text acknowledges this but does not provide a quantitative explanation. Please clarify how this inverse correlation is consistent with the central claim, or explicitly restrict the 'intensity' part of the claim to the regimes where a positive correlation is observed. Without this, the reader cannot assess whether the mismatch represents a physical limitation of linear theory or an artifact of the comparison procedure.

minor comments (5)

[Section 3, Eq. (2)] The parameter beta is described as a 'ring-distribution shape parameter,' but the normalization of Eq. (2) becomes singular for beta = 1. Please state the allowed range of beta and note that values in (0,1) are assumed throughout.
[Section 3, Fig. 3] The wave normal angle is reported as values above 90 degrees (e.g., WNA about 105 degrees for the cyclotron mode). Since wave normal angle is often defined in the range [0,90] degrees, please state the sign convention used here, for example whether psi = arccos(k_z/k) with signed k_z, so that counter-streaming waves take values between 90 and 180 degrees.
[Section 4, captions of Fig. 4] The caption says 'maximum linear growth rates' while the text says the largest linear growth rate is extracted over all possible WNAs for each frequency. Please clarify whether the maximum is taken over WNA only, and whether the same mode (cyclotron, Landau, or anomalous) is selected consistently across the scan.
[Section 4] In Fig. 4(a,b), the density scan at fixed beam energy and beam density simultaneously varies omega_pe/Omega_e and n_b/n_0; the text notes this but the coupling between these two dimensionless parameters is not discussed. A brief comment on how the comparison would change if the beam density were adjusted to maintain a constant n_b/n_0 would be helpful.
[Section 1 and 5] The introduction and summary refer to 'bi-Maxwellian distribution is observed to be responsible for the excitation of whistler-mode chorus waves in space' and to 'a beam ring distribution in velocity space' here. Adding a citation for the space-observation claim and a brief reference to the beam-ring geometry would improve the context.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: HOTRAY is a forward model with parameters inferred from independent beam-plasma arguments, not from the observed whistler spectrum.

full rationale

The paper's central comparison is between measured kz-omega mode structures (Figures 3a-b) and linear growth rates computed with the HOTRAY code (Figures 3c-d). The HOTRAY input distribution, Eq. (2), has four shape parameters: vd, alpha_parallel, alpha_perp, and beta. These are not fitted to the wave data. The paper states that 'direct measurements of the distribution function are not available at this stage' and that the distribution is 'roughly inferred based on physical arguments.' The inference uses the Langmuir-wave relaxation estimate Delta-v from O'Neil et al. (1971), the trapping condition giving alpha_parallel = sqrt(2 Delta-v), and beam geometry giving alpha_perp = v_perp0, with beta = 0.8 as a lower-limit choice. All of these inputs come from beam parameters and separate plasma physics arguments, not from the measured whistler dispersion or wave normal angles. The resonance lines themselves, omega - kz u = n Omega_e, are a direct kinematic overlay on the experimentally extracted wave numbers, and the HOTRAY growth rates are subsequently computed, not reverse-engineered to match the data. Discrepancies, such as the Landau-resonance modes above 0.4 Omega_e and the inverse relation between saturated power and linear growth rate at low density, are explicitly acknowledged, which further indicates that the linear calculation is not tautologically consistent with the observations. Self-citations to Van Compernolle et al. (2014, 2015) document the beam source and setup rather than supplying the load-bearing resonance mechanism. The lack of direct electron distribution measurements is a legitimate empirical limitation and a correctness risk, but it does not make the derivation circular: the claimed agreement is a forward-model prediction with physically motivated, independently derived inputs. Therefore no circular step is present.

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

The central experimental claim does not depend on invented entities. The linear theory comparison relies on four free parameters in the model beam distribution (vd, alpha_parallel, alpha_perp, beta), plus standard plasma dispersion and resonance assumptions. No new physical entities are postulated.

free parameters (4)

vd (beam drift velocity in HOTRAY distribution) = u - delta_v, where u = v_beam_parallel, delta_v = [2 - (4/3)(nb/n0)^(1/3)] u
Set from Langmuir wave trapping theory rather than direct measurement; controls resonance line positions in the linear growth calculation.
alpha_parallel (parallel thermal spread of beam distribution) = sqrt(2 delta_v)
Chosen from Langmuir trapping width; affects the width of the growth-rate spectrum.
alpha_perp (perpendicular thermal spread) = v_perp0 (initial perpendicular beam velocity)
Set equal to the initial perpendicular beam velocity; authors note this is likely broader than the experiment but is the lower limit allowed by Eq. (2).
beta (ring-distribution shape parameter) = 0.8
Hand-chosen to make the perpendicular distribution peak at v_perp0 with FWHM approximately v_perp0; not directly measured.

assumptions (5)

standard math Cold plasma whistler dispersion relation n^2 = omega_pe^2 / [omega (Omega_e cos psi - omega)]
Used to interpret wave normal angles and resonance cone in Section 3.
domain assumption Hot plasma dispersion relation with Maxwellian/ring distributions as implemented in HOTRAY
Underpins all linear growth rate calculations; assumes linear perturbation theory and a homogeneous plasma.
standard math Resonance condition omega - k_z u = n Omega_e (n = 1, 0, -1)
Defines cyclotron, Landau, and anomalous cyclotron resonance lines used to classify wave modes.
domain assumption Langmuir wave relaxation model of O'Neil et al. (1971) to estimate beam slowing and spread
Used to set vd and alpha_parallel in the absence of a measured distribution function.
domain assumption Spatial growth approximated by temporal growth from a single representative distribution
Authors note this simplification; likely causes inconsistency in the Landau band above 0.4 Omega_e.

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Cite this review

Pith. "Pith review of Resonant excitation of whistler waves by a helical electron beam." pith.science (2026). https://pith.science/paper/HEH7THBQ

@misc{pith2026190806952,
  author       = {Pith},
  title        = {Pith review of: Resonant excitation of whistler waves by a helical electron beam},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HEH7THBQ}},
  note         = {Machine review of arXiv:1908.06952}
}

read the original abstract

Chorus-like whistler-mode waves that are known to play a fundamental role in driving radiation-belt dynamics are excited on the Large Plasma Device by the injection of a helical electron beam into a cold plasma. The mode structure of the excited whistler wave is identified using a phase-correlation technique showing that the waves are excited through a combination of Landau resonance, cyclotron resonance and anomalous cyclotron resonance. The dominant wave mode excited through cyclotron resonance is quasi-parallel propagating, whereas wave modes excited through Landau resonance and anomalous cyclotron resonance propagate at oblique angles that are close to the resonance cone. An analysis of the linear wave growth rates captures the major observations in the experiment. The results have important implications for the generation process of whistler waves in the Earth's inner magnetosphere.

Figures

Figures reproduced from arXiv: 1908.06952 by the authors.

**Figure 1.** (a) A schematic diagram of the experimental setup. A 10 cm diameter electron source launches an electron beam with energy up to 4 keV. Probes measure the plasma parameters and detect wave activity. A reference probe is added to construct the wave mode structure. (b) A typical wave spectrogram taken from LAPD experiment, showing the two-band structure with a gap at 0.5Ωe. Note that δBn is the spectral density of m… view at source ↗

**Figure 2.** (color online). Mode structure of whistler waves at 4 representative frequencies corresponding to each column. The first two rows show By in the x−y and the x − z planes, respectively. Wave amplitudes are normalized to the maximum wave amplitude in each panel. Arrows in the second row represent the wave vector direction. The third row shows the refractive index surface (which is a curve in 2D projection) for each … view at source ↗

**Figure 3.** Wave properties plotted on a kz − ω diagram from the LAPD experiment (a, b) and corresponding HOTRAY calculations (c, d), respectively, showing multiple resonance modes, color-coded by (a) power spectral density, (b) wave normal angle ψ from the experiment, (c) linear growth rates and (d) wave normal angle ψ from HOTRAY code [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: A comparison of observed wave properties (panels a, c, and e) and corresponding maximum linear growth rates (panels b, d, and f) obtained from three parameter scans: variation of the plasma density (a, b), beam energy (c, d) and beam density (e, f). δBn is the spectra…

**Figure 5.** Figure 5: A comparison of the spectral peak frequencies from experiment and linear theory (a, c, e), and also comparisons of maximal saturated wave power with maximal linear growth rate (b, d, f) for three parameter scans. Comparisons for plasma density scan are displayed in (a…

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Works this paper leans on

40 extracted references · 37 canonical work pages

[1]

Artemyev, V

Agapitov, O., A. Artemyev, V. Krasnoselskikh, Y. V. Khotyaint- sev, D. Mourenas, H. Breuillard, M. Balikhin, and G. Rolland (2013), Statistics of whistler mode waves in the outer radi- ation belt: Cluster staﬀ-sa measurements, Journal of Geo- physical Research: Space Physics , 118(6), 3407–3420, doi: 10.1002/jgra.50312

doi:10.1002/jgra.50312 2013
[2]

(2009), The THEMIS mission , Springer

Angelopoulos, V. (2009), The THEMIS mission , Springer

work page 2009
[3]

F., and O

Bell, T. F., and O. Buneman (1964), Plasma instability in the whistler mode caused by a gyrating electron stream, Phys. Rev., 133, A1300–A1302, doi:10.1103/PhysRev.133.A1300

work page doi:10.1103/physrev.133.a1300 1964
[4]

J., and R

Burtis, W. J., and R. A. Helliwell (1969), Banded chorusa new type of vlf radiation observed in the magnetosphere by ogo 1 and ogo 3, Journal of Geophysical Research , 74(11), 3002– 3010, doi:10.1029/JA074i011p03002

work page doi:10.1029/ja074i011p03002 1969
[5]

Gendrin, F

Cornilleau-Wehrlin, N., R. Gendrin, F. Lefeuvre, M. Par- rot, R. Grard, D. Jones, A. Bahnsen, E. Ungstrup, and W. Gibbons (1978), Vlf electromagnetic waves observed on- board geos-1, Space Science Reviews , 22(4), 371–382, doi: 10.1007/BF00210874

work page doi:10.1007/bf00210874 1978
[6]

Dupree, T. H. (1966), A perturbation theory for strong plasma turbulence, Physics of Fluids , 9(9)

work page 1966
[7]

Farrell, W. M., D. A. Gurnett, P. M. Banks, R. I. Bush, and W. J. Raitt (1988), An analysis of whistler mode radia- tion from the spacelab 2 electron beam, Journal of Geo- physical Research: Space Physics , 93(A1), 153–161, doi: 10.1029/JA093iA01p00153

work page doi:10.1029/ja093ia01p00153 1988
[8]

Fu, X., M. M. Cowee, R. H. Friedel, H. O. Funsten, S. P. Gary, G. B. Hospodarsky, C. Kletzing, W. Kurth, B. A. Larsen, K. Liu, E. A. MacDonald, K. Min, G. D. Reeves, R. M. Skoug, and D. Winske (2014), Whistler anisotropy instabil- ities as the source of banded chorus: Van allen probes ob- servations and particle-in-cell simulations, Journal of Geo- physic...

work page doi:10.1002/2014ja020364 2014

Show all 40 references

[9]

Fu, X., Z. Guo, C. Dong, and S. P. Gary (2015), Nonlinear subcy- clotron resonance as a formationmechanism for gaps in banded chorus, Geophysical Research Letters , 42(9), 3150–3159, doi: 10.1002/2015GL064182, 2015GL064182

2015 doi
[10]

Pﬁster, Z

Gekelman, W., H. Pﬁster, Z. Lucky, J. Bamber, D. Leneman, and J. Maggs (1991), Design, construction, and properties of the large plasma research device - The LAPD at UCLA, Rev. Sci. Instrum., 62, 2875–2883

1991
[11]

W., and J

Gentle, K. W., and J. Lohr (1973), Experimental determination of the nonlinear interaction in a one dimensional beamplasma system, Physics of Fluids , 16(9)

1973
[12]

Gurnett, D. A., S. D. Shawhan, and R. R. Shaw (1983), Auro- ral hiss, z mode radiation, and auroral kilometric radiation in the polar magnetosphere: De 1 observations, Journal of Geophysical Research: Space Physics , 88(A1), 329–340, doi: 10.1029/JA088iA01p00329

1983 doi
[13]

Gurnett, D. A., W. S. Kurth, J. T. Steinberg, P. M. Banks, R. I. Bush, and W. J. Raitt (1986), Whistler-mode radiation from the spacelab 2 electron beam, Geophysical Research Letters , 13(3), 225–228, doi:10.1029/GL013i003p00225

1986 doi
[14]

Yamanaka, M

Hayakawa, M., Y. Yamanaka, M. Parrot, and F. Lefeu- vre (1984), The wave normals of magnetospheric chorus emissions observed on board geos 2, Journal of Geophys- ical Research: Space Physics , 89(A5), 2811–2821, doi: 10.1029/JA089iA05p02811

1984 doi
[15]

Horne, R., and S. Sazhin (1990), Quasielectrostatic and electro- static approximations for whistler mode waves in the magne- tospheric plasma, Planetary and Space Science , 38(2), 311 – 318, doi:http://dx.doi.org/10.1016/0032-0633(90)90095-8

1990 doi
[16]

Horne, R. B. (1989), Path-integrated growth of electrostatic waves: The generation of terrestrial myriametric radiation, Journal of Geophysical Research: Space Physics , 94(A7), 8895–8909, doi:10.1029/JA094iA07p08895

1989 doi
[17]

(1966), Lowfrequency whistler mode, Physics of Flu- ids, 9(11)

Kennel, C. (1966), Lowfrequency whistler mode, Physics of Flu- ids, 9(11)

1966
[18]

F., and H

Kennel, C. F., and H. E. Petschek (1966), Limit on stably trapped particle ﬂuxes, Journal of Geophysical Research , 71(1), 1–28, doi:10.1029/JZ071i001p00001

1966 doi
[19]

Koons, H. C. (1981), The role of hiss in magnetospheric chorus emissions, Journal of Geophysical Research: Space Physics , 86(A8), 6745–6754, doi:10.1029/JA086iA08p06745. Kraﬀt, C., P. Th´ evenet, G. Matthieussent, B. Lundin, G. Belmont, B. Lemb` ege, J. Solomon, J. Lavergnat,...

1981 doi
[20]

R., and A

Kusse, B. R., and A. Bers (1970), Interactions of a plasma with a spiraling electron beam, Physics of Fluids , 13(9)

1970
[21]

Lavergnat, J., and R. Pellat (1979), High-frequency spontaneous emission of an electron beam injected into the ionospheric plasma, Journal of Geophysical Research: Space Physics , 84(A12), 7223–7238, doi:10.1029/JA084iA12p07223. AN ET AL.: WHISTLER W A VE EXCITATION X - 5

1979 doi
[22]

Gekelman, and J

Leneman, D., W. Gekelman, and J. Maggs (2006), The plasma source of the Large Plasma Device at University of California, Los Angeles, Rev. Sci. Instrum. , 77, 015,108

2006
[23]

Li, W., R. M. Thorne, J. Bortnik, X. Tao, and V. Angelopoulos (2012), Characteristics of hiss-like and discrete whistler-mode emissions, Geophysical Research Letters, 39(18), n/a–n/a, doi: 10.1029/2012GL053206, l18106

2012 doi
[24]

Bortnik, R

Li, W., J. Bortnik, R. M. Thorne, C. M. Cully, L. Chen, V. Angelopoulos, Y. Nishimura, J. B. Tao, J. W. Bonnell, and O. LeContel (2013), Characteristics of the poynting ﬂux and wave normal vectors of whistler-mode waves observed on themis, Journal of Geophysical Research: Spac...

2013 doi
[25]

Liu, K., S. P. Gary, and D. Winske (2011), Excitation of banded whistler waves in the magnetosphere, Geophysical Research Letters, 38(14), L14,108, doi:10.1029/2011GL048375

2011 doi
[26]

Maggs, J. E. (1976), coherent generation of vlf hiss, Jour- nal of Geophysical Research , 81(10), 1707–1724, doi: 10.1029/JA081i010p01707

1976 doi
[27]

Sugaya, and S

Mizuno, K., R. Sugaya, and S. Tanaka (1971), erenkov and cyclotron excitation of bernstein waves with elec- tron beams, Physics Letters A , 36(5), 441 – 442, doi: http://dx.doi.org/10.1016/0375-9601(71)90299-4

1971 doi
[28]

Mourenas, D., A. V. Artemyev, O. V. Agapitov, V. Kras- noselskikh, and F. S. Mozer (2015), Very oblique whistler generation by low-energy electron streams, Journal of Geo- physical Research: Space Physics , 120(5), 3665–3683, doi: 10.1002/2015JA021135, 2015JA021135

2015 doi
[29]

Neubert, T., and P. M. Banks (1992), Recent results from studies of electron beam phenomena in space plasmas, Planetary and Space Science , 40(23), 153 – 183, doi: http://dx.doi.org/10.1016/0032-0633(92)90055-S

1992 doi
[30]

Hikishima, Y

Omura, Y., M. Hikishima, Y. Katoh, D. Summers, and S. Yagi- tani (2009), Nonlinear mechanisms of lower-band and upper- band vlf chorus emissions in the magnetosphere, Journal of Geophysical Research: Space Physics , 114(A7), A07,217, doi: 10.1029/2009JA014206. O’Neil, T. M., J...

2009 doi
[31]

Pope, J. H. (1963), A high-latitude investigation of the nat- ural very-low-frequency electromagnetic radiation known as chorus, Journal of Geophysical Research , 68(1), 83–99, doi: 10.1029/JZ068i001p00083

1963 doi
[32]

Santolk, O., D. A. Gurnett, J. S. Pickett, J. Chum, and N. Cornilleau-Wehrlin (2009), Oblique propagation of whistler mode waves in the chorus source region, Journal of Geo- physical Research: Space Physics , 114(A12), n/a–n/a, doi: 10.1029/2009JA014586, a00F03

2009 doi
[33]

Bullough, and M

Sazhin, S., K. Bullough, and M. Hayakawa (1993), Auroral hiss: a review, Planetary and Space Science , 41(2), 153 – 166, doi: http://dx.doi.org/10.1016/0032-0633(93)90045-4

1993 doi
[34]

Kraﬀt (1999), Resonant cyclotron emis- sion of whistler waves by a modulated electron beam, Phys

Starodubtsev, M., and C. Kraﬀt (1999), Resonant cyclotron emis- sion of whistler waves by a modulated electron beam, Phys. Rev. Lett., 83, 1335–1338, doi:10.1103/PhysRevLett.83.1335

1999 doi
[35]

Kraﬀt, P

Starodubtsev, M., C. Kraﬀt, P. Thvenet, and A. Kostrov (1999), Whistler wave emission by a modulated electron beam through transition radiation, Physics of Plasmas , 6(5)

1999
[36]

Stenzel, R. L. (1977), Observation of beam-generated vlf hiss in a large laboratory plasma, Journal of Geophysical Research , 82(29), 4805–4814, doi:10.1029/JA082i029p04805

1977 doi
[37]

Thorne, R., W. Li, B. Ni, Q. Ma, J. Bortnik, L. Chen, D. Baker, H. E. Spence, G. Reeves, M. Henderson, C. A. AU Kletzing, W. S. Kurth, G. B. Hospodarsky, J. B. Blake, J. F. Fen- nell, S. G. Claudepierre, and S. G. Kanekal (2013), Rapid local acceleration of relativistic radiat...

2013 doi
[38]

Thorne, R. M. (2010), Radiation belt dynamics: The importance of wave-particle interactions, Geophysical Research Letters , 37(22), L22,107, doi:10.1029/2010GL044990

2010 doi
[39]

Tokar, R. L., D. A. Gurnett, and W. C. Feldman (1984), Whistler mode turbulence generated by electron beams in earth’s bow shock, Journal of Geophysical Research: Space Physics, 89(A1), 105–114, doi:10.1029/JA089iA01p00105

1984 doi
[40]

T., and E

Tsurutani, B. T., and E. J. Smith (1974), Postmidnight chorus: A substorm phenomenon, Journal of Geophysical Research , 79(1), 118–127, doi:10.1029/JA079i001p00118. Van Compernolle, B., J. Bortnik, P. Pribyl, W. Gekelman, M. Nakamoto, X. Tao, and R. M. Thorne (2014), Direct de...

1974 doi

Pith tools

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

[1] [1]

Artemyev, V

Agapitov, O., A. Artemyev, V. Krasnoselskikh, Y. V. Khotyaint- sev, D. Mourenas, H. Breuillard, M. Balikhin, and G. Rolland (2013), Statistics of whistler mode waves in the outer radi- ation belt: Cluster staﬀ-sa measurements, Journal of Geo- physical Research: Space Physics , 118(6), 3407–3420, doi: 10.1002/jgra.50312

doi:10.1002/jgra.50312 2013

[2] [2]

(2009), The THEMIS mission , Springer

Angelopoulos, V. (2009), The THEMIS mission , Springer

work page 2009

[3] [3]

F., and O

Bell, T. F., and O. Buneman (1964), Plasma instability in the whistler mode caused by a gyrating electron stream, Phys. Rev., 133, A1300–A1302, doi:10.1103/PhysRev.133.A1300

work page doi:10.1103/physrev.133.a1300 1964

[4] [4]

J., and R

Burtis, W. J., and R. A. Helliwell (1969), Banded chorusa new type of vlf radiation observed in the magnetosphere by ogo 1 and ogo 3, Journal of Geophysical Research , 74(11), 3002– 3010, doi:10.1029/JA074i011p03002

work page doi:10.1029/ja074i011p03002 1969

[5] [5]

Gendrin, F

Cornilleau-Wehrlin, N., R. Gendrin, F. Lefeuvre, M. Par- rot, R. Grard, D. Jones, A. Bahnsen, E. Ungstrup, and W. Gibbons (1978), Vlf electromagnetic waves observed on- board geos-1, Space Science Reviews , 22(4), 371–382, doi: 10.1007/BF00210874

work page doi:10.1007/bf00210874 1978

[6] [6]

Dupree, T. H. (1966), A perturbation theory for strong plasma turbulence, Physics of Fluids , 9(9)

work page 1966

[7] [7]

Farrell, W. M., D. A. Gurnett, P. M. Banks, R. I. Bush, and W. J. Raitt (1988), An analysis of whistler mode radia- tion from the spacelab 2 electron beam, Journal of Geo- physical Research: Space Physics , 93(A1), 153–161, doi: 10.1029/JA093iA01p00153

work page doi:10.1029/ja093ia01p00153 1988

[8] [8]

Fu, X., M. M. Cowee, R. H. Friedel, H. O. Funsten, S. P. Gary, G. B. Hospodarsky, C. Kletzing, W. Kurth, B. A. Larsen, K. Liu, E. A. MacDonald, K. Min, G. D. Reeves, R. M. Skoug, and D. Winske (2014), Whistler anisotropy instabil- ities as the source of banded chorus: Van allen probes ob- servations and particle-in-cell simulations, Journal of Geo- physic...

work page doi:10.1002/2014ja020364 2014