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Diffusive scattering of energetic electrons by intense whistler-mode waves in an inhomogeneous plasma

Published online by Cambridge University Press:  06 January 2023

Viktor A. Frantsuzov Open the ORCID record for Viktor A. Frantsuzov [Opens in a new window] ,
Anton V. Artemyev Open the ORCID record for Anton V. Artemyev [Opens in a new window] ,
Xiao-Jia Zhang ,
Oliver Allanson Open the ORCID record for Oliver Allanson [Opens in a new window] ,
Pavel I. Shustov  and
Anatoli A. Petrukovich
Viktor A. Frantsuzov*
Affiliation:
Space Research Institute of the Russian Academy of Sciences (IKI), 84/32 Profsoyuznaya Str., Moscow 117997, Russia Faculty of Physics, National Research University Higher School of Economics, 21/4 Staraya Basmannaya Ulitsa, Moscow 105066, Russia
Anton V. Artemyev
Affiliation:
Space Research Institute of the Russian Academy of Sciences (IKI), 84/32 Profsoyuznaya Str., Moscow 117997, Russia Institute of Geophysics and Planetary Physics, UCLA, Los Angeles, CA 90095, USA
Xiao-Jia Zhang
Affiliation:
Institute of Geophysics and Planetary Physics, UCLA, Los Angeles, CA 90095, USA
Oliver Allanson
Affiliation:
Department of Mathematics, University of Exeter, Penryn/Cornwall Campus, Penryn, TR10 9FE, UK
Pavel I. Shustov
Affiliation:
Space Research Institute of the Russian Academy of Sciences (IKI), 84/32 Profsoyuznaya Str., Moscow 117997, Russia Faculty of Physics, National Research University Higher School of Economics, 21/4 Staraya Basmannaya Ulitsa, Moscow 105066, Russia
Anatoli A. Petrukovich
Affiliation:
Space Research Institute of the Russian Academy of Sciences (IKI), 84/32 Profsoyuznaya Str., Moscow 117997, Russia
*
†Email address for correspondence: [email protected]
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Abstract

Electron resonant interactions with electromagnetic whistler-mode waves play an important role in electron flux dynamics in various space plasma systems: planetary radiation belts, bow shocks, solar wind and magnetic reconnection regions. Two key wave characteristics determining the regime of wave–particle interactions are the wave intensity and the wave coherency. The classical quasi-linear diffusion approach describes well electron diffusion by incoherent and low-amplitude waves, whereas the nonlinear resonant models describe electron phase bunching and trapping by highly coherent intense waves. This study is devoted to the investigation of the regime of electron resonant interactions with incoherent but intense waves. Although this regime is characterized by electron diffusion, we show that diffusion rates scale linearly with the wave amplitude, $D\propto B_w$, in contrast to the quasi-linear diffusion scaling $D_{QL}\propto B_w^2$. Using observed wave amplitude distributions, we demonstrate that the quasi-linear diffusion model significantly overestimates electron scattering by incoherent, but intense whistler-mode waves. We discuss the results obtained in the context of simulations of long-term electron flux dynamics in space plasma systems.

Keywords

plasma dynamicsspace plasma physicsplasma nonlinear phenomena
Type
Research Article
Information
Journal of Plasma Physics , Volume 89 , Issue 1 , February 2023 , 905890101
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Copyright © The Author(s), 2023. Published by Cambridge University Press

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References

REFERENCES

Agapitov, O.V., Artemyev, A., Krasnoselskikh, V., Khotyaintsev, Y.V., Mourenas, D., Breuillard, H., Balikhin, M. & Rolland, G. 2013 Statistics of whistler mode waves in the outer radiation belt: cluster STAFF-SA measurements. J. Geophys. Res. 118, 3407–3420.CrossRefGoogle Scholar
Agapitov, O.V., Mourenas, D., Artemyev, A.V., Mozer, F.S., Hospodarsky, G., Bonnell, J. & Krasnoselskikh, V. 2018 Synthetic empirical chorus wave model from combined van allen probes and cluster statistics. J. Geophys. Res. 123 (1), 297–314.CrossRefGoogle Scholar
Albert, J.M. 1993 Cyclotron resonance in an inhomogeneous magnetic field. Phys. Fluids B 5, 2744–2750.CrossRefGoogle Scholar
Albert, J.M. 2001 Comparison of pitch angle diffusion by turbulent and monochromatic whistler waves. J. Geophys. Res. 106, 8477–8482.CrossRefGoogle Scholar
Albert, J.M. 2010 Diffusion by one wave and by many waves. J. Geophys. Res. 115, A00F05.Google Scholar
Albert, J.M., Artemyev, A., Li, W., Gan, L. & Ma, Q. 2022 Analytical results for phase bunching in the pendulum model of wave–particle interactions. Front. Astron. Space Sci. 9, 971358.CrossRefGoogle Scholar
Allanson, O., Watt, C.E.J., Allison, H.J. & Ratcliffe, H. 2021 Electron diffusion and advection during nonlinear interactions with whistler mode waves. J. Geophys. Res. 126 (5), e28793.CrossRefGoogle Scholar
Allanson, O., Watt, C.E.J., Ratcliffe, H., Allison, H.J., Meredith, N.P., Bentley, S.N., Ross, J.P.J. & Glauert, S.A. 2020 Particle-in-cell experiments examine electron diffusion by whistler-mode waves: 2. Quasi-linear and nonlinear dynamics. J. Geophys. Res. 125 (7), e27949.CrossRefGoogle Scholar
Allison, H.J., Shprits, Y.Y., Zhelavskaya, I.S., Wang, D. & Smirnov, A.G. 2021 Gyroresonant wave–particle interactions with chorus waves during extreme depletions of plasma density in the Van Allen radiation belts. Sci. Adv. 7 (5), eabc0380.CrossRefGoogle ScholarPubMed
Andronov, A.A. & Trakhtengerts, V.Y. 1964 Kinetic instability of the Earth's outer radiation belt. Geomagn. Aeron. 4, 233–242.Google Scholar
Angelopoulos, V. 2008 The THEMIS mission. Space Sci. Rev. 141, 5–34.CrossRefGoogle Scholar
An, Z., Wu, Y. & Tao, X. 2022 Electron dynamics in a chorus wave field generated from particle-in-cell simulations. Geophys. Res. Lett. 49 (3), e97778.CrossRefGoogle Scholar
Artemyev, A.V., Neishtadt, A.I., Vainchtein, D.L., Vasiliev, A.A., Vasko, I.Y. & Zelenyi, L.M. 2018 a Trapping (capture) into resonance and scattering on resonance: summary of results for space plasma systems. Commun. Nonlinear Sci. Numer. Simul. 65, 111–160.CrossRefGoogle Scholar
Artemyev, A.V., Neishtadt, A.I., Vasiliev, A.A. & Mourenas, D. 2018 b Long-term evolution of electron distribution function due to nonlinear resonant interaction with whistler mode waves. J. Plasma Phys. 84, 905840206.CrossRefGoogle Scholar
Artemyev, A.V., Neishtadt, A.I., Vasiliev, A.A. & Mourenas, D. 2021 a Transitional regime of electron resonant interaction with whistler-mode waves in inhomogeneous space plasma. Phys. Rev. E 104 (5), 055203.CrossRefGoogle ScholarPubMed
Artemyev, A.V., Neishtadt, A.I., Vasiliev, A.A., Zhang, X.-J., Mourenas, D. & Vainchtein, D. 2021 b Long-term dynamics driven by resonant wave–particle interactions: from Hamiltonian resonance theory to phase space mapping. J. Plasma Phys. 87 (2), 835870201.CrossRefGoogle Scholar
Artemyev, A.V., Shi, X., Liu, T.Z., Zhang, X.J., Vasko, I. & Angelopoulos, V. 2022 Electron resonant interaction with whistler waves around foreshock transients and the bow shock behind the terminator. J. Geophys. Res. 127 (2), e29820.CrossRefGoogle Scholar
Artemyev, A.V., Vasiliev, A.A., Mourenas, D., Agapitov, O.V. & Krasnoselskikh, V.V. 2014 Electron scattering and nonlinear trapping by oblique whistler waves: the critical wave intensity for nonlinear effects. Phys. Plasmas 21 (10), 102903.CrossRefGoogle Scholar
Bell, T.F. 1984 The nonlinear gyroresonance interaction between energetic electrons and coherent VLF waves propagating at an arbitrary angle with respect to the Earth's magnetic field. J. Geophys. Res. 89, 905–918.CrossRefGoogle Scholar
Bespalov, P.A., Zaitsev, V.V. & Stepanov, A.V. 1991 Consequences of strong pitch-angle diffusion of particles in solar flares. Astrophys. J. 374, 369.CrossRefGoogle Scholar
Bortnik, J., Thorne, R.M. & Inan, U.S. 2008 Nonlinear interaction of energetic electrons with large amplitude chorus. Geophys. Res. Lett. 35, 21102.CrossRefGoogle Scholar
Breuillard, H., Le Contel, O., Retino, A., Chasapis, A., Chust, T., Mirioni, L., Graham, D.B., Wilder, F.D., Cohen, I., Vaivads, A., et al. 2016 Multispacecraft analysis of dipolarization fronts and associated whistler wave emissions using MMS data. Geophys. Res. Lett. 43, 7279–7286.CrossRefGoogle Scholar
Cattell, C.A., Short, B., Breneman, A.W. & Grul, P. 2020 Narrowband large amplitude whistler-mode waves in the solar wind and their association with electrons: STEREO waveform capture observations. Astrophys. J. 897 (2), 126.CrossRefGoogle Scholar
Cattell, C., Short, B., Breneman, A., Halekas, J., Whittesley, P., Larson, D., Kasper, J.C., Stevens, M., Case, T., Moncuquet, M., et al. 2021 Narrowband oblique whistler-mode waves: comparing properties observed by Parker Solar Probe at $<0.3$ AU and STEREO at 1 AU. Astron. Astrophys. 650, A8.CrossRefGoogle Scholar
Demekhov, A.G., Taubenschuss, U. & Santolık, O. 2017 Simulation of VLF chorus emissions in the magnetosphere and comparison with THEMIS spacecraft data. J. Geophys. Res. 122, 166–184.CrossRefGoogle Scholar
Drozdov, A.Y., Shprits, Y.Y., Orlova, K.G., Kellerman, A.C., Subbotin, D.A., Baker, D.N., Spence, H.E. & Reeves, G.D. 2015 Energetic, relativistic, and ultrarelativistic electrons: comparison of long-term VERB code simulations with Van Allen Probes measurements. J. Geophys. Res. 120, 3574–3587.CrossRefGoogle Scholar
Drummond, W.E. & Pines, D. 1962 Nonlinear stability of plasma oscillations. Nucl. Fusion Suppl. 3, 1049–1058.Google Scholar
Filatov, L.V. & Melnikov, V.F. 2017 Influence of whistler turbulence on fast electron distribution and their microwave emissions in a flare loop. Geomagn. Aeron. 57 (8), 1001–1008.CrossRefGoogle Scholar
Foster, J.C., Erickson, P.J. & Omura, Y. 2021 Subpacket structure in strong VLF chorus rising tones: characteristics and consequences for relativistic electron acceleration. Earth Planet. Space 73 (1), 140.CrossRefGoogle ScholarPubMed
Gan, L., Li, W., Ma, Q., Albert, J.M., Artemyev, A.V. & Bortnik, J. 2020 Nonlinear interactions between radiation belt electrons and chorus waves: dependence on wave amplitude modulation. Geophys. Res. Lett. 47 (4), e85987.CrossRefGoogle Scholar
Gan, L., Li, W., Ma, Q., Artemyev, A.V. & Albert, J.M. 2022 Dependence of nonlinear effects on whistler-mode wave bandwidth and amplitude: a perspective from diffusion coefficients. J. Geophys. Res. 127 (5), e30063.CrossRefGoogle Scholar
Hsieh, Y.-K., Kubota, Y. & Omura, Y. 2020 Nonlinear evolution of radiation belt electron fluxes interacting with oblique whistler mode chorus emissions. J. Geophys. Res 125, e2019JA027465.CrossRefGoogle Scholar
Hsieh, Y.-K. & Omura, Y. 2017 a Nonlinear dynamics of electrons interacting with oblique whistler mode chorus in the magnetosphere. J. Geophys. Res. 122, 675–694.CrossRefGoogle Scholar
Hsieh, Y.-K. & Omura, Y. 2017 b Study of wave–particle interactions for whistler mode waves at oblique angles by utilizing the gyroaveraging method. Radio Sci. 52 (10), 1268–1281.CrossRefGoogle Scholar
Hull, A.J., Muschietti, L., Le Contel, O., Dorelli, J.C. & Lindqvist, P.A. 2020 MMS observations of intense whistler waves within Earth's supercritical bow shock: source mechanism and impact on shock structure and plasma transport. J. Geophys. Res. 125 (7), e27290.CrossRefGoogle Scholar
Hull, A.J., Muschietti, L., Oka, M., Larson, D.E., Mozer, F.S., Chaston, C.C., Bonnell, J.W. & Hospodarsky, G.B. 2012 Multiscale whistler waves within Earth's perpendicular bow shock. J. Geophys. Res. 117, 12104.Google Scholar
Inan, U.S., Bell, T.F. & Helliwell, R.A. 1978 Nonlinear pitch angle scattering of energetic electrons by coherent VLF waves in the magnetosphere. J. Geophys. Res. 83 (A7), 3235–3254.CrossRefGoogle Scholar
Itin, A.P., Neishtadt, A.I. & Vasiliev, A.A. 2000 Captures into resonance and scattering on resonance in dynamics of a charged relativistic particle in magnetic field and electrostatic wave. Physica D 141, 281–296.CrossRefGoogle Scholar
Karpman, V.I. 1974 Nonlinear effects in the elf waves propagating along the magnetic field in the magnetosphere. Space Sci. Rev. 16, 361–388.CrossRefGoogle Scholar
Karpman, V.I., Istomin, J.N. & Shklyar, D.R. 1974 Nonlinear theory of a quasi-monochromatic whistler mode packet in inhomogeneous plasma. Plasma Phys. 16, 685–703.CrossRefGoogle Scholar
Karpman, V.I. & Shklyar, D.R. 1977 Particle precipitation caused by a single whistler-mode wave injected into the magnetosphere. Planet. Space Sci. 25, 395–403.CrossRefGoogle Scholar
Katoh, Y. & Omura, Y. 2016 Electron hybrid code simulation of whistler-mode chorus generation with real parameters in the Earth's inner magnetosphere. Earth Planet. Space 68 (1), 192.CrossRefGoogle Scholar
Kennel, C.F. & Engelmann, F. 1966 Velocity space diffusion from weak plasma turbulence in a magnetic field. Phys. Fluids 9, 2377–2388.CrossRefGoogle Scholar
Landau, L.D. & Lifshitz, E.M. 1988 Vol. 1: Mechanics. Pergamon.Google Scholar
Le Contel, O., Roux, A., Jacquey, C., Robert, P., Berthomier, M., Chust, T., Grison, B., Angelopoulos, V., Sibeck, D., Chaston, C.C., et al. 2009 Quasi-parallel whistler mode waves observed by THEMIS during near-earth dipolarizations. Ann. Geophys. 27, 2259–2275.CrossRefGoogle Scholar
Le Queau, D. & Roux, A. 1987 Quasi-monochromatic wave–particle interactions in magnetospheric plasmas. Sol. Phys. 111, 59–80.CrossRefGoogle Scholar
Li, W., Ma, Q., Shen, X.C., Zhang, X.J., Mauk, B.H., Clark, G., Allegrini, F., Kurth, W.S., Hospodarsky, G.B., Hue, V., et al. 2021 Quantification of diffuse auroral electron precipitation driven by whistler mode waves at jupiter. Geophys. Res. Lett. 48 (19), e95457.CrossRefGoogle Scholar
Li, W., Thorne, R.M., Ma, Q., Ni, B., Bortnik, J., Baker, D.N., Spence, H.E., Reeves, G.D., Kanekal, S.G., Green, J.C., et al. 2014 Radiation belt electron acceleration by chorus waves during the 17 March 2013 storm. J. Geophys. Res. 119, 4681–4693.CrossRefGoogle Scholar
Lyons, L.R. & Williams, D.J. 1984 Quantitative Aspects of Magnetospheric Physics. D. Reidel Publishing Company.CrossRefGoogle Scholar
Ma, Q., Li, W., Bortnik, J., Thorne, R.M., Chu, X., Ozeke, L.G., Reeves, G.D., Kletzing, C.A., Kurth, W.S., Hospodarsky, G.B., et al. 2018 Quantitative evaluation of radial diffusion and local acceleration processes during gem challenge events. J. Geophys. Res. 123 (3), 1938–1952.CrossRefGoogle Scholar
Melnikov, V.F. & Filatov, L.V. 2020 Conditions for whistler generation by nonthermal electrons in flare loops. Geomagn. Aeron. 60 (8), 1126–1131.CrossRefGoogle Scholar
Menietti, J.D., Averkamp, T.F., Kurth, W.S., Imai, M., Faden, J.B., Hospodarsky, G.B., Santolik, O., Clark, G., Allegrini, F., Elliott, S.S., et al. 2021 Analysis of whistler-mode and Z-mode emission in the juno primary mission. J. Geophys. Res. 126 (11), e29885.CrossRefGoogle Scholar
Meredith, N.P., Horne, R.B., Sicard-Piet, A., Boscher, D., Yearby, K.H., Li, W. & Thorne, R.M. 2012 Global model of lower band and upper band chorus from multiple satellite observations. J. Geophys. Res. 117, 10225.Google Scholar
Meredith, N.P., Horne, R.B., Thorne, R.M. & Anderson, R.R. 2003 Favored regions for chorus-driven electron acceleration to relativistic energies in the Earth's outer radiation belt. Geophys. Res. Lett. 30 (16), 160000.CrossRefGoogle Scholar
Mourenas, D., Zhang, X.-J., Artemyev, A.V., Angelopoulos, V., Thorne, R.M., Bortnik, J., Neishtadt, A.I. & Vasiliev, A.A. 2018 Electron nonlinear resonant interaction with short and intense parallel chorus wave packets. J. Geophys. Res. 123, 4979–4999.CrossRefGoogle Scholar
Mourenas, D., Zhang, X.J., Nunn, D., Artemyev, A.V., Angelopoulos, V., Tsai, E. & Wilkins, C. 2022 Short chorus wave packets: generation within chorus elements, statistics, and consequences on energetic electron precipitation. J. Geophys. Res. 127 (5), e30310.CrossRefGoogle ScholarPubMed
Mozer, F.S., Bonnell, J.W., Halekas, J.S., Rahmati, A., Schum, G. & Vasko, I.V. 2021 Whistlers in the solar vicinity that are spiky in time and frequency. Astrophys. J. 908 (1), 26.CrossRefGoogle Scholar
Neishtadt, A.I. 1999 On adiabatic invariance in two-frequency systems. In Hamiltonian Systems with Three or More Degrees of Freedom (ed. C. Simo), NATO ASI Series C, vol. 533, pp. 193–213. Kluwer Academic Publishers.CrossRefGoogle Scholar
Neishtadt, A.I. & Vasiliev, A.A. 2006 Destruction of adiabatic invariance at resonances in slow fast Hamiltonian systems. Nucl. Instrum. Meth. Phys. Res. A 561, 158–165.CrossRefGoogle Scholar
Nunn, D. 1971 Wave–particle interactions in electrostatic waves in an inhomogeneous medium. J. Plasma Phys. 6, 291.CrossRefGoogle Scholar
Nunn, D. 1974 A self-consistent theory of triggered VLF emissions. Planet. Space Sci. 22, 349–378.CrossRefGoogle Scholar
Nunn, D. 1986 A nonlinear theory of sideband stability in ducted whistler mode waves. Planet. Space Sci. 34, 429–451.CrossRefGoogle Scholar
Nunn, D. & Omura, Y. 2012 A computational and theoretical analysis of falling frequency VLF emissions. J. Geophys. Res. 117, 8228.Google Scholar
Nunn, D., Zhang, X.J., Mourenas, D. & Artemyev, A.V. 2021 Generation of realistic short chorus wave packets. Geophys. Res. Lett. 48 (7), e92178.CrossRefGoogle Scholar
Oka, M., Otsuka, F., Matsukiyo, S., Wilson, L.B.I., Argall, M.R., Amano, T., Phan, T.D., Hoshino, M., Le Contel, O., Gershman, D.J., et al. 2019 Electron scattering by low-frequency whistler waves at Earth's bow shock. Astrophys. J. 886 (1), 53.CrossRefGoogle Scholar
Oka, M., Wilson III, L.B., Phan, T.D., Hull, A.J., Amano, T., Hoshino, M., Argall, M.R., Le Contel, O., Agapitov, O., Gershman, D.J., et al. 2017 Electron scattering by high-frequency whistler waves at Earth's bow shock. Astrophys. J. Lett. 842, L11.CrossRefGoogle Scholar
Omura, Y., Furuya, N. & Summers, D. 2007 Relativistic turning acceleration of resonant electrons by coherent whistler mode waves in a dipole magnetic field. J. Geophys. Res. 112, 6236.Google Scholar
Omura, Y., Matsumoto, H., Nunn, D. & Rycroft, M.J. 1991 A review of observational, theoretical and numerical studies of VLF triggered emissions. J. Atmos. Terr. Phys. 53, 351–368.CrossRefGoogle Scholar
Omura, Y., Miyashita, Y., Yoshikawa, M., Summers, D., Hikishima, M., Ebihara, Y. & Kubota, Y. 2015 Formation process of relativistic electron flux through interaction with chorus emissions in the Earth's inner magnetosphere. J. Geophys. Res. 120, 9545–9562.CrossRefGoogle Scholar
Page, B., Vasko, I.Y., Artemyev, A.V. & Bale, S.D. 2021 Generation of high-frequency whistler waves in the Earth's quasi-perpendicular bow shock. Astrophys. J. Lett. 919 (2), L17.CrossRefGoogle Scholar
Schulz, M. & Lanzerotti, L.J. 1974 Particle Diffusion in the Radiation Belts. Springer.CrossRefGoogle Scholar
Shapiro, V.D. & Sagdeev, R.Z. 1997 Nonlinear wave–particle interaction and conditions for the applicability of quasilinear theory. Phys. Rep. 283, 49–71.CrossRefGoogle Scholar
Shi, X., Liu, T.Z., Angelopoulos, V. & Zhang, X.-J. 2020 Whistler mode waves in the compressional boundary of foreshock transients. J. Geophys. Res. 125 (8), e27758.CrossRefGoogle Scholar
Shklyar, D.R. 2021 A theory of interaction between relativistic electrons and magnetospherically reflected whistlers. J. Geophys. Res. 126 (2), e28799.CrossRefGoogle Scholar
Shklyar, D.R. & Matsumoto, H. 2009 Oblique whistler-mode waves in the inhomogeneous magnetospheric plasma: resonant interactions with energetic charged particles. Surv. Geophys. 30, 55–104.CrossRefGoogle Scholar
Solovev, V.V. & Shkliar, D.R. 1986 Particle heating by a low-amplitude wave in an inhomogeneous magnetoplasma. Sov. Phys. JETP 63, 272–277.Google Scholar
Stix, T.H. 1962 The Theory of Plasma Waves. McGraw-Hill.Google Scholar
Summers, D. & Omura, Y. 2007 Ultra-relativistic acceleration of electrons in planetary magnetospheres. Geophys. Res. Lett. 34, 24205.CrossRefGoogle Scholar
Tao, X., Bortnik, J., Albert, J.M., Liu, K. & Thorne, R.M. 2011 Comparison of quasilinear diffusion coefficients for parallel propagating whistler mode waves with test particle simulations. Geophys. Res. Lett. 38, 6105.CrossRefGoogle Scholar
Tao, X., Bortnik, J., Albert, J.M. & Thorne, R.M. 2012 a Comparison of bounce-averaged quasi-linear diffusion coefficients for parallel propagating whistler mode waves with test particle simulations. J. Geophys. Res. 117, 10205.Google Scholar
Tao, X., Bortnik, J., Albert, J.M., Thorne, R.M. & Li, W. 2013 The importance of amplitude modulation in nonlinear interactions between electrons and large amplitude whistler waves. J. Atmos. Sol.-Terr. Phys. 99, 67–72.CrossRefGoogle Scholar
Tao, X., Bortnik, J., Thorne, R.M., Albert, J.M. & Li, W. 2012 b Effects of amplitude modulation on nonlinear interactions between electrons and chorus waves. Geophys. Res. Lett. 39, 6102.CrossRefGoogle Scholar
Tao, X., Zonca, F., Chen, L. & Wu, Y. 2020 Theoretical and numerical studies of chorus waves: a review. Sci. China Earth Sci. 63 (1), 78–92.CrossRefGoogle Scholar
Thorne, R.M., Bortnik, J., Li, W. & Ma, Q. 2021 Wave–Particle Interactions in the Earth's Magnetosphere, chap. 6, pp. 93–108. American Geophysical Union (AGU).Google Scholar
Thorne, R.M., Li, W., Ni, B., Ma, Q., Bortnik, J., Chen, L., Baker, D.N., Spence, H.E., Reeves, G.D., Henderson, M.G., et al. 2013 Rapid local acceleration of relativistic radiation-belt electrons by magnetospheric chorus. Nature 504, 411–414.CrossRefGoogle ScholarPubMed
Tong, Y., Vasko, I.Y., Artemyev, A.V., Bale, S.D. & Mozer, F.S. 2019 Statistical Study of Whistler Waves in the Solar Wind at 1 au. Astrophys. J. 878 (1), 41.CrossRefGoogle Scholar
Trakhtengerts, V.Y. & Rycroft, M.J. 2008 Whistler and Alfvén Mode Cyclotron Masers in Space. Cambridge University Press.CrossRefGoogle Scholar
Vainchtein, D., Zhang, X.J., Artemyev, A.V., Mourenas, D., Angelopoulos, V. & Thorne, R.M. 2018 Evolution of electron distribution driven by nonlinear resonances with intense field-aligned chorus waves. J. Geophys. Res. 123 (10), 8149–8169.CrossRefGoogle Scholar
Vedenov, A.A., Velikhov, E. & Sagdeev, R. 1962 Quasilinear theory of plasma oscillations. Nucl. Fusion Suppl. 2, 465–475.Google Scholar
Verscharen, D., Chandran, B.D.G., Boella, E., Halekas, J., Innocenti, M.E., Jagarlamudi, V.K., Micera, A., Pierrard, V., Štverák, Š., Vasko, I.Y., et al. 2022 Electron-driven instabilities in the solar wind. Front. Astron. Space Sci. 9, 951628.CrossRefGoogle Scholar
Wilson, L.B., Koval, A., Szabo, A., Breneman, A., Cattell, C.A., Goetz, K., Kellogg, P.J., Kersten, K., Kasper, J.C., Maruca, B.A., et al. 2013 Electromagnetic waves and electron anisotropies downstream of supercritical interplanetary shocks. J. Geophys. Res. 118, 5–16.CrossRefGoogle Scholar
Yao, S.T., Shi, Q.Q., Zong, Q.G., Degeling, A.W., Guo, R.L., Li, L., Li, J.X., Tian, A.M., Zhang, H., Yao, Z.H., et al. 2021 Low-frequency whistler waves modulate electrons and generate higher-frequency whistler waves in the solar wind. Astrophys. J. 923 (2), 216.CrossRefGoogle Scholar
Zhang, X.-J., Artemyev, A., Angelopoulos, V., Tsai, E., Wilkins, C., Kasahara, S., Mourenas, D., Yokota, S., Keika, K., Hori, T., et al. 2022 Superfast precipitation of energetic electrons in the radiation belts of the Earth. Nat. Commun. 13, 1611.CrossRefGoogle ScholarPubMed
Zhang, X., Angelopoulos, V., Artemyev, A.V. & Liu, J. 2018 a Whistler and electron firehose instability control of electron distributions in and around dipolarizing flux bundles. Geophys. Res. Lett. 45, 9380–9389.CrossRefGoogle Scholar
Zhang, X.J., Agapitov, O., Artemyev, A.V., Mourenas, D., Angelopoulos, V., Kurth, W.S., Bonnell, J.W. & Hospodarsky, G.B. 2020 a Phase decoherence within intense chorus wave packets constrains the efficiency of nonlinear resonant electron acceleration. Geophys. Res. Lett. 47 (20), e89807.CrossRefGoogle Scholar
Zhang, X.J., Demekhov, A.G., Katoh, Y., Nunn, D., Tao, X., Mourenas, D., Omura, Y., Artemyev, A.V. & Angelopoulos, V. 2021 Fine structure of chorus wave packets: comparison between observations and wave generation models. J. Geophys. Res. 126 (8), e29330.Google Scholar
Zhang, X.J., Mourenas, D., Artemyev, A.V., Angelopoulos, V., Bortnik, J., Thorne, R.M., Kurth, W.S., Kletzing, C.A. & Hospodarsky, G.B. 2019 Nonlinear electron interaction with intense chorus waves: statistics of occurrence rates. Geophys. Res. Lett. 46 (13), 7182–7190.CrossRefGoogle Scholar
Zhang, X.J., Mourenas, D., Artemyev, A.V., Angelopoulos, V., Kurth, W.S., Kletzing, C.A. & Hospodarsky, G.B. 2020 b Rapid frequency variations within intense chorus wave packets. Geophys. Res. Lett. 47 (15), e88853.Google Scholar
Zhang, X.J., Thorne, R., Artemyev, A., Mourenas, D., Angelopoulos, V., Bortnik, J., Kletzing, C.A., Kurth, W.S. & Hospodarsky, G.B. 2018 b Properties of intense field-aligned lower-band chorus waves: implications for nonlinear wave–particle interactions. J. Geophys. Res. 123 (7), 5379–5393.CrossRefGoogle Scholar
Zhang, Y., Matsumoto, H., Kojima, H. & Omura, Y. 1999 Extremely intense whistler mode waves near the bow shock: geotail observations. J. Geophys. Res. 104, 449–462.CrossRefGoogle Scholar