Articles | Volume 41, issue 2
https://doi.org/10.5194/angeo-41-429-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/angeo-41-429-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Relativistic kinematic effects in the interaction time of whistler-mode chorus waves and electrons in the outer radiation belt
Heliophysics Division, Planetary Sciences and Aeronomy, National Institute for Space Research (INPE), São José dos Campos, SP, 12227-010, Brazil
Márcio E. S. Alves
Universidade Estadual Paulista (UNESP), Instituto de Ciência e Tecnologia, São José dos Campos, SP, 12247-004, Brazil
now at: Universidade Estadual Paulista (UNESP), Faculdade de Engenharia e Ciências de Guaratinguetá, Departamento de Física e Química, Guaratinguetá, SP, 12516-410, Brazil
Ligia A. da Silva
Heliophysics Division, Planetary Sciences and Aeronomy, National Institute for Space Research (INPE), São José dos Campos, SP, 12227-010, Brazil
State Key Laboratory of Space Weather, National Space Science Center, Chinese Academy of Sciences, São José dos Campos, SP, Brazil
Vinicius Deggeroni
Heliophysics Division, Planetary Sciences and Aeronomy, National Institute for Space Research (INPE), São José dos Campos, SP, 12227-010, Brazil
Paulo R. Jauer
Heliophysics Division, Planetary Sciences and Aeronomy, National Institute for Space Research (INPE), São José dos Campos, SP, 12227-010, Brazil
State Key Laboratory of Space Weather, National Space Science Center, Chinese Academy of Sciences, São José dos Campos, SP, Brazil
David G. Sibeck
NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
Related authors
No articles found.
Toyese Tunde Ayorinde, Cristiano Max Wrasse, Hisao Takahashi, Luiz Fernando Sapucci, Mohamadou A. Diallo, Cosme Alexandre Oliveira Barros Figueiredo, Diego Barros, Ligia Alves da Silva, Patrick Essien, and Anderson Vestena Bilibio
Atmos. Chem. Phys., 25, 12357–12378, https://doi.org/10.5194/acp-25-12357-2025, https://doi.org/10.5194/acp-25-12357-2025, 2025
Short summary
Short summary
We studied how the Intertropical Convergence Zone (ITCZ) interacts with atmospheric gravity waves high in the sky and how global climate patterns like El Niño affect them. Using RO, ERA5, and NCEP reanalysis data, we found that the ITCZ shifts with season but stays strong year-round, influencing weather and energy flow. Our findings show how climate patterns shape weather systems and help predict changes, improving understanding of the atmosphere and its effects on global climate.
Niklas Grimmich, Adrian Pöppelwerth, Martin Owain Archer, David Gary Sibeck, Ferdinand Plaschke, Wenli Mo, Vicki Toy-Edens, Drew Lawson Turner, Hyangpyo Kim, and Rumi Nakamura
Ann. Geophys., 43, 151–173, https://doi.org/10.5194/angeo-43-151-2025, https://doi.org/10.5194/angeo-43-151-2025, 2025
Short summary
Short summary
The boundary of Earth's magnetic field, the magnetopause, deflects and reacts to the solar wind, the energetic particles emanating from the Sun. We find that certain types of solar wind favour the occurrence of deviations between the magnetopause locations observed by spacecraft and those predicted by models. In addition, the turbulent region in front of the magnetopause, the foreshock, has a large influence on the location of the magnetopause and thus on the accuracy of the model predictions.
Niklas Grimmich, Ferdinand Plaschke, Benjamin Grison, Fabio Prencipe, Christophe Philippe Escoubet, Martin Owain Archer, Ovidiu Dragos Constantinescu, Stein Haaland, Rumi Nakamura, David Gary Sibeck, Fabien Darrouzet, Mykhaylo Hayosh, and Romain Maggiolo
Ann. Geophys., 42, 371–394, https://doi.org/10.5194/angeo-42-371-2024, https://doi.org/10.5194/angeo-42-371-2024, 2024
Short summary
Short summary
In our study, we looked at the boundary between the Earth's magnetic field and the interplanetary magnetic field emitted by the Sun, called the magnetopause. While other studies focus on the magnetopause motion near Earth's Equator, we have studied it in polar regions. The motion of the magnetopause is faster towards the Earth than towards the Sun. We also found that the occurrence of unusual magnetopause locations is due to similar solar influences in the equatorial and polar regions.
Laysa C. A. Resende, Yajun Zhu, Clezio M. Denardini, Sony S. Chen, Ronan A. J. Chagas, Lígia A. Da Silva, Carolina S. Carmo, Juliano Moro, Diego Barros, Paulo A. B. Nogueira, José P. Marchezi, Giorgio A. S. Picanço, Paulo Jauer, Régia P. Silva, Douglas Silva, José A. Carrasco, Chi Wang, and Zhengkuan Liu
Ann. Geophys., 40, 191–203, https://doi.org/10.5194/angeo-40-191-2022, https://doi.org/10.5194/angeo-40-191-2022, 2022
Short summary
Short summary
This study showed the ionospheric response over low-latitude regions in Brazil predicted by Martínez-Ledesma et al. (2020) for the solar eclipse event on 14 December 2020. We used a multi-instrumental and modeling analysis to observe the modifications in the E and F regions and the Es layers over Campo Grande and Cachoeira Paulista. The results showed that solar eclipses can cause significant ionosphere modifications even though they only partially reach the Brazilian low-latitude regions.
Galina Korotova, David Sibeck, Mark Engebretson, Michael Balikhin, Scott Thaller, Craig Kletzing, Harlan Spence, and Robert Redmon
Ann. Geophys., 38, 1267–1281, https://doi.org/10.5194/angeo-38-1267-2020, https://doi.org/10.5194/angeo-38-1267-2020, 2020
Short summary
Short summary
We used multipoint magnetic field, electric field, plasma, and energetic particle observations to study the spatial, temporal, and spectral characteristics of compressional Pc5 pulsations observed deep within the magnetosphere at the end of a strong magnetic storm. We investigated the mode of the waves and their nodal structure. The energetic particles responded directly to the compressional Pc5 pulsations. We interpret the compressional Pc5 waves in terms of drift-mirror instability.
Cited articles
Allanson, O., Thomas, E., Clare, W., and Thomas, N.: Weak Turbulence and quasi-linear Diffusion for Relativistic Wave-Particle Interactions Via a Markov Approach, Front. Astron. Space Sci., 8, 805699, https://doi.org/10.3389/fspas.2021.805699, 2022. a, b
Allison, H. J., Shprits, Y. Y., Zhelavskaya, I. S., Wang, D., and Smirnov, A. G.: Gyroresonant wave-particle interactions with chorus waves during extreme depletions of plasma density in the Van Allen radiation belts, Sci. Adv., 7, eabc0380, https://doi.org/10.1126/sciadv.abc0380, 2021. a, b
Alves, L. R., Da Silva, L. A., Souza, V. M., Sibeck, D. G., Jauer P. R., Vieira, L. E. A., Walsh, B. M., Silveira, M. V. D., Marchezi, J. P., Rockenbach, M., Dal Lago, A., Mendes, O., Tsurutani, B. T., Koga, D., Kanekal, S. G., Baker, D. N., Wygant, J. R., and Kletzing, C. A: Outer radiation belt dropout dynamics following the arrival of two interplanetary coronal mass ejections, Geophys. Res. Lett., 43, 978–987, https://doi.org/10.1002/2015GL067066, 2016. a
Anderson, R. R., Gurnett, D. A., and Odem, D. L.: CRRES plasma wave experiment, J. Spacecr. Rocket., 29, 570–573, https://doi.org/10.2514/3.25501, 1992. a
Artemyev, A., Agapitov, O., Mourenas, D., Krasnoselskikh, V., Shastun, V., and Mozer, F.: Oblique Whistler-Mode Waves in the Earth’s Inner Magnetosphere: Energy Distribution, Origins, and Role in Radiation Belt Dynamics, Space Sci. Rev., 200, 261–355, https://doi.org/10.1007/s11214-016-0252-5, 2016. a, b, c, d, e, f
Artemyev, A., Neishtadt, A., Vasiliev, A., Zhang, X., Mourenas, D., and Vainchtein, D.: Long-term dynamics driven by resonant wave-particle interactions: From Hamiltonian resonance theory to phase space mapping, J. Plasma Phys., 87, 835870201, https://doi.org/10.1017/S0022377821000246, 2021.
Artemyev, A. V., Albert, J. M., Neishtadt, A. I., and Mourenas, A. I.: The effect of wave frequency drift on the electron nonlinear resonant interaction with whistler-mode waves, Phys. Plasmas, 30, 012901, https://doi.org/10.1063/5.0131297, 2023.
Baker, D. N., Kanekal, S. G., Hoxie, V. C., Batiste, S., Bolton, M., Li, X., Elkington, S. R., Monk, S., Reukauf, R., Steg, S., Westfall, J., Belting, C., and Bolton, B.: The relativistic electron-proton telescope (rept) instrument on board the radiation belt storm probes (rbsp) spacecraft: Characterization of earth's radiation belt high-energy particle populations, in: The Van Allen Probes Mission, edited by: Fox, N. and Burch, J. L., 337–381, Springer, New York, https://doi.org/10.1007/978-1-4899-7433-4_11, 2013. a
Baumjohann, W. and Treumann, R. A.: Basic Space Plasma Physics, Imperial College Press, 1st Edn., ISBN 1-86094-079-X, 1997.
Blake, J. B., Carranza, P. A., Claudepierre, S. G., Clemmons, J. H., Crain Jr., W. R., Dotan, Y., Fennell, J. F., Fuentes, F. H., Galvan, R. M., George, J. S., Henderson, M. G., Lalic, M., Lin, A. Y., Looper, M. D., Mabry, D. J., Mazur, J. E., McCarthy, B., Nguyen, C. Q., O'Brien, T. P., Perez, M. A., Redding, M. T., Roeder, J. L., Salvaggio, D. J., Sorensen, G. A., Spence, H. E., Yi, S., and Zakrzewski, M. P.: The Magnetic Electron Ion Spectrometer (MagEIS) Instruments Aboard the Radiation Belt Storm Probes (RBSP) Spacecraft, Space Sci. Rev., 179, 383–421, https://doi.org/10.1007/s11214-013-9991-8, 2013. a
Bittencourt, J. A.: Fundamentals of Plasma Physics, 3nd Edn., Springer, New York, NY, https://doi.org/10.1007/978-1-4757-4030-1, 1995. a, b
Bortnik, J., Inan, U. S., and Bell, T. F.: Landau damping and resultant unidirectional propagation of chorus waves, Geophys. Res. Lett., 33, L03102, https://doi.org/10.1029/2005GL024553, 2006. a
Bortnik, J., Thorne, R. M., and Inan, U. S.: Nonlinear interaction of energetic electrons with large amplitude chorus, Geophys. Res. Lett., 35, L21102, https://doi.org/10.1029/2008GL035500, 2008. a
Boyd, A. J., Spence, H., Reeves, G., Funsten, H., Skoug, R. M., Larsen, B. A., Blake, J., Fennell, J., Claudepierre, S., and Baker, D. N.: RBSP-ECT combined pitch angle resolved electron flux data product, Science operation and data access, https://rbsp-ect.newmexicoconsortium.org/data_pub/, last access: 2 October 2023. a, b
Breneman, A. W., Wygant, J. R., Tian, S., Cattell, C. A., Thaller, S. A., Goetz, K., Tyler, E., Colpitts, C., Dai, L., Kersten, K., Bonnell, J. W., Bale, S. D., Mozer, F. S., Harvey, P. R., Dalton, G., Ergun, R. E., Malaspina, D. M., Kletzing, C. A., Kurth, W. S., Hospodarsky, G. B., Smith, C., Holzworth, R. H., Lejosne, S., Agapitov, O., Artemyev, A., Hudson, M. K., Strangeway, R. J., Baker, D. N., Li, X., Albert, J., Foster, J. C., Erickson, P. J., Chaston, C. C. , Mann, I., Donovan, E., Cully, C. M., Krasnoselskikh, V., Blake, J. B., Millan, R., and Halford, A. J.: The Van Allen Probes Electric Field and Waves Instrument: Science Results, Measurements, and Access to Data, Space Sci. Rev., 218, 69, https://doi.org/10.1007/s11214-022-00934-y, 2022.
Camporeale, E.: Resonant and nonresonant whistlers-particle interaction in the radiation belts, Geophys. Res. Lett., 42, 3114–3121, https://doi.org/10.1002/2015GL063874, 2015.
da Silva, L. A., Shi, J., Alves, L. R., Sibeck, D., Marchezi, J. P., Medeiros, C., Vieira, L. E. A., Agapitov, O., Cardoso, F. R., Souza, V. M., Dal Lago, A., Jauer, P. R., Wang, C., Li, H., Liu, Z., Alves, M. V., and Rockenbach, M. S.: High‐Energy Electron Flux Enhancement Pattern in the Outer Radiation Belt in Response to the Alfvénic Fluctuations Within High‐Speed Solar Wind Stream: A Statistical Analysis, J. Geophys. Res.-Space, 126, e2021JA029363, https://doi.org/10.1029/2021JA029363, 2021. a
Glauert, S. A. and Horne, R. B.: Calculation of pitch angle and energy diffusion coefficients with the PADIE code, J. Geophys. Res., 110, A04206, https://doi.org/10.1029/2004JA010851, 2005. a
Guo, D., Xiang, Z., Ni, B., Cao, X., Fu, S., Zhou, R., Gu, X., Yi, J., Guo, Y., and Jiao, L.: Bounce resonance scattering of radiation belt energetic electrons by extremely low-frequency chorus waves, Geophys. Res. Lett., 48, e2021GL095714, https://doi.org/10.1029/2021GL095714, 2021. a, b
Helliwell, R. A.: Whistlers and Related Ionospheric Phenomena, 3rd Edn., Stanford University Press, Stanford, https://doi.org/10.1007/s11214-013-9991-8 1965. a
Horne, R. B. and Thorne, R. M.: Relativistic electron acceleration and precipitation during resonant interactions with whistler-mode chorus, Geophys. Res. Lett., 30, 1527, https://doi.org/10.1029/2003GL016973, 2003. a, b
Hsieh, Y.-K. and Omura, Y.: Nonlinear dynamics of electrons interacting with oblique whistler mode chorus in the magnetosphere, J. Geophys. Res.-Space, 122, 675–694, https://doi.org/10.1002/2016JA023255, 2017.
Hsieh, Y.-K., Kubota, Y., and Omura, Y.: Nonlinear evolution of radiation belt electron fluxes interacting with oblique whistler mode chorus emissions, J. Geophys. Res.-Space, 125, e2019JA027465, https://doi.org/10.1029/2019JA027465, 2020. a, b, c
Hsieh, Y.-K., Omura, Y., and Kubota, Y.: Energetic electron precipitation induced by oblique whistler mode chorus emissions, J. Geophys. Res.-Space, 127, e2021JA029583, https://doi.org/10.1029/2021JA029583, 2022. a, b, c, d
Hua, M., Bortnik, J., and Ma, Q.: Upper limit of outer radiation belt electron acceleration driven by whistler-mode chorus waves, Geophys. Res. Lett., 49, e2022GL099618, https://doi.org/10.1029/2022GL099618, 2022. a
Jackson, J. D.: 1925–2016, Classical Electrodynamics, New York, Wiley, ISBN 0-486-44572-0, 1999. a
Jaynes, A. N., Baker D. N., Singer, H. J., Rodriguez, J. V., Loto'aniu, T. M., Ali, A. F., Elkington, S. R., Li, X., Kanekal, S. G., Claudepierre, S. G., Fennell, J. F., Li, W., Thorne, R. M., Kletzing C. A., Spence H. E., and Reeves, G. D.: Source and seed populations for relativistic electrons: Their roles in radiation belt changes, J. Geophys. Res.-Space, 120, 7240–7254, https://doi.org/10.1002/2015JA021234, 2015. a
Kennel, C. F. and Engelmann, F.: Velocity Space Diffusion from Weak Plasma Turbulence in a Magnetic Field, Phys. Fluid., 9, 2377, https://doi.org/10.1063/1.1761629, 1966.
Kletzing, C. A., Kurth, W. S., Acuna, M., MacDowall, R. J., Torbert, R. B., Averkamp, T., Bodet, D., Bounds, S. R., Chutter, M., Connerney, J., Crawford, D., Dolan, J. S., Dvorsky, R., Hospodarsky, G. B., Howard, J., Jordanova, V., Johnson, R. A., Kirchner, D. L., Mokrzycki, B., Needell, G., Odom, J., Mark, D., Pfaff, R., Phillips, J. R., Piker, C. W., Remington, S. L., Rowland, D., Santolik, O., Schnurr, R., Sheppard, D., Smith, C. W., Thorne, R. M., and Tyler, J.: The Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) on RBSP, Space Sci. Rev., 179, 127–181, https://doi.org/10.1007/s11214-013-9993-6, 2013 (data available at: http://emfisis.physics.uiowa.edu/Flight/, last access: 2 October 2023). a, b, c
Lam, M. M., Horne, R. B., Meredith, N. P., Glauert, S. A., Moffat-Griffin, T., and Green, J. C.: Origin of energetic electron precipitation >30 keV into the atmosphere, J. Geophys. Res.-Space, 115, A00F08, https://doi.org/10.1029/2009JA014619, 2010. a
Lejosne, S., Allison, H. J., Blum, L. W., Drozdov, A. Y., Hartinger, M. D., Hudson, M. K., Jaynes, A. N., Ozeke, L., Roussos, E., and Zhao, H.: Differentiating Between the Leading Processes for Electron Radiation Belt Acceleration, Front. Astron. Space Sci., 9, 896245, https://doi.org/10.3389/fspas.2022.896245 2022. a
Li, J., Ni, B., Xie, L., Pu, Z., Bortnik, J., Thorne, R. M., Chen, L., Ma, Q., Fu, S., Zong, Q., Wang, X., Xiao, C., Yao, Z., and Guo, R.: Interactions between magnetosonic waves and radiation belt electrons: Comparisons of quasi-linear calculations with test particle simulations, Geophys. Res. Lett., 41, 4828–4834, https://doi.org/10.1002/2014GL060461, 2014. a
Li, X., Tao, X., Lu, Q., and Dai, L.: Bounce resonance diffusion coefficients for spatially confined waves, Geophys. Res. Lett., 42, 9591–9599, https://doi.org/10.1002/2015GL066324, 2015.
Liu, S., Xie, Y., Zhang, S., Shang, X., Yang, C., Zhou, Q., He, Y., and Xiao, F.: Unusual loss of Van Allen belt relativistic electrons by extremely low-frequency chorus, Geophys. Res. Lett., 47, e2020GL089994, https://doi.org/10.1029/2020GL089994, 2020. a, b, c
Lorentzen, K. R., Blake, J. B., Inan, U. S., and Bortnik, J.: Observations of relativistic electron microbursts in association with VLF chorus, J. Geophys. Res., 106, 6017–6027, https://doi.org/10.1029/2000JA003018, 2001. a
Lyons, L. R., Thorne, R. M., and Kennel, C. F.: Pitch-angle diffusion of radiation belt electrons within the plasmasphere, J. Geophys. Res., 77, 3455–3474, https://doi.org/10.1029/ja077i019p03455, 1972. a
Mauk, B. H., Fox, N. J., Kanekal, S. G., Kessel, R. L., Sibeck, D. G., and Ukhorskiy, A.: Science Objectives and Rationale for the Radiation Belt Storm Probes Mission, Space Sci. Rev., 179, 3–27, https://doi.org/10.1007/s11214-012-9908-y, 2013. a
Mourenas, D., Artemyev, A. V., Agapitov, O. V., Krasnoselskikh, V., and Mozer, F. S.: Very oblique whistler generation by low-energy electron streams, J. Geophys. Res.-Space, 120, 3665–3683, https://doi.org/10.1002/2015JA021135, 2015. a
Omura, Y.: Nonlinear wave growth theory of whistler-mode chorus and hiss emissions in the magnetosphere, Earth Planet. Space, 73, 95, https://doi.org/10.1186/s40623-021-01380-w, 2021. a, b
Omura, Y., Katoh, Y., and Summers, D.: Theory and simulation of the generation of whistler-mode chorus, J. Geophys. Res., 113, A04223, https://doi.org/10.1029/2007JA012622, 2008.
Orlova, K. G., Shprits, Y. Y., and Ni, B.: Bounce-averaged diffusion coefficients due to resonant interaction of the outer radiation belt electrons with oblique chorus waves computed in a realistic magnetic field model, J. Geophys. Res., 117, A07209, https://doi.org/10.1029/2012JA017591, 2012. a
Osmane, A., Wilson, L. B., Blum, L., and Pulkkinen, T. I.: On The Connection Between Microbursts And Nonlinear Electronic Structures In Planetary Radiation Belts, Astrophys. J., 816, 51, https://doi.org/10.3847/0004-637X/816/2/51, 2016.
Reeves, G. D., McAdams, K. L., Friedel, R. H. W., and O'Brien, T. P.: Acceleration and loss of relativistic electrons during geomagnetic storms, Geophys. Res. Lett., 30, 1529, https://doi.org/10.1029/2002GL016513, 2003. a
Reeves, G. D., Spence, H. E., Henderson, M. G., Morley, S. K., Fiedel, R. H. W., Funsten, H. O., Baker, D. N., Kanekal S. G., Blake, J. B., Fennell, J. F., Claudepierre, S. G., Thorne, R. M., Turner, D. L., Kletzing, C. A., Kurth, W. S., Larsen, B. A., and Niehof, J. T.: Electron Acceleration in the Heart of the Van Allen Radiation Belts, Science, 341, 6149, https://doi.org/10.1126/science.1237743, 2013. a
Santolík, O., Parrot, M., and Lefeuvre, F.: Singular value decomposition methods for wave propagation analysis, Radio Sci., 38, 1010, https://doi.org/10.1029/2000RS002523, 2003. a
Santolík, O., Gurnett, D. A., Pickett, J. S., Parrot, M., and Cornilleau‐Wehrlin, N.: A microscopic and nanoscopic view of storm‐time chorus on 31 March 2001, Geophys. Res. Lett., 31, L02801, https://doi.org/10.1029/2003GL018757, 2004. a
Santolík, O., Gurnett, D. A., and Pickett, J. S.: Observations of very high amplitudes of whistler‐mode chorus: consequences for nonlinear trapping of energetic electrons in the outer radiation belt, Eos Trans, AGU, 88, Fall Meet. Suppl., Abstract SM14B‐07, ISBN 047130932X, 2007.
Santolík, O., Gurnett, D. A., Pickett, J. S., Chum, J., and Cornilleau-Wehrlin, N.: Oblique propagation of whistler mode waves in the chorus source region, J. Geophys. Res., 114, A00F03, https://doi.org/10.1029/2009JA014586, 2009. a, b
Shprits, Y. Y., Meredith, N. P., and Thorne, R. M.: Parameterization of radiation belt electron loss timescales due to interactions with chorus waves, Geophys. Res. Lett., 34, L11110, https://doi.org/10.1029/2006GL029050, 2007. a
Shprits, Y. Y., Subbotin, D. A., Meredith, N. P., and Elkington, S. R.: Review of modeling of losses and sources of relativistic electrons in the outer radiation belt II: Local acceleration and loss, J. Atmos. Sol.-Terr. Phys., 70, 1694–1713, https://doi.org/10.1016/j.jastp.2008.06.014, 2008. a, b
Sicard-Piet, A., Boscher, D., Horne, R. B., Meredith, N. P., and Maget, V.: Effect of plasma density on diffusion rates due to wave particle interactions with chorus and plasmaspheric hiss: extreme event analysis, Ann. Geophys., 32, 1059–1071, https://doi.org/10.5194/angeo-32-1059-2014, 2014. a
Subbotin, D., Shprits, Y., and Ni, B.: Three-dimensional VERB radiation belt simulations including mixed diffusion, J. Geophys. Res., 115, A03205, https://doi.org/10.1029/2009JA015070, 2010. a
Summers, D., Thorne, R. M., and Xiao, F.: Relativistic theory of wave-particle resonant diffusion with application to electron acceleration in the magnetosphere, J. Geophys. Res., 103, 20487–20500, https://doi.org/10.1029/98JA01740, 1998. a
Summers, D., Ni, B., and Meredith, N. P.: Timescales for radiation belt electron acceleration and loss due to resonant wave-particle interactions: 1. Theory, J. Geophys. Res., 112, A04206, https://doi.org/10.1029/2006JA011801, 2007.
Summers, D., Omura, Y., Miyashita, Y., and Lee, D.-H.: Nonlinear spatiotemporal evolution of whistler modechorus waves in Earth’s inner magnetosphere, J. Geophys. Res., 117, A09206, https://doi.org/10.1029/2012JA017842, 2012. a, b
Tao, X., Bortnik, J., Albert, J. M., Liu, K., and Thorne, R. M.: Comparison of quasilinear diffusion coefficients for parallel propagating whistler mode waves with test particle simulations, Geophys. Res. Lett., 38, L06105, https://doi.org/10.1029/2011GL046787, 2011.
Tao, X., Bortnik, J., Albert, J. M., and Thorne, R. M.: Comparison of bounce-averaged quasi-linear diffusion coefficients for parallel propagating whistler mode waves with test particle simulations, J. Geophys. Res., 117, A10205, https://doi.org/10.1029/2012JA017931, 2012.
Teng, S., Tao, X., Li, W., Qi, Y., Gao, X., Dai, L., Lu, Q., and Wang, S.: A statistical study of the spatial distribution and source-region size of chorus waves using Van Allen Probes data, Ann. Geophys., 36, 867–878, https://doi.org/10.5194/angeo-36-867-2018, 2018.
Thorne, R. M., Horne, R. B., Glauert, S., Meredith, N. P., Shprits, Y. Y., Summers, D., and Anderson, R. R.: The Influence of Wave-Particle Interactions on Relativistic Electron Dynamics During Storms, in: Inner Magnetosphere Interactions: New Perspectives from Imaging, edited by: Burch, J., Schulz, M., and Spence, H., American Geophysical Union (AGU), https://doi.org/10.1029/159GM07, 2005. a, b
Tsurutani, B. T. and Smith, E. J.: Postmidnight chorus: A substorm phenomenon, J. Geophys. Res., 79, 118–127, https://doi.org/10.1029/JA079i001p00118, 1974. a, b, c
Tsurutani, B. T. and Smith, E. J.: Two types of magnetospheric ELF chorus and their substorm dependences, J. Geophys. Res., 82, 5112–5128, https://doi.org/10.1029/JA082i032p05112, 1977. a
Tsurutani, B. T., Lakhina, G. S., and Verkhoglyadova, O. P.: Energetic electron (>10 keV) microburst precipitation, 5–15 s X-ray pulsations, chorus, and wave-particle interactions: A review, J. Geophys. Re.-Space, 118, 2296–2312, https://doi.org/10.1002/jgra.50264, 2013. a, b
Tsyganenko, N. A. and Sitnov, M. I.: Modeling the dynamics of the inner magnetosphere during strong geomagnetic storms, J. Geophys. Res., 110, A03208, https://doi.org/10.1029/2004JA010798, 2005. a
Tu, W., Cunningham, G. S., Chen, Y., Morley, S. K., Reeves, G. D., Blake, J. B., Baker, D. N., and Spence, H.: Event-specific chorus wave and electron seed population models in DREAM3D using the Van Allen Probes, Geophys. Res. Lett., 41, 1359–1366, https://doi.org/10.1002/2013GL058819, 2014. a, b, c
Verkhoglyadova, O. P., Tsurutani, B. T., and Lakhina, G. S.: Properties of obliquely propagating chorus, J. Geophys. Res., 115, A00F19, https://doi.org/10.1029/2009JA014809, 2010. a
Walker, A. D. M.: The Effect of Wave Fields on Energetic Particles, in: Plasma Waves in the Magnetosphere, Physics and Chemistry in Space Planetology, Vol. 24, Springer Berlin, Heidelberg, https://doi.org/10.1007/978-3-642-77867-4, 1993. a, b, c
Wygant, J. R., Bonnell, J. W. Goetz, K., Ergun, R. E., Mozer, F. S., Bale, S. D., Ludlam, M., Turin, P., Harvey, P. R., Hochmann, R., Harps, K., Dalton, G., McCauley, J., Rachelson, W., Gordon, D., Donakowski, B., Shultz, C., Smith, C., Diaz-Aguado, M., Fischer, J., Heavner, S., Berg, P., Malsapina, D. M., Bolton, M. K., Hudson, M., Strangeway, R. J., Baker, D. N., Li, X., Albert, J., Foster, J. C., Chaston, C. C., Mann, I., Donovan, E., Cully, C. M., Cattell, C. A., Krasnoselskikh, V., Kersten, K., Brenneman, A., and Tao, J. B.: The Electric Field and Waves Instruments on the Radiation Belt Storm Probes Mission, Space Sci. Rev., 179, 183–220, https://doi.org/10.1007/s11214-013-0013-7, 2013 (data available at: http://www.space.umn.edu/rbspefw-data/, last access: 2 October 2023). a, b
Zhang, J., Thorne, R., Artemyev, A., Mourenas, D., Angelopoulos, V., Bortnik, J., Kletzing, C. A., Kurth, W. S., and Hospodarsky, G. B.: Properties of Intense Field-Aligned Lower-Band Chorus Waves: Implications for Nonlinear Wave-Particle Interactions, J. Geophys. Res.-Space, 123, 5379-5393, https://doi.org/10.1029/2018JA025390, 2008.
Zhang, X.-J., Mourenas, D., Artemyev, A. V., Angelopoulos, V., and Thorne, R. M.: Contemporaneous EMIC and whistler mode waves: Observations and consequences for MeV electron loss, Geophys. Res. Lett., 44, 8113–8121, https://doi.org/10.1002/2017GL073886, 2017. a
Zhelavskaya, I. S., Spasojevic, M., Shprits, Y. Y., and Kurth, W. S.: Automated determination of electron density from electric field measurements on the Van Allen Probes spacecraft, J. Geophys. Res.-Space, 121, 4611–4625, https://doi.org/10.1002/2015JA022132, 2016. a, b
Short summary
We derive the wave–particle interaction time (IT) equation considering the effects of special relativity theory for whistler-mode chorus waves and relativistic electrons in Earth's radiation belt. Results show that IT has a non-linear dependence on the wave group velocity, electrons' energy, and initial pitch angle. Our results show that the interaction time is generally longer when applying the complete relativistic approach compared to a non-relativistic calculation.
We derive the wave–particle interaction time (IT) equation considering the effects of special...