Advertisement

Space Science Reviews

, Volume 200, Issue 1–4, pp 261–355 | Cite as

Oblique Whistler-Mode Waves in the Earth’s Inner Magnetosphere: Energy Distribution, Origins, and Role in Radiation Belt Dynamics

  • Anton Artemyev
  • Oleksiy Agapitov
  • Didier Mourenas
  • Vladimir Krasnoselskikh
  • Vitalii Shastun
  • Forrest Mozer
Article

Abstract

In this paper we review recent spacecraft observations of oblique whistler-mode waves in the Earth’s inner magnetosphere as well as the various consequences of the presence of such waves for electron scattering and acceleration. In particular, we survey the statistics of occurrences and intensity of oblique chorus waves in the region of the outer radiation belt, comprised between the plasmapause and geostationary orbit, and discuss how their actual distribution may be explained by a combination of linear and non-linear generation, propagation, and damping processes. We further examine how such oblique wave populations can be included into both quasi-linear diffusion models and fully nonlinear models of wave-particle interaction. On this basis, we demonstrate that varying amounts of oblique waves can significantly change the rates of particle scattering, acceleration, and precipitation into the atmosphere during quiet times as well as in the course of a storm. Finally, we discuss possible generation mechanisms for such oblique waves in the radiation belts. We demonstrate that oblique whistler-mode chorus waves can be considered as an important ingredient of the radiation belt system and can play a key role in many aspects of wave-particle resonant interactions.

Keywords

Wave-particle interaction Earth radiation belts Whistler waves 

Notes

Acknowledgements

A.A. and D.M. are grateful to A. Vasiliev for fruitful discussions and important inputs. A.A. appreciates the useful discussions with D. Shklyar and A. Demekhov.

V.K., A.A. and O.A. are grateful to D. Boscher and G. Rolland for persistent support of radiation belts studies in LPC2E. V.K. is grateful to CNES for financial support of the activities presented in this Review during years 2008–2014 through a series of grants Modele d’Ondes and Modele d’ondes pour le code SALAMMBO. Part of this work was also supported by a contract with CEA.

The work of O.A. and F.S.M. has been supported by JHU/APL Contract No. 922613 (RBSP-EFW), NASA contract NAS5-02099 and NASA Grant NNX09AE41G.

References

  1. G.A. Abel, A.N. Fazakerley, A.D. Johnstone, Statistical distributions of field-aligned electron events in the near-equatorial magnetosphere observed by the Low Energy Plasma Analyzer on CRRES. J. Geophys. Res. 107, 1393 (2002). doi: 10.1029/2001JA005073 CrossRefGoogle Scholar
  2. O.V. Agapitov, A.V. Artemyev, D. Mourenas, Y. Kasahara, V. Krasnoselskikh, Inner belt and slot region electron lifetimes and energization rates based on AKEBONO statistics of whistler waves. J. Geophys. Res. 119, 2876–2893 (2014). doi: 10.1002/2014JA019886 CrossRefGoogle Scholar
  3. O.V. Agapitov, A.V. Artemyev, D. Mourenas, F.S. Mozer, V. Krasnoselskikh, Empirical model of lower band chorus wave distribution in the outer radiation belt. J. Geophys. Res. 120, 10 (2015a). doi: 10.1002/2015JA021829 CrossRefGoogle Scholar
  4. O.V. Agapitov, V. Krasnoselskikh, F.S. Mozer, A.V. Artemyev, A.S. Volokitin, Generation of nonlinear electric field bursts in the outer radiation belt through the parametric decay of whistler waves. Geophys. Res. Lett. 42, 3715–3722 (2015b). doi: 10.1002/2015GL064145 ADSCrossRefGoogle Scholar
  5. O.V. Agapitov, A.V. Artemyev, D. Mourenas, F.S. Mozer, V. Krasnoselskikh, Nonlinear local parallel acceleration of electrons through Landau trapping by oblique whistler mode waves in the outer radiation belt. Geophys. Res. Lett. 42, 10 (2015c). doi: 10.1002/2015GL066887 Google Scholar
  6. O. Agapitov, V. Krasnoselskikh, Y. Zaliznyak, V. Angelopoulos, O. Le Contel, G. Rolland, Chorus source region localization in the Earth’s outer magnetosphere using THEMIS measurements. Ann. Geophys. 28, 1377–1386 (2010) ADSCrossRefGoogle Scholar
  7. O. Agapitov, V. Krasnoselskikh, Y. Zaliznyak, V. Angelopoulos, O. Le Contel, G. Rolland, Observations and modeling of forward and reflected chorus waves captured by THEMIS. Ann. Geophys. 29, 541–550 (2011). doi: 10.5194/angeo-29-541-2011 ADSCrossRefGoogle Scholar
  8. O. Agapitov, V. Krasnoselskikh, Y.V. Khotyaintsev, G. Rolland, Correction to “A statistical study of the propagation characteristics of whistler waves observed by Cluster”. Geophys. Res. Lett. 39, 24102 (2012). doi: 10.1029/2012GL054320 ADSCrossRefGoogle Scholar
  9. O. Agapitov, A. Artemyev, V. Krasnoselskikh, Y.V. Khotyaintsev, D. Mourenas, H. Breuillard, M. Balikhin, G. Rolland, Statistics of whistler mode waves in the outer radiation belt: Cluster STAFF-SA measurements. J. Geophys. Res. 118, 3407–3420 (2013). doi: 10.1002/jgra.50312 CrossRefGoogle Scholar
  10. O. Agapitov, A. Artemyev, D. Mourenas, V. Krasnoselskikh, J. Bonnell, O. Le Contel, C.M. Cully, V. Angelopoulos, The quasi-electrostatic mode of chorus waves and electron nonlinear acceleration. J. Geophys. Res. 119, 1606–1626 (2014). doi: 10.1002/2013JA019223 CrossRefGoogle Scholar
  11. J. Aguado, C. Cid, E. Saiz, Y. Cerrato, Hyperbolic decay of the Dst Index during the recovery phase of intense geomagnetic storms. J. Geophys. Res. 115, 7220 (2010). doi: 10.1029/2009JA014658 CrossRefGoogle Scholar
  12. J.M. Albert, Cyclotron resonance in an inhomogeneous magnetic field. Phys. Fluids, B Plasma Phys. 5, 2744–2750 (1993). doi: 10.1063/1.860715 CrossRefGoogle Scholar
  13. J.M. Albert, Gyroresonant interactions of radiation belt particles with a monochromatic electromagnetic wave. J. Geophys. Res. 105, 21191 (2000). doi: 10.1029/2000JA000008 ADSCrossRefGoogle Scholar
  14. J.M. Albert, Nonlinear interaction of outer zone electrons with VLF waves. Geophys. Res. Lett. 29, 1275 (2002). doi: 10.1029/2001GL013941 ADSCrossRefGoogle Scholar
  15. J.M. Albert, Evaluation of quasi-linear diffusion coefficients for whistler mode waves in a plasma with arbitrary density ratio. J. Geophys. Res. 110, 3218 (2005). doi: 10.1029/2004JA010844 CrossRefGoogle Scholar
  16. J.M. Albert, Simple approximations of quasi-linear diffusion coefficients. J. Geophys. Res. 112, 12202 (2007). doi: 10.1029/2007JA012551 CrossRefGoogle Scholar
  17. J.M. Albert, Diffusion by one wave and by many waves. J. Geophys. Res. 115 (2010). doi: 10.1029/2009JA014732
  18. J.M. Albert, Dependence of quasi-linear diffusion coefficients on wave parameters. J. Geophys. Res. 117, 9224 (2012). doi: 10.1029/2012JA017718 CrossRefGoogle Scholar
  19. J.M. Albert, Y.Y. Shprits, Estimates of lifetimes against pitch angle diffusion. J. Atmos. Sol.-Terr. Phys. 71, 1647–1652 (2009). doi: 10.1016/j.jastp.2008.07.004 ADSCrossRefGoogle Scholar
  20. J.M. Albert, N.P. Meredith, R.B. Horne, Three-dimensional diffusion simulation of outer radiation belt electrons during the 9 October 1990 magnetic storm. J. Geophys. Res. 114, 9214 (2009). doi: 10.1029/2009JA014336 CrossRefGoogle Scholar
  21. J.M. Albert, X. Tao, J. Bortnik, Aspects of nonlinear wave-particle interactions, in Dynamics of the Earth’s Radiation Belts and Inner Magnetosphere, ed. by D. Summers, I.U. Mann, D.N. Baker, M. Schulz American Geophysical Union (2013). doi: 10.1029/2012GM001324 Google Scholar
  22. J.K. Alekhin, D.R. Shklyar, Some questions of VLF wave propagation in the magnetosphere. Geomagn. Aeron. 20, 501–507 (1980) ADSGoogle Scholar
  23. X. An, B. Van Compernolle, J. Bortnik, R.M. Thorne, L. Chen, W. Li, Resonant excitation of whistler waves by a helical electron beam. Geophys. Res. Lett. 121 (2015). doi: 10.1002/2015GL067126
  24. M.E. Andersson, P.T. Verronen, C.J. Rodger, M.A. Clilverd, S. Wang, Longitudinal hotspots in the mesospheric oh variations due to energetic electron precipitation. Atmos. Chem. Phys. 14(2), 1095–1105 (2014). doi: 10.5194/acp-14-1095-2014. http://www.atmos-chem-phys.net/14/1095/2014/ ADSCrossRefGoogle Scholar
  25. A.A. Andronov, V.Y. Trakhtengerts, Kinetic instability of the Earth’s outer radiation belt. Geomagn. Aeron. 4, 233–242 (1964) Google Scholar
  26. V. Angelopoulos, The THEMIS mission. Space Sci. Rev. 141, 5–34 (2008). doi: 10.1007/s11214-008-9336-1 ADSCrossRefGoogle Scholar
  27. J.J. Angerami, Whistler duct properties deduced from VLF observations made with the Ogo 3 satellite near the magnetic equator. J. Geophys. Res. 75, 6115–6135 (1970). doi: 10.1029/JA075i031p06115 ADSCrossRefGoogle Scholar
  28. S.V. Apatenkov, V.A. Sergeev, M.V. Kubyshkina, R. Nakamura, W. Baumjohann, A. Runov, I. Alexeev, A. Fazakerley, H. Frey, S. Muhlbachler, P.W. Daly, J. Sauvaud, N. Ganushkina, T. Pulkkinen, G.D. Reeves, Y. Khotyaintsev, Multi-spacecraft observation of plasma dipolarization/injection in the inner magnetosphere. Ann. Geophys. 25, 801–814 (2007) ADSCrossRefGoogle Scholar
  29. V.I. Arnold, V.V. Kozlov, A.I. Neishtadt, Mathematical Aspects of Classical and Celestial Mechanics, 3rd edn. Dynamical Systems III. Encyclopedia of Mathematical Sciences (Springer, New York, 2006) zbMATHGoogle Scholar
  30. A.V. Artemyev, A.A. Vasiliev, D. Mourenas, O. Agapitov, V. Krasnoselskikh, Nonlinear electron acceleration by oblique whistler waves: Landau resonance vs. cyclotron resonance. Phys. Plasmas 20, 122901 (2013a). doi: 10.1063/1.4836595 ADSCrossRefGoogle Scholar
  31. A.V. Artemyev, D. Mourenas, O.V. Agapitov, V.V. Krasnoselskikh, Parametric validations of analytical lifetime estimates for radiation belt electron diffusion by whistler waves. Ann. Geophys. 31, 599–624 (2013b). doi: 10.5194/angeo-31-599-2013 ADSCrossRefGoogle Scholar
  32. A.V. Artemyev, O.V. Agapitov, D. Mourenas, V. Krasnoselskikh, L.M. Zelenyi, Storm-induced energization of radiation belt electrons: effect of wave obliquity. Geophys. Res. Lett. 40, 4138–4143 (2013c). doi: 10.1002/grl.50837 ADSCrossRefGoogle Scholar
  33. A.V. Artemyev, A.A. Vasiliev, D. Mourenas, O.V. Agapitov, V.V. Krasnoselskikh, Electron scattering and nonlinear trapping by oblique whistler waves: the critical wave intensity for nonlinear effects. Phys. Plasmas 21(10), 102903 (2014a). doi: 10.1063/1.4897945 ADSCrossRefGoogle Scholar
  34. A.V. Artemyev, A.A. Vasiliev, D. Mourenas, O. Agapitov, V. Krasnoselskikh, D. Boscher, G. Rolland, Fast transport of resonant electrons in phase space due to nonlinear trapping by whistler waves. Geophys. Res. Lett. 41, 5727–5733 (2014b). doi: 10.1002/2014GL061380 ADSCrossRefGoogle Scholar
  35. A.V. Artemyev, O. Agapitov, F. Mozer, V. Krasnoselskikh, Thermal electron acceleration by localized bursts of electric field in the radiation belts. Geophys. Res. Lett. 41, 5734–5739 (2014c). doi: 10.1002/2014GL061248 ADSCrossRefGoogle Scholar
  36. A.V. Artemyev, A.A. Vasiliev, D. Mourenas, A.I. Neishtadt, O.V. Agapitov, V. Krasnoselskikh, Probability of relativistic electron trapping by parallel and oblique whistler-mode waves in Earth’s radiation belts. Phys. Plasmas 22(11), 112903 (2015a). doi: 10.1063/1.4935842 ADSCrossRefGoogle Scholar
  37. A.V. Artemyev, D. Mourenas, O.V. Agapitov, V.V. Krasnoselskikh, Relativistic electron scattering by magnetosonic waves: effects of discrete wave emission and high wave amplitudes. Phys. Plasmas 22, 062901 (2015b). doi: 10.1063/1.4922061 ADSCrossRefGoogle Scholar
  38. A.V. Artemyev, D. Mourenas, O.V. Agapitov, D.L. Vainchtein, F.S. Mozer, V.V. Krasnoselskikh, Stability of relativistic electron trapping by strong whistler or electromagnetic ion cyclotron waves. Phys. Plasmas 22, 082901 (2015c). doi: 10.1063/1.4927774 ADSCrossRefGoogle Scholar
  39. A.V. Artemyev, O.V. Agapitov, D. Mourenas, V.V. Krasnoselskikh, F.S. Mozer, Wave energy budget analysis in the Earth’s radiation belts uncovers a missing energy. Nat. Commun. 6, 8143 (2015d). doi: 10.1038/ncomms8143 ADSCrossRefGoogle Scholar
  40. A. Artemyev, O. Agapitov, H. Breuillard, V. Krasnoselskikh, G. Rolland, Electron pitch-angle diffusion in radiation belts: the effects of whistler wave oblique propagation. Geophys. Res. Lett. 39, 8105 (2012a). doi: 10.1029/2012GL051393 ADSCrossRefGoogle Scholar
  41. A. Artemyev, V. Krasnoselskikh, O. Agapitov, D. Mourenas, G. Rolland, Non-diffusive resonant acceleration of electrons in the radiation belts. Phys. Plasmas 19, 122901 (2012b). doi: 10.1063/1.4769726 ADSCrossRefGoogle Scholar
  42. A. Artemyev, O. Agapitov, V. Krasnoselskikh, H. Breuillard, G. Rolland, Statistical model of electron pitch-angle diffusion in the outer radiation belt. J. Geophys. Res. 117, 08219 (2012c). doi: 10.1029/2012JA017826 Google Scholar
  43. H. Aryan, K. Yearby, M. Balikhin, O. Agapitov, V. Krasnoselskikh, R. Boynton, Statistical study of chorus wave distributions in the inner magnetosphere using Ae and solar wind parameters. J. Geophys. Res. 119, 6131–6144 (2014). doi: 10.1002/2014JA019939 CrossRefGoogle Scholar
  44. D.N. Baker, S.G. Kanekal, X. Li, S.P. Monk, J. Goldstein, J.L. Burch, An extreme distortion of the Van Allen belt arising from the ‘Hallowe’en’ solar storm in 2003. Nature 432, 878–881 (2004). doi: 10.1038/nature03116 ADSCrossRefGoogle Scholar
  45. D.N. Baker, S.G. Kanekal, V.C. Hoxie, S. Batiste, M. Bolton, X. Li, S.R. Elkington, S. Monk, R. Reukauf, S. Steg, J. Westfall, C. Belting, B. Bolton, D. Braun, B. Cervelli, K. Hubbell, M. Kien, S. Knappmiller, S. Wade, B. Lamprecht, K. Stevens, J. Wallace, A. Yehle, H.E. Spence, R. Friedel, 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. Space Sci. Rev. 179, 337–381 (2013). doi: 10.1007/s11214-012-9950-9 ADSCrossRefGoogle Scholar
  46. D.N. Baker, A.N. Jaynes, X. Li, M.G. Henderson, S.G. Kanekal, G.D. Reeves, H.E. Spence, S.G. Claudepierre, J.F. Fennell, M.K. Hudson, R.M. Thorne, J.C. Foster, P.J. Erickson, D.M. Malaspina, J.R. Wygant, A. Boyd, C.A. Kletzing, A. Drozdov, Y.Y. Shprits, Gradual diffusion and punctuated phase space density enhancements of highly relativistic electrons: van Allen probes observations. Geophys. Res. Lett. 41, 1351–1358 (2014). doi: 10.1002/2013GL058942 ADSCrossRefGoogle Scholar
  47. M.F. Bakhareva, Time variations in energetic particle fluxes at different types of statistical acceleration and the variation properties during geomagnetic disturbances. Geomagn. Aeron. 45, 551–561 (2005) Google Scholar
  48. M.A. Balikhin, M. Gedalin, G.D. Reeves, R.J. Boynton, S.A. Billings, Time scaling of the electron flux increase at GEO: the local energy diffusion model vs observations. J. Geophys. Res. 117, 10208 (2012). doi: 10.1029/2012JA018114 Google Scholar
  49. M.A. Balikhin, Y.Y. Shprits, S.N. Walker, L. Chen, N. Cornilleau-Wehrlin, I. Dandouras, O. Santolik, C. Carr, K.H. Yearby, B. Weiss, Observations of discrete harmonics emerging from equatorial noise. Nat. Commun. 6, 7703 (2015). doi: 10.1038/ncomms8703 ADSCrossRefGoogle Scholar
  50. T.F. Bell, 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 (1984). doi: 10.1029/JA089iA02p00905 ADSCrossRefGoogle Scholar
  51. T.F. Bell, The wave magnetic field amplitude threshold for nonlinear trapping of energetic gyroresonant and Landau resonant electrons by nonducted VLF waves in the magnetosphere. J. Geophys. Res. 91, 4365–4379 (1986). doi: 10.1029/JA091iA04p04365 ADSCrossRefGoogle Scholar
  52. T.F. Bell, U.S. Inan, J. Bortnik, J.D. Scudder, The Landau damping of magnetospherically reflected whistlers within the plasmasphere. Geophys. Res. Lett. 29, 1733 (2002). doi: 10.1029/2002GL014752 ADSCrossRefGoogle Scholar
  53. P.A. Bespalov, V.I. Trakhtengerts, Cherenkov generation of ELF and VLF emissions in the magnetosphere. Geomagn. Aeron. 15, 313–316 (1975) ADSGoogle Scholar
  54. J. Birn, A.V. Artemyev, D.N. Baker, M. Echim, M. Hoshino, L.M. Zelenyi, Particle acceleration in the magnetotail and aurora. Space Sci. Rev. 173, 49–102 (2012). doi: 10.1007/s11214-012-9874-4 ADSCrossRefGoogle Scholar
  55. J.B. Blake, P.A. Carranza, S.G. Claudepierre, J.H. Clemmons, W.R. Crain, Y. Dotan, J.F. Fennell, F.H. Fuentes, R.M. Galvan, J.S. George, M.G. Henderson, M. Lalic, A.Y. Lin, M.D. Looper, D.J. Mabry, J.E. Mazur, B. McCarthy, C.Q. Nguyen, T.P. O’Brien, M.A. Perez, M.T. Redding, J.L. Roeder, D.J. Salvaggio, G.A. Sorensen, H.E. Spence, S. Yi, M.P. Zakrzewski, The Magnetic Electron Ion Spectrometer (MagEIS) instruments aboard the Radiation Belt Storm Probes (RBSP) spacecraft. Space Sci. Rev. 179, 383–421 (2013). doi: 10.1007/s11214-013-9991-8 ADSCrossRefGoogle Scholar
  56. J. Bortnik, R.M. Thorne, The dual role of ELF/VLF chorus waves in the acceleration and precipitation of radiation belt electrons. J. Atmos. Sol.-Terr. Phys. 69, 378–386 (2007). doi: 10.1016/j.jastp.2006.05.030 ADSCrossRefGoogle Scholar
  57. J. Bortnik, U.S. Inan, T.F. Bell, Frequency-time spectra of magnetospherically reflecting whistlers in the plasmasphere. J. Geophys. Res. 108, 1030 (2003). doi: 10.1029/2002JA009387 CrossRefGoogle Scholar
  58. J. Bortnik, U.S. Inan, T.F. Bell, Landau damping and resultant unidirectional propagation of chorus waves. Geophys. Res. Lett. 33, 3102 (2006). doi: 10.1029/2005GL024553 ADSCrossRefGoogle Scholar
  59. J. Bortnik, R.M. Thorne, U.S. Inan, Nonlinear interaction of energetic electrons with large amplitude chorus. Geophys. Res. Lett. 35, 21102 (2008). doi: 10.1029/2008GL035500 ADSCrossRefGoogle Scholar
  60. J. Boskova, F. Jiricek, P. Triska, B.V. Lundin, D.R. Shkliar, A possible common nature of equatorial half-gyrofrequency VLF emissions and discrete plasmaspheric emissions. Ann. Geophys. 8, 755–763 (1990) ADSGoogle Scholar
  61. J. Bošková, F. Jiříček, P. Tříska, B.V. Lundin, D.R. Shklyar, M. Hvoždara, On the problem of quasi-electrostatic whistler mode waves: a possible interpretation of discrete plasmaspheric emissions. Stud. Geophys. Geod. 32, 199–212 (1988). doi: 10.1007/BF01637582 CrossRefGoogle Scholar
  62. H. Breuillard, Y. Zaliznyak, V. Krasnoselskikh, O. Agapitov, A. Artemyev, G. Rolland, Chorus wave-normal statistics in the Earth’s radiation belts from ray tracing technique. Ann. Geophys. 30, 1223–1233 (2012). doi: 10.5194/angeo-30-1223-2012 ADSCrossRefGoogle Scholar
  63. H. Breuillard, Y. Zaliznyak, O. Agapitov, A. Artemyev, V. Krasnoselskikh, G. Rolland, Spatial spreading of magnetospherically reflected chorus elements in the inner magnetosphere. Ann. Geophys. 31, 1429–1435 (2013). doi: 10.5194/angeo-31-1429-2013 ADSCrossRefGoogle Scholar
  64. H. Breuillard, O. Agapitov, A. Artemyev, V. Krasnoselskikh, O. Le Contel, C.M. Cully, V. Angelopoulos, Y. Zaliznyak, G. Rolland, On the origin of falling-tone chorus elements in Earth’s inner magnetosphere. Ann. Geophys. 32, 1477–1485 (2014). doi: 10.5194/angeo-32-1477-2014 ADSCrossRefGoogle Scholar
  65. H. Breuillard, O. Agapitov, A. Artemyev, E.A. Kronberg, S.E. Haaland, P.W. Daly, V.V. Krasnoselskikh, D. Boscher, S. Bourdarie, Y. Zaliznyak, G. Rolland, Field-aligned chorus wave spectral power in Earth’s outer radiation belt. Ann. Geophys. 33(5), 583–597 (2015). doi: 10.5194/angeo-33-583-2015. http://www.ann-geophys.net/33/583/2015/ ADSCrossRefGoogle Scholar
  66. A.L. Brinca, On the evolution of the geomagnetospheric coherent cyclotron resonance in the midst of noise. J. Geophys. Res. 85, 4711–4714 (1980). doi: 10.1029/JA085iA09p04711 ADSCrossRefGoogle Scholar
  67. N.L. Bunch, M. Spasojevic, Y.Y. Shprits, Off-equatorial chorus occurrence and wave amplitude distributions as observed by the Polar Plasma Wave Instrument. J. Geophys. Res. 117, 4205 (2012). doi: 10.1029/2011JA017228 CrossRefGoogle Scholar
  68. N.L. Bunch, M. Spasojevic, Y.Y. Shprits, X. Gu, F. Foust, The spectral extent of chorus in the off-equatorial magnetosphere. J. Geophys. Res. 118, 1700–1705 (2013). doi: 10.1029/2012JA018182 CrossRefGoogle Scholar
  69. W.J. Burtis, R.A. Helliwell, Banded chorus—a new type of VLF radiation observed in the magnetosphere by OGO 1 and OGO 3. J. Geophys. Res. 74, 3002 (1969). doi: 10.1029/JA074i011p03002 ADSCrossRefGoogle Scholar
  70. R.K. Burton, R.E. Holzer, The origin and propagation of chorus in the outer magnetosphere. J. Geophys. Res. 79, 1014–1023 (1974). doi: 10.1029/JA079i007p01014 ADSCrossRefGoogle Scholar
  71. D.L. Carpenter, T.F. Bell, T.R. Miller, R.R. Anderson, A comparison of equatorial electron densities measured by whistlers and by a satellite radio technique. Geophys. Res. Lett. 8, 1107–1110 (1981). doi: 10.1029/GL008i010p01107 ADSCrossRefGoogle Scholar
  72. C.A. Cattell, A.W. Breneman, S.A. Thaller, J.R. Wygant, C.A. Kletzing, W.S. Kurth, Van Allen probes observations of unusually low frequency whistler mode waves observed in association with moderate magnetic storms: statistical study. Geophys. Res. Lett. 42, 7273–7281 (2015). doi: 10.1002/2015GL065565 ADSCrossRefGoogle Scholar
  73. C. Cattell, J.R. Wygant, K. Goetz, K. Kersten, P.J. Kellogg, T. von Rosenvinge, S.D. Bale, I. Roth, M. Temerin, M.K. Hudson, R.A. Mewaldt, M. Wiedenbeck, M. Maksimovic, R. Ergun, M. Acuna, C.T. Russell, Discovery of very large amplitude whistler-mode waves in Earth’s radiation belts. Geophys. Res. Lett. 35, 1105 (2008). doi: 10.1029/2007GL032009 ADSCrossRefGoogle Scholar
  74. L. Chen, R.M. Thorne, W. Li, J. Bortnik, Modeling the wave normal distribution of chorus waves. J. Geophys. Res. 118, 1074–1088 (2013). doi: 10.1029/2012JA018343 CrossRefGoogle Scholar
  75. Y. Chen, G.D. Reeves, R.H.W. Friedel, The energization of relativistic electrons in the outer van Allen radiation belt. Nat. Phys. 3, 614–617 (2007). doi: 10.1038/nphys655 CrossRefGoogle Scholar
  76. N. Cornilleau-Wehrlin, G. Chanteur, S. Perraut, L. Rezeau, P. Robert, A. Roux, C. de Villedary, P. Canu, M. Maksimovic, Y. de Conchy, D.H.C. Lacombe, F. Lefeuvre, M. Parrot, J.L. Pinçon, P.M.E. Décréau, C.C. Harvey, P. Louarn, O. Santolik, H.S.C. Alleyne, M. Roth, T. Chust, O. Le Contel, Staff Team, First results obtained by the Cluster STAFF experiment. Ann. Geophys. 21, 437–456 (2003). doi: 10.5194/angeo-21-437-2003 ADSCrossRefGoogle Scholar
  77. C.M. Cully, J.W. Bonnell, R.E. Ergun, THEMIS observations of long-lived regions of large-amplitude whistler waves in the inner magnetosphere. Geophys. Res. Lett. 35, 17 (2008). doi: 10.1029/2008GL033643 CrossRefGoogle Scholar
  78. C.M. Cully, V. Angelopoulos, U. Auster, J. Bonnell, O. Le Contel, Observational evidence of the generation mechanism for rising-tone chorus. Geophys. Res. Lett. 38, 1106 (2011). doi: 10.1029/2010GL045793 ADSCrossRefGoogle Scholar
  79. I.A. Daglis, R.M. Thorne, W. Baumjohann, S. Orsini, The terrestrial ring current: origin, formation, and decay. Rev. Geophys. 37, 407–438 (1999). doi: 10.1029/1999RG900009 ADSCrossRefGoogle Scholar
  80. F. Darrouzet, D.L. Gallagher, N. André, D.L. Carpenter, I. Dandouras, P.M.E. Décréau, J. de Keyser, R.E. Denton, J.C. Foster, J. Goldstein, M.B. Moldwin, B.W. Reinisch, B.R. Sandel, J. Tu, Plasmaspheric density structures and dynamics: properties observed by the CLUSTER and IMAGE missions. Space Sci. Rev. 145, 55–106 (2009). doi: 10.1007/s11214-008-9438-9 ADSCrossRefGoogle Scholar
  81. G.T. Davidson, An improved empirical description of the bounce motion of trapped particles. J. Geophys. Res. 81, 4029 (1976). doi: 10.1029/JA081i022p04029 ADSCrossRefGoogle Scholar
  82. A.G. Demekhov, Generation of VLF emissions with the increasing and decreasing frequency in the magnetosperic cyclotron maser in the backward wave oscillator regime. Radiophys. Quantum Electron. 53, 609–622 (2011). doi: 10.1007/s11141-011-9256-x ADSCrossRefGoogle Scholar
  83. A.G. Demekhov, V.Y. Trakhtengerts, Dynamics of the magnetospheric cyclotron ELF/VLF maser in the backward-wave-oscillator regime. II. The influence of the magnetic-field inhomogeneity. Radiophys. Quantum Electron. 51, 880–889 (2008). doi: 10.1007/s11141-009-9093-3 ADSCrossRefGoogle Scholar
  84. A.G. Demekhov, V.Y. Trakhtengerts, M.J. Rycroft, D. Nunn, Electron acceleration in the magnetosphere by whistler-mode waves of varying frequency. Geomagn. Aeron. 46, 711–716 (2006). doi: 10.1134/S0016793206060053 ADSCrossRefGoogle Scholar
  85. A.G. Demekhov, V.Y. Trakhtengerts, M. Rycroft, D. Nunn, Efficiency of electron acceleration in the Earth’s magnetosphere by whistler mode waves. Geomagn. Aeron. 49, 24–29 (2009). doi: 10.1134/S0016793209010034 ADSCrossRefGoogle Scholar
  86. M.H. Denton, J.E. Borovsky, R.M. Skoug, M.F. Thomsen, B. Lavraud, M.G. Henderson, R.L. McPherron, J.C. Zhang, M.W. Liemohn, Geomagnetic storms driven by ICME- and CIR-dominated solar wind. J. Geophys. Res. 111, 7 (2006a). doi: 10.1029/2005JA011436 CrossRefGoogle Scholar
  87. R.E. Denton, K. Takahashi, I.A. Galkin, P.A. Nsumei, X. Huang, B.W. Reinisch, R.R. Anderson, M.K. Sleeper, W.J. Hughes, Distribution of density along magnetospheric field lines. J. Geophys. Res. 111, 4213 (2006b). doi: 10.1029/2005JA011414 CrossRefGoogle Scholar
  88. D. Dolgopyat, Repulsion from resonances, in Memoires de la Societe Mathematique de France, vol. 128 (2012) Google Scholar
  89. R.L. Dowden, Detrapping by an additional wave of wave-trapped electrons. J. Geophys. Res. 87, 6237–6242 (1982). doi: 10.1029/JA087iA08p06237 ADSCrossRefGoogle Scholar
  90. J.F. Drake, O.V. Agapitov, F.S. Mozer, The development of a bursty precipitation front with intense localized parallel electric fields driven by whistler waves. Geophys. Res. Lett. 42, 2563–2570 (2015). doi: 10.1002/2015GL063528 ADSCrossRefGoogle Scholar
  91. W.E. Drummond, D. Pines, Nonlinear stability of plasma oscillations. Nucl. Fusion Suppl. 3, 1049–1058 (1962) Google Scholar
  92. K.B. Dysthe, Some studies of triggered whistler emissions. J. Geophys. Res. 76, 6915–6931 (1971). doi: 10.1029/JA076i028p06915 ADSCrossRefGoogle Scholar
  93. J. Eeckhout, Gibrat’s law for (all) cities. Am. Econ. Rev. 94(5), 1429–1451 (2004). www.jstor.org/stable/3592829 CrossRefGoogle Scholar
  94. R.E. Ergun, G.T. Delory, E. Klementis, C.W. Carlson, J.P. McFadden, I. Roth, M. Temerin, VLF wave growth from dispersive bursts of field-aligned electron fluxes. J. Geophys. Res. 98, 3777–3787 (1993). doi: 10.1029/92JA02193 ADSCrossRefGoogle Scholar
  95. H.S. Fu, J.B. Cao, Z. Zhima, Y.V. Khotyaintsev, V. Angelopoulos, O. Santolík, Y. Omura, U. Taubenschuss, L. Chen, S.Y. Huang, First observation of rising-tone magnetosonic waves. Geophys. Res. Lett. 41, 7419–7426 (2014a). doi: 10.1002/2014GL061867 ADSCrossRefGoogle Scholar
  96. X. Fu, 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, D. Winske, Whistler anisotropy instabilities as the source of banded chorus: Van Allen Probes observations and particle-in-cell simulations. J. Geophys. Res. 119 (2014b). doi: 10.1002/2014JA020364
  97. X. Fu, Z. Guo, C. Dong, S.P. Gary, Nonlinear subcyclotron resonance as a formationmechanism for gaps in banded chorus. Geophys. Res. Lett. 42, 3150–3159 (2015). doi: 10.1002/2015GL064182 ADSCrossRefGoogle Scholar
  98. H.O. Funsten, R.M. Skoug, A.A. Guthrie, E.A. MacDonald, J.R. Baldonado, R.W. Harper, K.C. Henderson, K.H. Kihara, J.E. Lake, B.A. Larsen, A.D. Puckett, V.J. Vigil, R.H. Friedel, M.G. Henderson, J.T. Niehof, G.D. Reeves, M.F. Thomsen, J.J. Hanley, D.E. George, J.-M. Jahn, S. Cortinas, A. De Los Santos, G. Dunn, E. Edlund, M. Ferris, M. Freeman, M. Maple, C. Nunez, T. Taylor, W. Toczynski, C. Urdiales, H.E. Spence, J.A. Cravens, L.L. Suther, J. Chen, Helium, Oxygen, Proton, and Electron (HOPE) mass spectrometer for the radiation belt storm probes mission. Space Sci. Rev. 179, 423–484 (2013). doi: 10.1007/s11214-013-9968-7 ADSCrossRefGoogle Scholar
  99. C. Gabrielse, V. Angelopoulos, A. Runov, D.L. Turner, Statistical characteristics of particle injections throughout the equatorial magnetotail. J. Geophys. Res. 119, 2512–2535 (2014). doi: 10.1002/2013JA019638 CrossRefGoogle Scholar
  100. A.A. Galeev, R.Z. Sagdeev, Nonlinear plasma theory, in Reviews of Plasma Physics, ed. by A.M.A. Leontovich Reviews of Plasma Physics, vol. 7 (1979), p. 1 Google Scholar
  101. N.Y. Ganushkina, O.A. Amariutei, Y.Y. Shprits, M.W. Liemohn, Transport of the plasma sheet electrons to the geostationary distances. J. Geophys. Res. 118, 82–98 (2013). doi: 10.1029/2012JA017923 CrossRefGoogle Scholar
  102. N.Y. Ganushkina, M.W. Liemohn, S. Dubyagin, I.A. Daglis, I. Dandouras, D.L. De Zeeuw, Y. Ebihara, R. Ilie, R. Katus, M. Kubyshkina, S.E. Milan, S. Ohtani, N. Ostgaard, J.P. Reistad, P. Tenfjord, F. Toffoletto, S. Zaharia, O. Amariutei, Defining and resolving current systems in geospace. Ann. Geophys. 33, 1369–1402 (2015). doi: 10.5194/angeo-33-1369-2015 ADSCrossRefGoogle Scholar
  103. R. Gendrin, Le guidage des whistlers par le champ magnetique. Planet. Space Sci. 5, 274 (1961). doi: 10.1016/0032-0633(61)90096-4 ADSCrossRefGoogle Scholar
  104. V.L. Ginzburg, A.A. Rukhadze, Waves in Magnetoactive Plasma, 2nd revised edition edn. (Nauka, Moscow, 1975) Google Scholar
  105. S.A. Glauert, R.B. Horne, Calculation of pitch angle and energy diffusion coefficients with the PADIE code. J. Geophys. Res. 110, 4206 (2005). doi: 10.1029/2004JA010851 CrossRefGoogle Scholar
  106. S.A. Glauert, R.B. Horne, N.P. Meredith, Three-dimensional electron radiation belt simulations using the BAS radiation belt model with new diffusion models for chorus, plasmaspheric hiss, and lightning-generated whistlers. J. Geophys. Res. Space Phys. 119, 268–289 (2014). doi: 10.1002/2013JA019281 ADSCrossRefGoogle Scholar
  107. M.V. Goldman, D.F. Dubois, Beam-plasma instability in the presence of low-frequency turbulence. Phys. Fluids 25, 1062–1072 (1982). doi: 10.1063/1.863839 ADSzbMATHCrossRefGoogle Scholar
  108. J. Goldstein, Plasmasphere response: tutorial and review of recent imaging results. Space Sci. Rev. 124, 203–216 (2006). doi: 10.1007/s11214-006-9105-y ADSCrossRefGoogle Scholar
  109. J.L. Green, S. Boardsen, L. Garcia, W.W.L. Taylor, S.F. Fung, B.W. Reinisch, On the origin of whistler mode radiation in the plasmasphere. J. Geophys. Res. 110, 3201 (2005). doi: 10.1029/2004JA010495 CrossRefGoogle Scholar
  110. D.A. Gurnett, L.A. Reinleitner, Electron acceleration by Landau resonance with whistler mode wave packets. Geophys. Res. Lett. 10, 603–606 (1983). doi: 10.1029/GL010i008p00603 ADSCrossRefGoogle Scholar
  111. T. Hada, A. Nishida, T. Terasawa, E.W. Hones Jr., Bi-directional electron pitch angle anisotropy in the plasma sheet. J. Geophys. Res. 86, 11211–11224 (1981). doi: 10.1029/JA086iA13p11211 ADSCrossRefGoogle Scholar
  112. N. Haque, U.S. Inan, T.F. Bell, J.S. Pickett, J.G. Trotignon, G. Facskó, Cluster observations of whistler mode ducts and banded chorus. Geophys. Res. Lett. 38, 18107 (2011). doi: 10.1029/2011GL049112 ADSCrossRefGoogle Scholar
  113. K. Hashimoto, I. Kimura, H. Kumagai, Estimation of electron temperature by VLF waves propagating in directions near the resonance cone. Planet. Space Sci. 25, 871–877 (1977). doi: 10.1016/0032-0633(77)90040-X ADSCrossRefGoogle Scholar
  114. M. Hayakawa, Y. Yamanaka, M. Parrot, F. Lefeuvre, The wave normals of magnetospheric chorus emissions observed on board GEOS 2. J. Geophys. Res. 89, 2811–2821 (1984). doi: 10.1029/JA089iA05p02811 ADSCrossRefGoogle Scholar
  115. Y. He, K. Xiao, Q. Zhou, C. Yang, S. Liu, D.N. Baker, C.A. Kletzing, W.S. Kurth, G.B. Hospodarsky, H.E. Spence, G.D. Reeves, H.O. Funsten, J.B. Blake, Van Allen Probes observation and modeling of chorus excitation and propagation during weak geomagnetic activities. J. Geophys. Res. (2015). doi: 10.1002/2015JA021376 Google Scholar
  116. R.A. Helliwell, Whistlers and Related Ionospheric Phenomena (Stanford University Press, Stanford, 1965) Google Scholar
  117. R.A. Helliwell, A theory of discrete VLF emissions from the magnetosphere. J. Geophys. Res. 72, 4773–4790 (1967). doi: 10.1029/JZ072i019p04773 ADSCrossRefGoogle Scholar
  118. R.B. Horne, Path-integrated growth of electrostatic waves—the generation of terrestrial myriametric radiation. J. Geophys. Res. 94, 8895–8909 (1989). doi: 10.1029/JA094iA07p08895 ADSCrossRefGoogle Scholar
  119. R.B. Horne, Trapping and acceleration of upflowing ionospheric electrons in the magnetosphere by electrostatic electron cyclotron harmonic waves. Geophys. Res. Lett. 42, 975–980 (2015). doi: 10.1002/2014GL062406 ADSCrossRefGoogle Scholar
  120. R.B. Horne, S.S. Sazhin, Quasielectrostatic and electrostatic approximations for whistler mode waves in the magnetospheric plasma. Planet. Space Sci. 38, 311–318 (1990). doi: 10.1016/0032-0633(90)90095-8 ADSCrossRefGoogle Scholar
  121. R.B. Horne, R.M. Thorne, Electron pitch angle diffusion by electrostatic electron cyclotron harmonic waves: the origin of pancake distributions. J. Geophys. Res. 105, 5391–5402 (2000). doi: 10.1029/1999JA900447 ADSCrossRefGoogle Scholar
  122. R.B. Horne, R.M. Thorne, Relativistic electron acceleration and precipitation during resonant interactions with whistler-mode chorus. Geophys. Res. Lett. 30(10) (2003). doi: 10.1029/2003GL016973
  123. R.B. Horne, S.A. Glauert, R.M. Thorne, Resonant diffusion of radiation belt electrons by whistler-mode chorus. Geophys. Res. Lett. 30 (2003a). doi: 10.1029/2003GL016963
  124. R.B. Horne, R.M. Thorne, N.P. Meredith, R.R. Anderson, Diffuse auroral electron scattering by electron cyclotron harmonic and whistler mode waves during an isolated substorm. J. Geophys. Res. 108, 1290 (2003b). doi: 10.1029/2002JA009736 CrossRefGoogle Scholar
  125. R.B. Horne, R.M. Thorne, S.A. Glauert, J.M. Albert, N.P. Meredith, R.R. Anderson, Timescale for radiation belt electron acceleration by whistler mode chorus waves. J. Geophys. Res. 110, 3225 (2005a). doi: 10.1029/2004JA010811 CrossRefGoogle Scholar
  126. R.B. Horne, R.M. Thorne, Y.Y. Shprits, N.P. Meredith, S.A. Glauert, A.J. Smith, S.G. Kanekal, D.N. Baker, M.J. Engebretson, J.L. Posch, M. Spasojevic, U.S. Inan, J.S. Pickett, P.M.E. Decreau, Wave acceleration of electrons in the van Allen radiation belts. Nature 437, 227–230 (2005b). doi: 10.1038/nature03939 ADSCrossRefGoogle Scholar
  127. R.B. Horne, R.M. Thorne, S.A. Glauert, N.P. Meredith, D. Pokhotelov, O. Santolík, Electron acceleration in the van Allen radiation belts by fast magnetosonic waves. Geophys. Res. Lett. 34, 17107 (2007). doi: 10.1029/2007GL030267 ADSCrossRefGoogle Scholar
  128. R.B. Horne, T. Kersten, S.A. Glauert, N.P. Meredith, D. Boscher, A. Sicard-Piet, R.M. Thorne, W. Li, A new diffusion matrix for whistler mode chorus waves. J. Geophys. Res. 118, 6302–6318 (2013a). doi: 10.1002/jgra.50594 CrossRefGoogle Scholar
  129. R.B. Horne, S.A. Glauert, N.P. Meredith, D. Boscher, V. Maget, D. Heynderickx, D. Pitchford, Space weather impacts on satellites and forecasting the Earth’s electron radiation belts with SPACECAST. Space Weather 11, 169–186 (2013b). doi: 10.1002/swe.20023 ADSCrossRefGoogle Scholar
  130. U.S. Inan, T.F. Bell, The plasmapause as a VLF wave guide. J. Geophys. Res. 82, 2819–2827 (1977). doi: 10.1029/JA082i019p02819 ADSCrossRefGoogle Scholar
  131. Y. Isono, A. Mizuno, T. Nagahama, Y. Miyoshi, T. Nakamura, R. Kataoka, M. Tsutsumi, M.K. Ejiri, H. Fujiwara, H. Maezawa, M. Uemura, Ground-based observations of nitric oxide in the mesosphere and lower thermosphere over Antarctica in 2012–2013. J. Geophys. Res. 119, 7745–7761 (2014). doi: 10.1002/2014JA019881 CrossRefGoogle Scholar
  132. N. Iucci, A.E. Levitin, A.V. Belov, E.A. Eroshenko, N.G. Ptitsyna, G. Villoresi, G.V. Chizhenkov, L.I. Dorman, L.I. Gromova, M. Parisi, M.I. Tyasto, V.G. Yanke, Space weather conditions and spacecraft anomalies in different orbits. Space Weather 3, 1001 (2005). doi: 10.1029/2003SW000056 ADSCrossRefGoogle Scholar
  133. F. Jirícek, D.R. Shklyar, P. Tríska, LHR effects in nonducted whistler propogation—new observations and numerical modelling. Ann. Geophys. 19, 147–157 (2001). doi: 10.5194/angeo-19-147-2001 ADSCrossRefGoogle Scholar
  134. J.R. Kan, L. Zhu, S.-I. Akasofu, A theory of substorms—onset and subsidence. J. Geophys. Res. 93, 5624–5640 (1988). doi: 10.1029/JA093iA06p05624 ADSCrossRefGoogle Scholar
  135. V.I. Karpman, Nonlinear effects in the ELF waves propagating along the magnetic field in the magnetosphere. Space Sci. Rev. 16, 361–388 (1974). doi: 10.1007/BF00171564 ADSCrossRefGoogle Scholar
  136. V.I. Karpman, D.R. Shkliar, Particle precipitation caused by a single whistler-mode wave injected into the magnetosphere. Planet. Space Sci. 25, 395–403 (1977). doi: 10.1016/0032-0633(77)90055-1 ADSCrossRefGoogle Scholar
  137. V.I. Karpman, D.R. Shklyar, Nonlinear damping of potential monochromatic waves in an inhomogeneous plasma. Sov. Phys. JETP 35, 500 (1972) ADSGoogle Scholar
  138. V.I. Karpman, D.R. Shklyar, Nonlinear Landau damping in an inhomogeneous plasma. Sov. Phys. JETP 40, 53–56 (1975) ADSGoogle Scholar
  139. V.I. Karpman, I.N. Istomin, D.R. Shkliar, Effects of nonlinear interaction of monochromatic waves with resonant particles in the inhomogeneous plasma. Phys. Scr. 11, 278–284 (1975). doi: 10.1088/0031-8949/11/5/008 ADSCrossRefGoogle Scholar
  140. V.I. Karpman, J.N. Istomin, D.R. Shklyar, Nonlinear theory of a quasi-monochromatic whistler mode packet in inhomogeneous plasma. Plasma Phys. 16, 685–703 (1974). doi: 10.1088/0032-1028/16/8/001 ADSCrossRefGoogle Scholar
  141. V.I. Karpman, J.N. Istomin, D.R. Shklyar, Particle acceleration by a non-linear langmuir wave in an inhomogeneous plasma. Phys. Lett. A 53, 101–102 (1975). doi: 10.1016/0375-9601(75)90364-3 ADSCrossRefGoogle Scholar
  142. Y. Katoh, A simulation study of the propagation of whistler-mode chorus in the Earth’s inner magnetosphere. Earth Planets Space 66, 6 (2014). doi: 10.1186/1880-5981-66-6 ADSCrossRefGoogle Scholar
  143. Y. Katoh, Y. Omura, Amplitude dependence of frequency sweep rates of whistler mode chorus emissions. J. Geophys. Res. 116, 7201 (2011). doi: 10.1029/2011JA016496 Google Scholar
  144. Y. Katoh, Y. Omura, D. Summers, Rapid energization of radiation belt electrons by nonlinear wave trapping. Ann. Geophys. 26, 3451–3456 (2008). doi: 10.5194/angeo-26-3451-2008 ADSCrossRefGoogle Scholar
  145. P.J. Kellogg, C.A. Cattell, K. Goetz, S.J. Monson, L.B. Wilson III, Electron trapping and charge transport by large amplitude whistlers. Geophys. Res. Lett. 37, 20106 (2010). doi: 10.1029/2010GL044845 ADSCrossRefGoogle Scholar
  146. P.J. Kellogg, C.A. Cattell, K. Goetz, S.J. Monson, L.B. Wilson III, Large amplitude whistlers in the magnetosphere observed with Wind-Waves. J. Geophys. Res. 116, 9224 (2011). doi: 10.1029/2010JA015919 CrossRefGoogle Scholar
  147. C. Kennel, Low-frequency whistler mode. Phys. Fluids 9, 2190–2202 (1966). doi: 10.1063/1.1761588 ADSCrossRefGoogle Scholar
  148. C.F. Kennel, H.E. Petschek, Limit on stably trapped particle fluxes. J. Geophys. Res. 71, 1–28 (1966) ADSCrossRefGoogle Scholar
  149. C.F. Kennel, H.V. Wong, Resonant particle instabilities in a uniform magnetic field. J. Plasma Phys. 1, 75 (1967). doi: 10.1017/S002237780000310X ADSCrossRefGoogle Scholar
  150. K. Kersten, C.A. Cattell, A. Breneman, K. Goetz, P.J. Kellogg, J.R. Wygant, L.B. Wilson III, J.B. Blake, M.D. Looper, I. Roth, Observation of relativistic electron microbursts in conjunction with intense radiation belt whistler-mode waves. Geophys. Res. Lett. 38, 8107 (2011) ADSCrossRefGoogle Scholar
  151. K. Kersten, J.R. Wygant, C.A. Cattell, A.W. Breneman, L. Dai, S. Zhang, J.W. Bonnell, J. Tao, I. Roth, C. Kletzing, W.S. Kurth, G.B. Hospodarsky, J.F. Fennell, J.B. Blake, S.G. Claudepierre, H. Spence, Van Allen Probes observations and test particle simulations of radiation belt wave-particle interactions during periods of intense wave activity. AGU Fall Meeting Abstracts (2013) Google Scholar
  152. H.-J. Kim, L. Lyons, V. Pinto, C.-P. Wang, K.-C. Kim, Re-visit of relationship between geosynchronous relativistic electron enhancements and magnetic storms. Geophys. Res. Lett. (2015). doi: 10.1002/2015GL065192 Google Scholar
  153. I. Kimura, Effects of ions on whistler-mode ray tracing. Radio Sci. 1(3), 269–283 (1966) ADSCrossRefGoogle Scholar
  154. I. Kimura, Whistler mode propagation in the Earth and planetary magnetospheres and ray tracing techniques. Space Sci. Rev. 42, 449–466 (1985). doi: 10.1007/BF00214998 ADSCrossRefGoogle Scholar
  155. C.A. Kletzing, W.S. Kurth, M. Acuna, R.J. MacDowall, R.B. Torbert, T. Averkamp, D. Bodet, S.R. Bounds, M. Chutter, J. Connerney, D. Crawford, J.S. Dolan, R. Dvorsky, G.B. Hospodarsky, J. Howard, V. Jordanova, R.A. Johnson, D.L. Kirchner, B. Mokrzycki, G. Needell, J. Odom, D. Mark, R. Pfaff, J.R. Phillips, C.W. Piker, S.L. Remington, D. Rowland, O. Santolik, R. Schnurr, D. Sheppard, C.W. Smith, R.M. Thorne, J. Tyler, The Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) on RBSP. Space Sci. Rev. 179, 127–181 (2013). doi: 10.1007/s11214-013-9993-6 ADSCrossRefGoogle Scholar
  156. D.M. Klumpar, J.M. Quinn, E.G. Shelley, Counter-streaming electrons at the geomagnetic equator near 9 Earth radii. Geophys. Res. Lett. 15, 1295–1298 (1988). doi: 10.1029/GL015i011p01295 ADSCrossRefGoogle Scholar
  157. G.A. Kotova, The Earth’s plasmasphere: state of studies (a review). Geomagn. Aeron. 47, 409–422 (2007). doi: 10.1134/S0016793207040019 ADSCrossRefGoogle Scholar
  158. C. Krafft, A.S. Volokitin, V.V. Krasnoselskikh, Interaction of energetic particles with waves in strongly inhomogeneous solar wind plasmas. Astrophys. J. 778, 111 (2013). doi: 10.1088/0004-637X/778/2/111 ADSCrossRefGoogle Scholar
  159. P. Kulkarni, M. Gołkowski, U.S. Inan, T.F. Bell, The effect of electron and ion temperature on the refractive index surface of 1–10 kHz whistler mode waves in the inner magnetosphere. J. Geophys. Res. 120, 581–591 (2015). doi: 10.1002/2014JA020669 CrossRefGoogle Scholar
  160. I.V. Kuzichev, D.R. Shklyar, Full-wave description of the lower hybrid reflection of whistler waves. Plasma Phys. Rep. 39, 795–808 (2013). doi: 10.1134/S1063780X13090043 ADSCrossRefGoogle Scholar
  161. J. LaBelle, R.A. Treumann, Auroral radio emissions, 1. Hisses, roars, and bursts. Space Sci. Rev. 101, 295–440 (2002) ADSCrossRefGoogle Scholar
  162. L.D. Landau, E.M. Lifshitz, Electrodynamics of Continuous Media. Course of Theoretical Physics, vol. 8 (Pergamon, Elmsford, 1960) zbMATHGoogle Scholar
  163. L.D. Landau, E.M. Lifshitz, The Classical Theory of Fields. Course of Theoretical Physics, vol. 2 (Pergamon, Elmsford, 1971) zbMATHGoogle Scholar
  164. L.D. Landau, E.M. Lifshitz, Mechanics. Course of Theoretical Physics, vol. 1 (Pergamon, Elmsford, 1988) zbMATHGoogle Scholar
  165. D.S. Lauben, U.S. Inan, T.F. Bell, D.A. Gurnett, Source characteristics of ELF/VLF chorus. J. Geophys. Res. 107, 1429 (2002). doi: 10.1029/2000JA003019 CrossRefGoogle Scholar
  166. G. Laval, R. Pellat, Particle acceleration by electrostatic waves propagating in an inhomogeneous plasma. J. Geophys. Res. 75, 3255–3256 (1970). doi: 10.1029/JA075i016p03255 ADSCrossRefGoogle Scholar
  167. M.J. LeDocq, D.A. Gurnett, G.B. Hospodarsky, Chorus source locations from VLF Poynting flux measurements with the polar spacecraft. Geophys. Res. Lett. 25, 4063 (1998). doi: 10.1029/1998GL900071 ADSCrossRefGoogle Scholar
  168. J. Li, B. Ni, L. Xie, Z. Pu, J. Bortnik, R.M. Thorne, L. Chen, Q. Ma, S. Fu, Q. Zong, X. Wang, C. Xiao, Z. Yao, R. Guo, Interactions between magnetosonic waves and radiation belt electrons: comparisons of quasi-linear calculations with test particle simulations. Geophys. Res. Lett. 41, 4828–4834 (2014). doi: 10.1002/2014GL060461 ADSCrossRefGoogle Scholar
  169. J. Li, J. Bortnik, L. Xie, Z. Pu, L. Chen, B. Ni, X. Tao, R.M. Thorne, S. Fu, Z. Yao, R. Guo, Comparison of formulas for resonant interactions between energetic electrons and oblique whistler-mode waves. Phys. Plasmas 22(5), 052902 (2015). doi: 10.1063/1.4914852 ADSCrossRefGoogle Scholar
  170. W. Li, R.M. Thorne, N.P. Meredith, R.B. Horne, J. Bortnik, Y.Y. Shprits, B. Ni, Evaluation of whistler mode chorus amplification during an injection event observed on CRRES. J. Geophys. Res. 113, 9210 (2008). doi: 10.1029/2008JA013129 CrossRefGoogle Scholar
  171. W. Li, R.M. Thorne, V. Angelopoulos, J. Bortnik, C.M. Cully, B. Ni, O. LeContel, A. Roux, U. Auster, W. Magnes, Global distribution of whistler-mode chorus waves observed on the THEMIS spacecraft. Geophys. Res. Lett. 36, 9104 (2009). doi: 10.1029/2009GL037595 ADSCrossRefGoogle Scholar
  172. W. Li, R.M. Thorne, J. Bortnik, Y. Nishimura, V. Angelopoulos, L. Chen, J.P. McFadden, J.W. Bonnell, Global distributions of suprathermal electrons observed on THEMIS and potential mechanisms for access into the plasmasphere. J. Geophys. Res. 115 (2010). doi: 10.1029/2010JA015687
  173. W. Li, J. Bortnik, R.M. Thorne, V. Angelopoulos, Global distribution of wave amplitudes and wave normal angles of chorus waves using THEMIS wave observations. J. Geophys. Res. 116, 12205 (2011). doi: 10.1029/2011JA017035 Google Scholar
  174. W. Li, J. Bortnik, R.M. Thorne, C.M. Cully, L. Chen, V. Angelopoulos, Y. Nishimura, J.B. Tao, J.W. Bonnell, O. Lecontel, Characteristics of the Poynting flux and wave normal vectors of whistler-mode waves observed on THEMIS. J. Geophys. Res. 118, 1461–1471 (2013). doi: 10.1002/jgra.50176 CrossRefGoogle Scholar
  175. W. Li, D. Mourenas, A. Artemyev, O. Agapitov, J. Bortnik, J. Albert, R.M. Thorne, B. Ni, C.A. Kletzing, W.S. Kurth, G.B. Hospodarsky, Evidence of stronger pitch angle scattering loss caused by oblique whistler-mode waves as compared with quasi-parallel waves. Geophys. Res. Lett. 41, 6063–6070 (2014a). doi: 10.1002/2014GL061260 ADSCrossRefGoogle Scholar
  176. W. Li, R.M. Thorne, Q. Ma, B. Ni, J. Bortnik, D.N. Baker, H.E. Spence, G.D. Reeves, S.G. Kanekal, J.C. Green, C.A. Kletzing, W.S. Kurth, G.B. Hospodarsky, J.B. Blake, J.F. Fennell, S.G. Claudepierre, Radiation belt electron acceleration by chorus waves during the 17 March 2013 storm. J. Geophys. Res. 119, 4681–4693 (2014b). doi: 10.1002/2014JA019945 CrossRefGoogle Scholar
  177. W. Li, R.M. Thorne, J. Bortnik, D.N. Baker, G.D. Reeves, S.G. Kanekal, H.E. Spence, J.C. Green, Solar wind conditions leading to efficient radiation belt electron acceleration: a superposed epoch analysis. Geophys. Res. Lett. 42, 6906–6915 (2015a). doi: 10.1002/2015GL065342 ADSCrossRefGoogle Scholar
  178. W. Li, Q. Ma, R.M. Thorne, J. Bortnik, C.A. Kletzing, W.S. Kurth, G.B. Hospodarsky, Y. Nishimura, Statistical properties of plasmaspheric hiss derived from van Allen Probes data and their effects on radiation belt electron dynamics. J. Geophys. Res. 120, 3393–3405 (2015b). doi: 10.1002/2015JA021048 CrossRefGoogle Scholar
  179. R.P. Lin, W.K. Levedahl, W. Lotko, D.A. Gurnett, F.L. Scarf, Evidence for nonlinear wave-wave interactions in solar type III radio bursts. Astrophys. J. 308, 954–965 (1986). doi: 10.1086/164563 ADSCrossRefGoogle Scholar
  180. L.R. Lyons, Pitch angle and energy diffusion coefficients from resonant interactions with ion-cyclotron and whistler waves. J. Plasma Phys. 12, 417–432 (1974). doi: 10.1017/S002237780002537X ADSCrossRefGoogle Scholar
  181. L.R. Lyons, R.M. Thorne, Equilibrium structure of radiation belt electrons. J. Geophys. Res. 78, 2142–2149 (1973). doi: 10.1029/JA078i013p02142 ADSCrossRefGoogle Scholar
  182. L.R. Lyons, D.J. Williams, Quantitative Aspects of Magnetospheric Physics (1984) CrossRefGoogle Scholar
  183. L.R. Lyons, R.M. Thorne, C.F. Kennel, Electron pitch-angle diffusion driven by oblique whistler-mode turbulence. J. Plasma Phys. 6, 589–606 (1971). doi: 10.1017/S0022377800006310 ADSCrossRefGoogle Scholar
  184. L.R. Lyons, R.M. Thorne, C.F. Kennel, Pitch-angle diffusion of radiation belt electrons within the plasmasphere. J. Geophys. Res. 77, 3455–3474 (1972). doi: 10.1029/JA077i019p03455 ADSCrossRefGoogle Scholar
  185. Q. Ma, W. Li, R.M. Thorne, J. Bortnik, C.A. Kletzing, W.S. Kurth, G.B. Hospodarsky, Electron scattering by magnetosonic waves in the inner magnetosphere. J. Geophys. Res. 121, 274–285 (2016). doi: 10.1002/2015JA021992 CrossRefGoogle Scholar
  186. J.E. Maggs, Coherent generation of VLF hiss. J. Geophys. Res. 81, 1707–1724 (1976). doi: 10.1029/JA081i010p01707 ADSCrossRefGoogle Scholar
  187. D.M. Malaspina, J.R. Wygant, R.E. Ergun, G.D. Reeves, R.M. Skoug, B.A. Larsen, Electric field structures and waves at plasma boundaries in the inner magnetosphere. J. Geophys. Res. 120 (2015). doi: 10.1002/2015JA021137
  188. B.H. Mauk, N.J. Fox, S.G. Kanekal, R.L. Kessel, D.G. Sibeck, A. Ukhorskiy, Science objectives and rationale for the radiation belt storm probes mission. Space Sci. Rev. 179, 3–27 (2013). doi: 10.1007/s11214-012-9908-y ADSCrossRefGoogle Scholar
  189. R.L. McPherron, The role of substorms in the generation of magnetic storms, in Washington DC American Geophysical Union Geophysical Monograph Series, vol. 98 (1997), pp. 131–147. doi: 10.1029/GM098p0131 Google Scholar
  190. N.P. Meredith, R.B. Horne, R.R. Anderson, Substorm dependence of chorus amplitudes: implications for the acceleration of electrons to relativistic energies. J. Geophys. Res. 106, 13165–13178 (2001). doi: 10.1029/2000JA900156 ADSCrossRefGoogle Scholar
  191. N.P. Meredith, A.D. Johnstone, S. Szita, R.B. Horne, R.R. Anderson, “Pancake” electron distributions in the outer radiation belts. J. Geophys. Res. 104, 12431–12444 (1999). doi: 10.1029/1998JA900083 ADSCrossRefGoogle Scholar
  192. N.P. Meredith, R.B. Horne, R.M. Thorne, R.R. Anderson, Favored regions for chorus-driven electron acceleration to relativistic energies in the Earth’s outer radiation belt. Geophys. Res. Lett. 30(16) (2003). doi: 10.1029/2003GL017698
  193. N.P. Meredith, R.B. Horne, S.A. Glauert, R.R. Anderson, Slot region electron loss timescales due to plasmaspheric hiss and lightning-generated whistlers. J. Geophys. Res. 112, 8214 (2007). doi: 10.1029/2007JA012413 CrossRefGoogle Scholar
  194. N.P. Meredith, R.B. Horne, A. Sicard-Piet, D. Boscher, K.H. Yearby, W. Li, R.M. Thorne, Global model of lower band and upper band chorus from multiple satellite observations. J. Geophys. Res. 117, 10225 (2012). doi: 10.1029/2012JA017978 CrossRefGoogle Scholar
  195. N.P. Meredith, R.B. Horne, J. Bortnik, R.M. Thorne, L. Chen, W. Li, A. Sicard-Piet, Global statistical evidence for chorus as the embryonic source of plasmaspheric hiss. Geophys. Res. Lett. 40, 2891–2896 (2013). doi: 10.1002/grl.50593 ADSCrossRefGoogle Scholar
  196. N.P. Meredith, R.B. Horne, T. Kersten, B.J. Fraser, R.S. Grew, Global morphology and spectral properties of EMIC waves derived from CRRES observations. J. Geophys. Res. 119, 5328–5342 (2014). doi: 10.1002/2014JA020064 CrossRefGoogle Scholar
  197. K. Min, K. Liu, W. Li, Signatures of electron Landau resonant interactions with chorus waves from THEMIS observations. J. Geophys. Res. 119, 5551–5560 (2014). doi: 10.1002/2014JA019903 CrossRefGoogle Scholar
  198. D. Mourenas, J.-F. Ripoll, Analytical estimates of quasi-linear diffusion coefficients and electron lifetimes in the inner radiation belt. J. Geophys. Res. 117, 01204 (2012). doi: 10.1029/2011JA016985 Google Scholar
  199. D. Mourenas, A. Artemyev, O. Agapitov, V. Krasnoselskikh, Acceleration of radiation belts electrons by oblique chorus waves. J. Geophys. Res. 117, 10212 (2012a). doi: 10.1029/2012JA018041 Google Scholar
  200. D. Mourenas, A.V. Artemyev, J.-F. Ripoll, O.V. Agapitov, V.V. Krasnoselskikh, Timescales for electron quasi-linear diffusion by parallel and oblique lower-band Chorus waves. J. Geophys. Res. 117, 06234 (2012b). doi: 10.1029/2012JA017717 Google Scholar
  201. D. Mourenas, A.V. Artemyev, O.V. Agapitov, V. Krasnoselskikh, Analytical estimates of electron quasi-linear diffusion by fast magnetosonic waves. J. Geophys. Res. 118, 3096–3112 (2013). doi: 10.1002/jgra.50349 CrossRefGoogle Scholar
  202. D. Mourenas, A.V. Artemyev, O.V. Agapitov, V. Krasnoselskikh, W. Li, Approximate analytical solutions for the trapped electron distribution due to quasi-linear diffusion by whistler mode waves. J. Geophys. Res. 119, 9962–9977 (2014a). doi: 10.1002/2014JA020443 CrossRefGoogle Scholar
  203. D. Mourenas, A.V. Artemyev, O.V. Agapitov, V. Krasnoselskikh, Consequences of geomagnetic activity on energization and loss of radiation belt electrons by oblique chorus waves. J. Geophys. Res. 119, 2775–2796 (2014b). doi: 10.1002/2013JA019674 CrossRefGoogle Scholar
  204. D. Mourenas, A.V. Artemyev, O.V. Agapitov, V. Krasnoselskikh, F.S. Mozer, Very oblique whistler generation by low-energy electron streams. J. Geophys. Res. 120, 3665–3683 (2015). doi: 10.1002/2015JA021135 CrossRefGoogle Scholar
  205. F.S. Mozer, S.D. Bale, J.W. Bonnell, C.C. Chaston, I. Roth, J. Wygant, Megavolt parallel potentials arising from double-layer streams in the Earth’s outer radiation belt. Phys. Rev. Lett. 111(23), 235002 (2013). doi: 10.1103/PhysRevLett.111.235002 ADSCrossRefGoogle Scholar
  206. F.S. Mozer, O. Agapitov, V. Krasnoselskikh, S. Lejosne, G.D. Reeves, I. Roth, Direct observation of radiation-belt electron acceleration from electron-volt energies to megavolts by nonlinear whistlers. Phys. Rev. Lett. 113(3), 035001 (2014). doi: 10.1103/PhysRevLett.113.035001 ADSCrossRefGoogle Scholar
  207. F.S. Mozer, O. Agapitov, A. Artemyev, J.F. Drake, V. Krasnoselskikh, S. Lejosne, I. Vasko, Time domain structures: what and where they are, what they do, and how they are made. Geophys. Res. Lett. 42, 3627–3638 (2015). doi: 10.1002/2015GL063946 ADSCrossRefGoogle Scholar
  208. F.S. Mozer, A. Artemyev, O.V. Agapitov, D. Mourenas, I. Vasko, Near-relativistic electron acceleration by Landau trapping in time domain structures. Geophys. Res. Lett. 43, 508–514 (2016). doi: 10.1002/2015GL067316 ADSCrossRefGoogle Scholar
  209. A.I. Neishtadt, Hamiltonian systems with three or more degrees of freedom, in NATO ASI Series C, vol. 533, (Kluwer Academic, Dordrecht, 1999), pp. 193–213. doi: 10.1063/1.166236 Google Scholar
  210. A.I. Neishtadt, Averaging, passage through resonances, and capture into resonance in two-frequency systems. Russ. Math. Surv. 69(5), 771 (2014). http://stacks.iop.org/0036-0279/69/i=5/a=771 MathSciNetzbMATHCrossRefGoogle Scholar
  211. A.I. Neishtadt, A.A. Vasiliev, Destruction of adiabatic invariance at resonances in slow fast Hamiltonian systems. Nucl. Instrum. Methods Phys. Res., Sect. A, Accel. Spectrom. Detect. Assoc. Equip. 561, 158–165 (2006). doi: 10.1016/j.nima.2006.01.008 ADSCrossRefGoogle Scholar
  212. D.A. Newnham, P.J. Espy, M.A. Clilverd, C.J. Rodger, A. Seppälä, D.J. Maxfield, P. Hartogh, K. Holmén, R.B. Horne, Direct observations of nitric oxide produced by energetic electron precipitation into the Antarctic middle atmosphere. Geophys. Res. Lett. 38, 20104 (2011). doi: 10.1029/2011GL048666 ADSCrossRefGoogle Scholar
  213. D.A. Newnham, P.J. Espy, M.A. Clilverd, C.J. Rodger, A. Seppälä, D.J. Maxfield, P. Hartogh, C. Straub, K. Holmén, R.B. Horne, Observations of nitric oxide in the Antarctic middle atmosphere during recurrent geomagnetic storms. J. Geophys. Res. 118, 7874–7885 (2013). doi: 10.1002/2013JA019056 CrossRefGoogle Scholar
  214. B. Ni, R.M. Thorne, Y.Y. Shprits, K.G. Orlova, N.P. Meredith, Chorus-driven resonant scattering of diffuse auroral electrons in nondipolar magnetic fields. J. Geophys. Res. 116, 6225 (2011a). doi: 10.1029/2011JA016453 Google Scholar
  215. B. Ni, R.M. Thorne, N.P. Meredith, Y.Y. Shprits, R.B. Horne, Diffuse auroral scattering by whistler mode chorus waves: dependence on wave normal angle distribution. J. Geophys. Res. 116, 10207 (2011b). doi: 10.1029/2011JA016517 Google Scholar
  216. B. Ni, R.M. Thorne, R.B. Horne, N.P. Meredith, Y.Y. Shprits, L. Chen, W. Li, Resonant scattering of plasma sheet electrons leading to diffuse auroral precipitation: 1. Evaluation for electrostatic electron cyclotron harmonic waves. J. Geophys. Res. 116, 4218 (2011c). doi: 10.1029/2010JA016232 Google Scholar
  217. B. Ni, R.M. Thorne, N.P. Meredith, R.B. Horne, Y.Y. Shprits, Resonant scattering of plasma sheet electrons leading to diffuse auroral precipitation: 2. Evaluation for whistler mode chorus waves. J. Geophys. Res. 116, 4219 (2011d). doi: 10.1029/2010JA016233 Google Scholar
  218. B. Ni, J. Liang, R.M. Thorne, V. Angelopoulos, R.B. Horne, M. Kubyshkina, E. Spanswick, E.F. Donovan, D. Lummerzheim, Efficient diffuse auroral electron scattering by electrostatic electron cyclotron harmonic waves in the outer magnetosphere: a detailed case study. J. Geophys. Res. 117, 1218 (2012). doi: 10.1029/2011JA017095 CrossRefGoogle Scholar
  219. B. Ni, J. Bortnik, R.M. Thorne, Q. Ma, L. Chen, Resonant scattering and resultant pitch angle evolution of relativistic electrons by plasmaspheric hiss. J. Geophys. Res. 118, 7740–7751 (2013). doi: 10.1002/2013JA019260 CrossRefGoogle Scholar
  220. B. Ni, R.M. Thorne, X. Zhang, J. Bortnik, Z. Pu, L. Xie, Z.-j. Hu, D. Han, R. Shi, C. Zhou, X. Gu, Origins of the Earth’s diffuse auroral precipitation. Space Sci. Rev. (2016). doi: 10.1007/s11214-016-0234-7 Google Scholar
  221. Y. Nishimura, J. Bortnik, W. Li, R.M. Thorne, L.R. Lyons, V. Angelopoulos, S.B. Mende, J.W. Bonnell, O. Le Contel, C. Cully, R. Ergun, U. Auster, Identifying the driver of pulsating aurora. Science 330, 81 (2010). doi: 10.1126/science.1193186 ADSCrossRefGoogle Scholar
  222. D. Nunn, Wave-particle interactions in electrostatic waves in an inhomogeneous medium. J. Plasma Phys. 6, 291 (1971). doi: 10.1017/S0022377800006061 ADSCrossRefGoogle Scholar
  223. D. Nunn, A self-consistent theory of triggered VLF emissions. Planet. Space Sci. 22, 349–378 (1974). doi: 10.1016/0032-0633(74)90070-1 ADSCrossRefGoogle Scholar
  224. D. Nunn, A nonlinear theory of sideband stability in ducted whistler mode waves. Planet. Space Sci. 34, 429–451 (1986). doi: 10.1016/0032-0633(86)90032-2 ADSCrossRefGoogle Scholar
  225. D. Nunn, Y. Omura, A computational and theoretical analysis of falling frequency VLF emissions. J. Geophys. Res. 117, 8228 (2012). doi: 10.1029/2012JA017557 CrossRefGoogle Scholar
  226. D. Nunn, Y. Omura, A computational and theoretical investigation of nonlinear wave-particle interactions in oblique whistlers. J. Geophys. Res. 120, 2890–2911 (2015). doi: 10.1002/2014JA020898 CrossRefGoogle Scholar
  227. D. Nunn, O. Santolik, M. Rycroft, V. Trakhtengerts, On the numerical modelling of VLF chorus dynamical spectra. Ann. Geophys. 27, 2341–2359 (2009). doi: 10.5194/angeo-27-2341-2009 ADSCrossRefGoogle Scholar
  228. T.P. O’Brien, M.B. Moldwin, Empirical plasmapause models from magnetic indices. Geophys. Res. Lett. 30, 1152 (2003). doi: 10.1029/2002GL016007 ADSGoogle Scholar
  229. Y. Omura, N. Furuya, D. Summers, Relativistic turning acceleration of resonant electrons by coherent whistler mode waves in a dipole magnetic field. J. Geophys. Res. 112, 6236 (2007). doi: 10.1029/2006JA012243 CrossRefGoogle Scholar
  230. Y. Omura, Y. Katoh, D. Summers, Theory and simulation of the generation of whistler-mode chorus. J. Geophys. Res. 113, 4223 (2008). doi: 10.1029/2007JA012622 CrossRefGoogle Scholar
  231. Y. Omura, D. Nunn, D. Summers, Generation processes of whistler mode chorus emissions: current status of nonlinear wave growth theory, in Dynamics of the Earth’s Radiation Belts and Inner Magnetosphere, ed. by D. Summers, I.U. Mann, D.N. Baker, M. Schulz American Geophysical Union (2013), pp. 243–254. doi: 10.1029/2012GM001347 CrossRefGoogle Scholar
  232. Y. Omura, H. Matsumoto, D. Nunn, M.J. Rycroft, A review of observational, theoretical and numerical studies of VLF triggered emissions. J. Atmos. Terr. Phys. 53, 351–368 (1991) ADSCrossRefGoogle Scholar
  233. Y. Omura, M. Hikishima, Y. Katoh, D. Summers, S. Yagitani, Nonlinear mechanisms of lower-band and upper-band VLF chorus emissions in the magnetosphere. J. Geophys. Res. 114, 7217 (2009). doi: 10.1029/2009JA014206 CrossRefGoogle Scholar
  234. Y. Omura, Y. Miyashita, M. Yoshikawa, D. Summers, M. Hikishima, Y. Ebihara, Y. Kubota, Formation process of relativistic electron flux through interaction with chorus emissions in the Earth’s inner magnetosphere. J. Geophys. Res. 120, 9545–9562 (2015). doi: 10.1002/2015JA021563 CrossRefGoogle Scholar
  235. K. Orlova, Y. Shprits, Model of lifetimes of the outer radiation belt electrons in a realistic magnetic field using realistic chorus wave parameters. J. Geophys. Res. 119, 770–780 (2014). doi: 10.1002/2013JA019596 CrossRefGoogle Scholar
  236. K.G. Orlova, Y.Y. Shprits, Dependence of pitch-angle scattering rates and loss timescales on the magnetic field model. Geophys. Res. Lett. 37, 5105 (2010). doi: 10.1029/2009GL041639 ADSCrossRefGoogle Scholar
  237. A. Osmane, A.M. Hamza, Relativistic surfatron process for Landau resonant electrons in radiation belts. Nonlinear Process. Geophys. 21, 115–125 (2014). doi: 10.5194/npg-21-115-2014 ADSCrossRefGoogle Scholar
  238. A. Osmane, L.B. Wilson III, L. Blum, T.I. Pulkkinen, On the connection between microbursts and nonlinear electronic structures in planetary radiation belts. Astrophys. J. 816, 51 (2016). doi: 10.3847/0004-637X/816/2/51 ADSCrossRefGoogle Scholar
  239. P. Ozhogin, J. Tu, P. Song, B.W. Reinisch, Field-aligned distribution of the plasmaspheric electron density: an empirical model derived from the IMAGE RPI measurements. J. Geophys. Res. 117, 6225 (2012). doi: 10.1029/2011JA017330 CrossRefGoogle Scholar
  240. E.V. Panov, A.V. Artemyev, W. Baumjohann, R. Nakamura, V. Angelopoulos, Transient electron precipitation during oscillatory BBF braking: THEMIS observations and theoretical estimates. J. Geophys. Res. 118, 3065–3076 (2013). doi: 10.1002/jgra.50203 CrossRefGoogle Scholar
  241. G.K. Parks, C.S. Lin, B. Mauk, S. Deforest, C.E. McIlwain, Characteristics of magnetospheric particle injection deduced from events observed on August 18, 1974. J. Geophys. Res. 82, 5208–5214 (1977). doi: 10.1029/JA082i032p05208 ADSCrossRefGoogle Scholar
  242. M. Parrot, O. Santolík, N. Cornilleau-Wehrlin, M. Maksimovic, C. Harvey, Magnetospherically reflected chorus waves revealed by ray tracing with CLUSTER data. Ann. Geophys. 21, 1111–1120 (2003a). doi: 10.5194/angeo-21-1111-2003 ADSCrossRefGoogle Scholar
  243. M. Parrot, O. Santolýk, N. Cornilleau-Wehrlin, M. Maksimovic, C.C. Harvey, Source location of chorus emissions observed by Cluster. Ann. Geophys. 21, 473–480 (2003b). doi: 10.5194/angeo-21-473-2003 ADSCrossRefGoogle Scholar
  244. G.D. Reeves, K.L. McAdams, R.H.W. Friedel, T.P. O’Brien, Acceleration and loss of relativistic electrons during geomagnetic storms. Geophys. Res. Lett. 30, 1529 (2003). doi: 10.1029/2002GL016513 ADSCrossRefGoogle Scholar
  245. G.D. Reeves, H.E. Spence, M.G. Henderson, S.K. Morley, R.H.W. Friedel, H.O. Funsten, D.N. Baker, S.G. Kanekal, J.B. Blake, J.F. Fennell, S.G. Claudepierre, R.M. Thorne, D.L. Turner, C.A. Kletzing, W.S. Kurth, B.L. Larsen, J.T. Niehof, Electron acceleration in the heart of the van Allen radiation belts. Science 341, 991–994 (2013). doi: 10.1126/science.1237743 ADSCrossRefGoogle Scholar
  246. L.A. Reinleitner, D.A. Gurnett, T.E. Eastman, Electrostatic bursts generated by electrons in Landau resonance with whistler mode chorus. J. Geophys. Res. 88, 3079–3093 (1983). doi: 10.1029/JA088iA04p03079 ADSCrossRefGoogle Scholar
  247. I. Roth, M. Temerin, M.K. Hudson, Resonant enhancement of relativistic electron fluxes during geomagnetically active periods. Ann. Geophys. 17, 631–638 (1999). doi: 10.1007/s00585-999-0631-2 ADSCrossRefGoogle Scholar
  248. R.Z. Sagdeev, V.D. Shafranov, On the instability of a plasma with an anisotropic distribution of velocities in a magnetic field. Sov. Phys. JETP 12(1), 130–132 (1961). doi: 10.5194/angeo-26-3525-2008 MathSciNetGoogle Scholar
  249. O. Santolík, D.A. Gurnett, J.S. Pickett, M. Parrot, N. Cornilleau-Wehrlin, Central position of the source region of storm-time chorus. Planet. Space Sci. 53, 299–305 (2005). doi: 10.1016/j.pss.2004.09.056 ADSCrossRefGoogle Scholar
  250. O. Santolík, D.A. Gurnett, J.S. Pickett, J. Chum, N. Cornilleau-Wehrlin, Oblique propagation of whistler mode waves in the chorus source region. J. Geophys. Res. 114 (2009). doi: 10.1029/2009JA014586
  251. O. Santolík, C.A. Kletzing, W.S. Kurth, G.B. Hospodarsky, S.R. Bounds, Fine structure of large-amplitude chorus wave packets. Geophys. Res. Lett. 41, 293–299 (2014a). doi: 10.1002/2013GL058889 ADSCrossRefGoogle Scholar
  252. O. Santolík, E. Macúšová, I. Kolmašová, N. Cornilleau-Wehrlin, Y. Conchy, Propagation of lower-band whistler-mode waves in the outer van Allen belt: systematic analysis of 11 years of multi-component data from the Cluster spacecraft. Geophys. Res. Lett. 41, 2729–2737 (2014b). doi: 10.1002/2014GL059815 ADSCrossRefGoogle Scholar
  253. K. Sauer, R.D. Sydora, Beam-excited whistler waves at oblique propagation with relation to STEREO radiation belt observations. Ann. Geophys. 28, 1317–1325 (2010). doi: 10.5194/angeo-28-1317-2010 ADSCrossRefGoogle Scholar
  254. M. Schulz, L.J. Lanzerotti, Particle Diffusion in the Radiation Belts (Springer, New York, 1974) CrossRefGoogle Scholar
  255. R.S. Selesnick, J.B. Blake, On the source location of radiation belt relativistic electrons. J. Geophys. Res. 105, 2607–2624 (2000). doi: 10.1029/1999JA900445 ADSCrossRefGoogle Scholar
  256. V.A. Sergeev, W. Baumjohann, K. Shiokawa, Bi-directional electron distributions associated with near-tail flux transport. Geophys. Res. Lett. 28, 3813–3816 (2001). doi: 10.1029/2001GL013334 ADSCrossRefGoogle Scholar
  257. V.D. Shapiro, R.Z. Sagdeev, Nonlinear wave-particle interaction and conditions for the applicability of quasilinear theory. Phys. Rep. 283, 49–71 (1997). doi: 10.1016/S0370-1573(96)00053-1 ADSCrossRefGoogle Scholar
  258. S.D. Shawhan, D.A. Gurnett, D.L. Odem, R.A. Helliwell, C.G. Park, The plasma wave and quasi-static electric field instrument /PWI/ for dynamics explorer-A. Space Sci. Instrum. 5, 535–550 (1981) ADSGoogle Scholar
  259. B.W. Sheeley, M.B. Moldwin, H.K. Rassoul, R.R. Anderson, An empirical plasmasphere and trough density model: CRRES observations. J. Geophys. Res. 106, 25631–25642 (2001). doi: 10.1029/2000JA000286 ADSCrossRefGoogle Scholar
  260. K. Shiokawa, W. Baumjohann, G. Paschmann, Bi-directional electrons in the near-Earth plasma sheet. Ann. Geophys. 21, 1497–1507 (2003). doi: 10.5194/angeo-21-1497-2003 ADSCrossRefGoogle Scholar
  261. D. Shklyar, H. Matsumoto, Oblique whistler-mode waves in the inhomogeneous magnetospheric plasma: resonant interactions with energetic charged particles. Surv. Geophys. 30, 55–104 (2009). doi: 10.1007/s10712-009-9061-7 ADSCrossRefGoogle Scholar
  262. D. Shklyar, J. Chum, F. Jirícek, Characteristic properties of Nu whistlers as inferred from observations and numerical modelling. Ann. Geophys. 22, 3589–3606 (2004). doi: 10.5194/angeo-22-3589-2004 ADSCrossRefGoogle Scholar
  263. D.R. Shklyar, Stochastic motion of relativistic particles in the field of a monochromatic wave. Sov. Phys. JETP 53 (1981) Google Scholar
  264. D.R. Shklyar, Nonlinear interaction between a resonance-mode (\(\mathrm{k}_{\parallel}=0\)) wave and energetic plasma particles. J. Plasma Phys. 75, 319–335 (2009). doi: 10.1017/S0022377808007496 ADSCrossRefGoogle Scholar
  265. D.R. Shklyar, On the nature of particle energization via resonant wave-particle interaction in the inhomogeneous magnetospheric plasma. Ann. Geophys. 29, 1179–1188 (2011). doi: 10.5194/angeo-29-1179-2011 ADSCrossRefGoogle Scholar
  266. D.R. Shklyar, F. Jiříček, Simulation of nonducted whistler spectrograms observed aboard the MAGION 4 and 5 satellites. J. Atmos. Sol.-Terr. Phys. 62, 347–370 (2000). doi: 10.1016/S1364-6826(99)00097-8 ADSCrossRefGoogle Scholar
  267. Y.Y. Shprits, B. Ni, Dependence of the quasi-linear scattering rates on the wave normal distribution of chorus waves. J. Geophys. Res. 114, 11205 (2009). doi: 10.1029/2009JA014223 Google Scholar
  268. Y.Y. Shprits, N.P. Meredith, R.M. Thorne, Parameterization of radiation belt electron loss timescales due to interactions with chorus waves. Geophys. Res. Lett. 34, 11110 (2007). doi: 10.1029/2006GL029050 ADSCrossRefGoogle Scholar
  269. Y.Y. Shprits, A. Runov, B. Ni, Gyro-resonant scattering of radiation belt electrons during the solar minimum by fast magnetosonic waves. J. Geophys. Res. 118, 648–652 (2013). doi: 10.1002/jgra.50108 CrossRefGoogle Scholar
  270. Y.Y. Shprits, S.R. Elkington, N.P. Meredith, D.A. Subbotin, Review of modeling of losses and sources of relativistic electrons in the outer radiation belt I: radial transport. J. Atmos. Sol.-Terr. Phys. 70, 1679–1693 (2008a). doi: 10.1016/j.jastp.2008.06.008 ADSCrossRefGoogle Scholar
  271. Y.Y. Shprits, D.A. Subbotin, N.P. Meredith, S.R. Elkington, 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 (2008b). doi: 10.1016/j.jastp.2008.06.014 ADSCrossRefGoogle Scholar
  272. A. Sicard-Piet, D. Boscher, R.B. Horne, N.P. Meredith, V. Maget, 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 (2014). doi: 10.5194/angeo-32-1059-2014 ADSCrossRefGoogle Scholar
  273. R.L. Smith, Electron densities in the outer ionosphere deduced from nose whistlers. J. Geophys. Res. 66, 2578–2579 (1961). doi: 10.1029/JZ066i008p02578 ADSCrossRefGoogle Scholar
  274. V.V. Solovev, D.R. Shkliar, Particle heating by a low-amplitude wave in an inhomogeneous magnetoplasma. Sov. Phys. JETP 63, 272–277 (1986) Google Scholar
  275. A.R. Soto-Chavez, G. Wang, A. Bhattacharjee, G.Y. Fu, H.M. Smith, A model for falling-tone chorus. Geophys. Res. Lett. 41, 1838–1845 (2014). doi: 10.1002/2014GL059320 ADSCrossRefGoogle Scholar
  276. M. Spasojevic, Y.Y. Shprits, Chorus functional dependencies derived from CRRES data. Geophys. Res. Lett. 40, 3793–3797 (2013). doi: 10.1002/grl.50755 ADSCrossRefGoogle Scholar
  277. T.H. Stix, The Theory of Plasma Waves (1962) zbMATHGoogle Scholar
  278. L.R.O. Storey, F. Lefeuvre, Theory for the interpretation of measurements of the six components of a random electromagnetic wave field in space, in Space Research XIV, ed. by M.J. Rycroft, R.D. Reasenberg (1974), pp. 381–386 Google Scholar
  279. A.V. Streltsov, J. Woodroffe, W. Gekelman, P. Pribyl, Modeling the propagation of whistler-mode waves in the presence of field-aligned density irregularities. Phys. Plasmas 19(5), 052104 (2012). doi: 10.1063/1.4719710 ADSCrossRefGoogle Scholar
  280. R.N. Sudan, Plasma electromagnetic instabilities. Phys. Fluids 6, 57–61 (1963). doi: 10.1063/1.1724508 ADSzbMATHCrossRefGoogle Scholar
  281. D. Summers, Quasi-linear diffusion coefficients for field-aligned electromagnetic waves with applications to the magnetosphere. J. Geophys. Res. 110, 8213 (2005). doi: 10.1029/2005JA011159 CrossRefGoogle Scholar
  282. D. Summers, B. Ni, Effects of latitudinal distributions of particle density and wave power on cyclotron resonant diffusion rates of radiation belt electrons. Earth Planets Space 60, 763–771 (2008) ADSCrossRefGoogle Scholar
  283. D. Summers, Y. Omura, Ultra-relativistic acceleration of electrons in planetary magnetospheres. Geophys. Res. Lett. 34, 24205 (2007). doi: 10.1029/2007GL032226 ADSCrossRefGoogle Scholar
  284. D. Summers, R.M. Thorne, Relativistic electron pitch-angle scattering by electromagnetic ion cyclotron waves during geomagnetic storms. J. Geophys. Res. 108, 1143 (2003). doi: 10.1029/2002JA009489 CrossRefGoogle Scholar
  285. D. Summers, B. Ni, N.P. Meredith, Timescales for radiation belt electron acceleration and loss due to resonant wave-particle interactions: 1. Theory. J. Geophys. Res. 112, 4206 (2007). doi: 10.1029/2006JA011801 CrossRefGoogle Scholar
  286. D. Summers, R. Tang, R.M. Thorne, Limit on stably trapped particle fluxes in planetary magnetospheres. J. Geophys. Res. 114, 10210 (2009). doi: 10.1029/2009JA014428 CrossRefGoogle Scholar
  287. D. Summers, R.M. Thorne, F. Xiao, Relativistic theory of wave-particle resonant diffusion with application to electron acceleration in the magnetosphere. J. Geophys. Res. 103, 20487–20500 (1998). doi: 10.1029/98JA01740 ADSCrossRefGoogle Scholar
  288. D. Summers, C. Ma, N.P. Meredith, R.B. Horne, R.M. Thorne, D. Heynderickx, R.R. Anderson, Model of the energization of outer-zone electrons by whistler-mode chorus during the October 9, 1990 geomagnetic storm. Geophys. Res. Lett. 29(24) (2002). doi: 10.1029/2002GL016039
  289. D. Summers, Y. Omura, Y. Miyashita, D.-H. Lee, Nonlinear spatiotemporal evolution of whistler mode chorus waves in Earth’s inner magnetosphere. J. Geophys. Res. 117, 9206 (2012). doi: 10.1029/2012JA017842 CrossRefGoogle Scholar
  290. D. Summers, R. Tang, Y. Omura, D.-H. Lee, Parameter spaces for linear and nonlinear whistler-mode waves. Phys. Plasmas 20(7), 072110 (2013). doi: 10.1063/1.4816022 ADSCrossRefGoogle Scholar
  291. D.W. Swift, Particle acceleration by electrostatic waves. J. Geophys. Res. 75, 6324–6328 (1970). doi: 10.1029/JA075i031p06324 ADSCrossRefGoogle Scholar
  292. X. Tao, J. Bortnik, Nonlinear interactions between relativistic radiation belt electrons and oblique whistler mode waves. Nonlinear Process. Geophys. 17, 599–604 (2010). doi: 10.5194/npg-17-599-2010 ADSCrossRefGoogle Scholar
  293. X. Tao, J. Bortnik, J.M. Albert, K. Liu, R.M. Thorne, Comparison of quasilinear diffusion coefficients for parallel propagating whistler mode waves with test particle simulations. Geophys. Res. Lett. 38, 6105 (2011). doi: 10.1029/2011GL046787 ADSCrossRefGoogle Scholar
  294. X. Tao, J. Bortnik, J.M. Albert, R.M. Thorne, Comparison of bounce-averaged quasi-linear diffusion coefficients for parallel propagating whistler mode waves with test particle simulations. J. Geophys. Res. 117, 10205 (2012a). doi: 10.1029/2012JA017931 Google Scholar
  295. X. Tao, J. Bortnik, R.M. Thorne, J.M. Albert, W. Li, Effects of amplitude modulation on nonlinear interactions between electrons and chorus waves. Geophys. Res. Lett. 39, 6102 (2012b). doi: 10.1029/2012GL051202 ADSGoogle Scholar
  296. U. Taubenschuss, Y.V. Khotyaintsev, O. Santolík, A. Vaivads, C.M. Cully, O.L. Contel, V. Angelopoulos, Wave normal angles of whistler mode chorus rising and falling tones. J. Geophys. Res. 119, 9567–9578 (2014). doi: 10.1002/2014JA020575 CrossRefGoogle Scholar
  297. E.M. Tejero, C. Crabtree, D.D. Blackwell, W.E. Amatucci, M. Mithaiwala, G. Ganguli, L. Rudakov, Laboratory studies of nonlinear whistler wave processes in the van Allen radiation belts. Phys. Plasmas 22(9), 091503 (2015). doi: 10.1063/1.4928944 ADSCrossRefGoogle Scholar
  298. R.M. Thorne, Radiation belt dynamics: the importance of wave-particle interactions. Geophys. Res. Lett. 372, 22107 (2010). doi: 10.1029/2010GL044990 ADSGoogle Scholar
  299. R.M. Thorne, T.P. O’Brien, Y.Y. Shprits, D. Summers, R.B. Horne, Timescale for MeV electron microburst loss during geomagnetic storms. J. Geophys. Res. 110, 9202 (2005). doi: 10.1029/2004JA010882 CrossRefGoogle Scholar
  300. R.M. Thorne, B. Ni, X. Tao, R.B. Horne, N.P. Meredith, Scattering by chorus waves as the dominant cause of diffuse auroral precipitation. Nature 467, 943–946 (2010). doi: 10.1038/nature09467 ADSCrossRefGoogle Scholar
  301. R.M. Thorne, W. Li, B. Ni, Q. Ma, J. Bortnik, L. Chen, D.N. Baker, H.E. Spence, G.D. Reeves, M.G. Henderson, C.A. Kletzing, W.S. Kurth, G.B. Hospodarsky, J.B. Blake, J.F. Fennell, S.G. Claudepierre, S.G. Kanekal, Rapid local acceleration of relativistic radiation-belt electrons by magnetospheric chorus. Nature 504, 411–414 (2013). doi: 10.1038/nature12889 ADSCrossRefGoogle Scholar
  302. E.E. Titova, B.V. Kozelov, F. Jiricek, J. Smilauer, A.G. Demekhov, V.Y. Trakhtengerts, Verification of the backward wave oscillator model of VLF chorus generation using data from MAGION 5 satellite. Ann. Geophys. 21, 1073–1081 (2003). doi: 10.5194/angeo-21-1073-2003 ADSCrossRefGoogle Scholar
  303. E.E. Titova, B.V. Kozelov, A.G. Demekhov, J. Manninen, O. Santolik, C.A. Kletzing, G. Reeves, Identification of the source of quasi-periodic VLF emissions using ground-based and van Allen Probes satellite observations. Geophys. Res. Lett. (2015). doi: 10.1002/2015GL064911 Google Scholar
  304. E.R. Tracy, A.J. Brizard, A.S. Richardson, A.N. Kaufman, Ray Tracing and Beyond: Phase Space Methods in Plasma Wave Theory (Cambridge University Press, Cambridge, 2014) CrossRefGoogle Scholar
  305. V.Y. Trakhtengerts, Stationary states of the Earth’s outer radiation zone. Geomagn. Aeron. 6, 827–836 (1966) Google Scholar
  306. V.Y. Trakhtengerts, Magnetosphere cyclotron maser: backward wave oscillator generation regime. J. Geophys. Res. 100, 17205–17210 (1995). doi: 10.1029/95JA00843 ADSCrossRefGoogle Scholar
  307. V.Y. Trakhtengerts, A generation mechanism for chorus emission. Ann. Geophys. 17, 95–100 (1999). doi: 10.1007/s00585-999-0095-4 ADSCrossRefGoogle Scholar
  308. V.Y. Trakhtengerts, M.J. Rycroft, Whistler and Alfvén Mode Cyclotron Masers in Space (Cambridge University Press, Cambridge, 2008) CrossRefGoogle Scholar
  309. V.Y. Trakhtengerts, A.G. Demekhov, E.E. Titova, B.V. Kozelov, O. Santolik, D. Gurnett, M. Parrot, Interpretation of Cluster data on chorus emissions using the backward wave oscillator model. Phys. Plasmas 11, 1345–1351 (2004). doi: 10.1063/1.1667495 ADSCrossRefGoogle Scholar
  310. B.T. Tsurutani, E.J. Smith, Postmidnight chorus: a substorm phenomenon. J. Geophys. Res. 79, 118–127 (1974). doi: 10.1029/JA079i001p00118 ADSCrossRefGoogle Scholar
  311. B.T. Tsurutani, W.D. Gonzalez, A.L.C. Gonzalez, F.L. Guarnieri, N. Gopalswamy, M. Grande, Y. Kamide, Y. Kasahara, G. Lu, I. Mann, R. McPherron, F. Soraas, V. Vasyliunas, Corotating solar wind streams and recurrent geomagnetic activity: a review. J. Geophys. Res. 111 (2006). doi: 10.1029/2005JA011273
  312. B.T. Tsurutani, B.J. Falkowski, O.P. Verkhoglyadova, J.S. Pickett, O. Santolík, G.S. Lakhina, Quasi-coherent chorus properties: 1. Implications for wave-particle interactions. J. Geophys. Res. 116, 9210 (2011). doi: 10.1029/2010JA016237 Google Scholar
  313. J. Tu, P. Song, B.W. Reinisch, J.L. Green, X. Huang, Empirical specification of field-aligned plasma density profiles for plasmasphere refilling. J. Geophys. Res. 111, 6216 (2006). doi: 10.1029/2005JA011582 CrossRefGoogle Scholar
  314. D.L. Turner, V. Angelopoulos, W. Li, M.D. Hartinger, M. Usanova, I.R. Mann, J. Bortnik, Y. Shprits, On the storm-time evolution of relativistic electron phase space density in Earth’s outer radiation belt. J. Geophys. Res. 118, 2196–2212 (2013). doi: 10.1002/jgra.50151 CrossRefGoogle Scholar
  315. D.L. Turner, T.P. O’Brien, J.F. Fennell, S.G. Claudepierre, J.B. Blake, E. Kilpua, H. Hietala, The effects of geomagnetic storms on electrons in Earth’s radiation belts. Geophys. Res. Lett. (2015). doi: 10.1002/2015GL064747 Google Scholar
  316. A.Y. Ukhorskiy, M.I. Sitnov, Dynamics of radiation belt particles. Space Sci. Rev. 179, 545–578 (2013). doi: 10.1007/s11214-012-9938-5 ADSCrossRefGoogle Scholar
  317. B. Van Compernolle, X. An, J. Bortnik, R.M. Thorne, P. Pribyl, W. Gekelman, Excitation of chirping whistler waves in a laboratory plasma. Phys. Rev. Lett. 114(24), 245002 (2015). doi: 10.1103/PhysRevLett.114.245002 ADSCrossRefGoogle Scholar
  318. I.Y. Vasko, O.V. Agapitov, F. Mozer, A.V. Artemyev, D. Jovanovic, Magnetic field depression within electron holes. Geophys. Res. Lett. 42, 2123–2129 (2015). doi: 10.1002/2015GL063370 ADSCrossRefGoogle Scholar
  319. A.A. Vedenov, E.P. Velikhov, R.Z. Sagdeev, Quasilinear theory of plasma oscillations. Nuclear Fusion Suppl. 2, 465–475 (1962) zbMATHGoogle Scholar
  320. O.P. Verkhoglyadova, B.T. Tsurutani, Polarization properties of Gendrin mode waves observed in the Earth’s magnetosphere: observations and theory. Ann. Geophys. 27, 4429–4433 (2009). doi: 10.5194/angeo-27-4429-2009 ADSCrossRefGoogle Scholar
  321. A. Voshchepynets, V. Krasnoselskikh, A. Artemyev, A. Volokitin, Probabilistic model of beam–plasma interaction in randomly inhomogeneous plasma. Astrophys. J. 807(1), 38 (2015). http://stacks.iop.org/0004-637X/807/i=1/a=38 ADSCrossRefGoogle Scholar
  322. S.N. Walker, M.A. Balikhin, P. Canu, N. Cornilleau-Wehrlin, I. Moiseenko, Investigation of the Chirikov resonance overlap criteria for equatorial magnetosonic waves. J. Geophys. Res. 120, 8774–8781 (2015). doi: 10.1002/2015JA021718 CrossRefGoogle Scholar
  323. K. Wang, C.-H. Lin, L.-Y. Wang, T. Hada, Y. Nishimura, D.L. Turner, V. Angelopoulos, Pitch angle distributions of electrons at dipolarization sites during geomagnetic activity: THEMIS observations. J. Geophys. Res. 119, 9747–9760 (2014). doi: 10.1002/2014JA020176 CrossRefGoogle Scholar
  324. C.E.J. Watt, R. Rankin, Alfvén wave acceleration of auroral electrons in warm magnetospheric plasma. Washington DC American Geophysical Union Geophysical Monograph Series 197, 251–260 (2012). doi: 10.1029/2011GM001171 ADSGoogle Scholar
  325. C.E.J. Watt, A.W. Degeling, R. Rankin, Constructing the frequency and wave normal distribution of whistler-mode wave power. J. Geophys. Res. 118, 1984–1991 (2013). doi: 10.1002/jgra.50231 CrossRefGoogle Scholar
  326. E. Whipple, R. Puetter, M. Rosenberg, A two-dimensional, time-dependent, near-Earth magnetotail. Adv. Space Res. 11, 133–142 (1991). doi: 10.1016/0273-1177(91)90024-E ADSCrossRefGoogle Scholar
  327. L.B. Wilson III, C.A. Cattell, P.J. Kellogg, J.R. Wygant, K. Goetz, A. Breneman, K. Kersten, The properties of large amplitude whistler mode waves in the magnetosphere: propagation and relationship with geomagnetic activity. Geophys. Res. Lett. 38, 17107 (2011). doi: 10.1029/2011GL048671 ADSGoogle Scholar
  328. J.R. Wygant, A. Keiling, C.A. Cattell, R.L. Lysak, M. Temerin, F.S. Mozer, C.A. Kletzing, J.D. Scudder, V. Streltsov, W. Lotko, C.T. Russell, Evidence for kinetic Alfvén waves and parallel electron energization at \(4\mbox{--}6~\mbox{R}_{E}\) altitudes in the plasma sheet boundary layer. J. Geophys. Res. 107, 1201 (2002). doi: 10.1029/2001JA900113 CrossRefGoogle Scholar
  329. M.A. Xapsos, P.M. O’Neill, T.P. O’Brien, Near-Earth space radiation models. IEEE Trans. Nucl. Sci. 60, 1691–1705 (2013). doi: 10.1109/TNS.2012.2225846 ADSCrossRefGoogle Scholar
  330. K. Yamaguchi, T. Matsumuro, Y. Omura, D. Nunn, Ray tracing of whistler-mode chorus elements: implications for generation mechanisms of rising and falling tone emissions. Ann. Geophys. 31, 665–673 (2013). doi: 10.5194/angeo-31-665-2013 ADSCrossRefGoogle Scholar
  331. K.H. Yearby, M.A. Balikhin, Y.V. Khotyaintsev, S.N. Walker, V.V. Krasnoselskikh, H.S.C.K. Alleyne, O. Agapitov, Ducted propagation of chorus waves: Cluster observations. Ann. Geophys. 29, 1629–1634 (2011). doi: 10.5194/angeo-29-1629-2011 ADSCrossRefGoogle Scholar
  332. P.H. Yoon, V.S. Pandey, D.-H. Lee, Relativistic electron acceleration by oblique whistler waves. Phys. Plasmas 20(11), 112902 (2013). doi: 10.1063/1.4831965 ADSCrossRefGoogle Scholar
  333. P.H. Yoon, V.S. Pandey, D.-H. Lee, Oblique nonlinear whistler wave. J. Geophys. Res. 119, 1851–1862 (2014). doi: 10.1002/2013JA018993 CrossRefGoogle Scholar
  334. X.-J. Zhang, V. Angelopoulos, B. Ni, R.M. Thorne, Predominance of ECH wave contribution to diffuse aurora in Earth’s outer magnetosphere. J. Geophys. Res. 120, 295–309 (2015). doi: 10.1002/2014JA020455 CrossRefGoogle Scholar
  335. X. Zhang, V. Angelopoulos, B. Ni, R.M. Thorne, R.B. Horne, Extent of ECH wave emissions in the Earth’s magnetotail. J. Geophys. Res. 119, 5561–5574 (2014). doi: 10.1002/2014JA019931 CrossRefGoogle Scholar
  336. Y.L. Zhang, H. Matsumoto, Y. Omura, Linear and nonlinear interactions of an electron beam with oblique whistler and electrostatic waves in the magnetosphere. J. Geophys. Res. 98, 21 (1993). doi: 10.1029/93JA01937 Google Scholar
  337. H. Zhao, X. Li, Inward shift of outer radiation belt electrons as a function of Dst index and the influence of the solar wind on electron injections into the slot region. J. Geophys. Res. 118, 756–764 (2013). doi: 10.1029/2012JA018179 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Anton Artemyev
    • 1
    • 4
  • Oleksiy Agapitov
    • 2
  • Didier Mourenas
    • 3
  • Vladimir Krasnoselskikh
    • 1
  • Vitalii Shastun
    • 1
  • Forrest Mozer
    • 2
  1. 1.LPC2E/CNRSUniversity of OrleansOrleans CEDEXFrance
  2. 2.Space Science LaboratoryUniversity of CaliforniaBerkeleyUSA
  3. 3.CEA, DAMDIFArpajonFrance
  4. 4.Department of Earth, Planetary, and Space Sciences and Institute of Geophysics and Planetary PhysicsUniversity of CaliforniaLos AngelesUSA

Personalised recommendations