Theoretical and numerical studies of chorus waves: A review

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Theoretical and numerical models of chorus waves are reviewed in this paper. Specifically, we focus on the nonlinear wave particle interactions and the current understanding of the frequency chirping of rising tone chorus waves. Various other related topics, such as the optimal excitation condition of chorus, the formation of subpackets, and the non-adiabaticity of the nonlinear interaction are also discussed. We end this review paper with a short list of questions of chorus waves that are still under research and debate.


  1. Albert J M. 1993. Cyclotron resonance in an inhomogeneous magnetic field. Phys Fluids B-Plasma Phys, 5: 2744–2750

  2. Albert J M, Tao X, Bortnik J. 2012. Aspects of nonlinear wave-particle interactions. In: Summers D, Mann I R, Baker D N, Schulz M, eds. AGU Chapman Dynamics of the Earth’s Radiation Belts and Inner Magnetosphere. Geophys Monogr Ser, 199: 255–264, doi:

  3. Al’Tshul’ L M, Karpman V I. 1966. Theory of nonlinear oscillations in a collisionless plasma. J Exptl Theoret Phys, 22: 361–369

  4. Angelopoulos V. 2008. The THEMIS mission. Space Sci Rev, 141: 5–34

  5. Bortnik J, Thorne R M. 2007. The dual role of ELF/VLF chorus waves in the acceleration and precipitation of radiation belt electrons. J Atmos Sol-Terrestrial Phys, 69: 378–386

  6. Bortnik J, Thorne R M, Meredith N P. 2008a. The unexpected origin of plasmaspheric hiss from discrete chorus emissions. Nature, 452: 62–66

  7. Bortnik J, Thorne R M, Inan U S. 2008b. Nonlinear interaction of energetic electrons with large amplitude chorus. Geophys Res Lett, 35: L21102

  8. Bortnik J, Li W, Thorne R M, Angelopoulos V, Cully C, Bonnell J, Le Contel O, Roux A. 2009. An observation linking the origin of plasmaspheric hiss to discrete chorus emissions. Science, 324: 775–778

  9. Burtis W J, Helliwell R A. 1976. Magnetospheric chorus: Occurrence patterns and normalized frequency. Planet Space Sci, 24: 1007–1024

  10. Chen L. 1974. Theory of ULF modulation of VLF emissions. Geophys Res Lett, 1: 73–75

  11. Chen L, Zonca F. 2016. Physics of Alfvén waves and energetic particles in burning plasmas. Rev Mod Phys, 88: 015008

  12. Chen Y, Reeves G D, Friedel R H W. 2007. The energization of relativistic electrons in the outer Van Allen radiation belt. Nat Phys, 3: 614–617

  13. Coroniti F V, Kennel C F. 1970. Electron precipitation pulsations. J Geophys Res, 75: 1279–1289

  14. Cully C M, Angelopoulos V, Auster U, Bonnell J, Le Contel O. 2011. Observational evidence of the generation mechanism for rising-tone chorus. Geophys Res Lett, 38: L01106

  15. Demekhov A G, Taubenschuss U, Santolík O. 2017. Simulation of VLF chorus emissions in the magnetosphere and comparison with THEMIS spacecraft data. J Geophys Res Space Phys, 122: 166–184

  16. Dysthe K B. 1971. Some studies of triggered whistler emissions. J Geophys Res, 76: 6915–6931

  17. Gurnett D A, Kurth W S, Scarf F L. 1981. Plasma waves near saturn: Initial results from Voyager 1. Science, 212: 235–239

  18. Helliwell R A. 1967. A theory of discrete VLF emissions from the magnetosphere. J Geophys Res, 72: 4773–4790

  19. Helliwell R A. 1983. Controlled stimulation of VLF emissions from Siple Station, Antarctica. Radio Sci, 18: 801–814

  20. Hikishima M, Yagitani S, Omura Y, Nagano I. 2009. Full particle simulation of whistler-mode rising chorus emissions in the magnetosphere. J Geophys Res, 114: A01203

  21. Horne R B, Thorne R M. 1998. Potential waves for relativistic electron scattering and stochastic acceleration during magnetic storms. Geophys Res Lett, 25: 3011–3014

  22. Horne R B, Thorne R M, Shprits Y Y, Meredith N P, Glauert S A, Smith A J, Kanekal S G, Baker D N, Engebretson M J, Posch J L, Spasojevic M, Inan U S, Pickett J S, Decreau P M E. 2005. Wave acceleration of electrons in the Van Allen radiation belts. Nature, 437: 227–230

  23. Hospodarsky G B, Averkamp T F, Kurth W S, Gurnett D A, Menietti J D, Santolik O, Dougherty M K. 2008. Observations of chorus at Saturn using the Cassini Radio and Plasma Wave Science instrument. J Geophys Res, 113: A12206

  24. Hu G, Krommes J A. 1994. Generalized weighting scheme for δf particle-simulation method. Phys Plasmas, 1: 863–874

  25. Inan U S, Bell T F, Helliwell R A. 1978. Nonlinear pitch angle scattering of energetic electrons by coherent VLF waves in the magnetosphere. J Geophys Res, 83: 3235–3253

  26. Katoh Y, Omura Y. 2007. Computer simulation of chorus wave generation in the Earth’s inner magnetosphere. Geophys Res Lett, 34: L03102

  27. Katoh Y, Omura Y. 2011. Amplitude dependence of frequency sweep rates of whistler mode chorus emissions. J Geophys Res, 116: A07201

  28. Katoh Y, Omura Y. 2013. Effect of the background magnetic field inhomogeneity on generation processes of whistler-mode chorus and broadband hiss-like emissions. J Geophys Res-Space Phys, 118: 4189–4198

  29. Ke Y, Gao X, Lu Q, Wang X, Wang S. 2017. Generation of rising-tone chorus in a two-dimensional mirror field by using the general curvilinear PIC code. J Geophys Res-Space Phys, 122: 8154–8165

  30. Kennel C F, Petschek H E. 1966. Limit on stably trapped particle fluxes. J Geophys Res, 71: 1–28

  31. Kurita S, Katoh Y, Omura Y, Angelopoulos V, Cully C M, Le Contel O, Misawa H. 2012. THEMIS observation of chorus elements without a gap at half the gyrofrequency. J Geophys Res, 117: A11223

  32. Lampe M, Joyce G, Manheimer W M, Ganguli G. 2010. Nonlinear whistler instability driven by a beamlike distribution of resonant electrons. Phys Plasmas, 17: 022902

  33. Li W, Thorne R M, Bortnik J, Nishimura Y, Angelopoulos V. 2011. Modulation of whistler mode chorus waves: 1. Role of compressional Pc4–5 pulsations. J Geophys Res, 116: A06205

  34. Li W, Bortnik J, Thorne R M, Cully C M, Chen L, Angelopoulos V, Nishimura Y, Tao J B, Bonnell J W, Le Contel O. 2013. Characteristics of the Poynting flux and wave normal vectors of whistler-mode waves observed on THEMIS. J Geophys Res Space Phys, 118: 1461–1471

  35. Liu K, Gary S P, Winske D. 2011. Excitation of banded whistler waves in the magnetosphere. Geophys Res Lett, 38: L14108

  36. Lyons L R, Thorne R M. 1973. Equilibrium structure of radiation belt electrons. J Geophys Res, 78: 2142–2149

  37. Macúšová E, Santolík O, Décréau P, Demekhov A G, Nunn D, Gurnett D A, Pickett J S, Titova E E, Kozelov B V, Rauch J L, Trotignon J G. 2010. Observations of the relationship between frequency sweep rates of chorus wave packets and plasma density. J Geophys Res, 115: A12257

  38. Maeda K, Smith P H, Anderson R R. 1976. v.l.f. emission from ring-current electrons. Nature, 263: 37–41

  39. Menietti J D, Shprits Y Y, Horne R B, Woodfield E E, Hospodarsky G B, Gurnett D A. 2012. Chorus, ECH, and Z mode emissions observed at Jupiter and Saturn and possible electron acceleration. J Geophys Res, 117: A12214

  40. Meredith N P, Johnstone A D, Szita S, Horne R B, Anderson R R. 1999. “Pancake” electron distributions in the outer radiation belts. J Geophys Res, 104: 12431–12444

  41. Miyoshi Y, Katoh Y, Nishiyama T, Sakanoi T, Asamura K, Hirahara M. 2010. Time of flight analysis of pulsating aurora electrons, considering wave-particle interactions with propagating whistler mode waves. J Geophys Res, 115: A10312

  42. Morales G J, O’Neil T M. 1972. Nonlinear frequency shift of an electron plasma wave. Phys Rev Lett, 28: 417–420

  43. Ni B, Thorne R M, Zhang X, Bortnik J, Pu Z, Xie L, Hu Z, Han D, Shi R, Zhou C, Gu X. 2016. Origins of the Earth’s diffuse auroral precipitation. Space Sci Rev, 200: 205–259

  44. Nishimura Y, Bortnik J, Li W, Thorne R M, Lyons L R, Angelopoulos V, Mende S B, Bonnell J W, Le Contel O, Cully C, Ergun R, Auster U. 2010. Identifying the driver of pulsating aurora. Science, 330: 81–84

  45. Nunn D. 1971. A theory of VLF emissions. Planet Space Sci, 19: 1141–1167

  46. Nunn D. 1974. A self-consistent theory of triggered VLF emissions. Planet Space Sci, 22: 349–378

  47. Nunn D. 1990. The numerical simulation of VLF nonlinear wave-particle interactions in collision-free plasmas using the Vlasov hybrid simulation technique. Comput Phys Commun, 60: 1–25

  48. Nunn D, Omura Y. 2012. A computational and theoretical analysis of falling frequency VLF emissions. J Geophys Res, 117: A08228

  49. Nunn D, Omura Y, Matsumoto H, Nagano I, Yagitani S. 1997. The numerical simulation of VLF chorus and discrete emissions observed on the Geotail satellite using a Vlasov code. J Geophys Res, 102: 27083–27097

  50. Nunn D, Santolik O, Rycroft M, Trakhtengerts V. 2009. On the numerical modelling of VLF chorus dynamical spectra. Ann Geophys, 27: 2341–2359

  51. Omura Y, Matsumoto H. 1982. Computer simulations of basic processes of coherent whistler wave-particle interactions in the magnetosphere. J Geophys Res, 87: 4435–4444

  52. Omura Y, Nunn D. 2011. Triggering process of whistler mode chorus emissions in the magnetosphere. J Geophys Res, 116: A05205

  53. Omura Y, Matsumoto H, Nunn D, Rycroft M J. 1991. A review of observational, theoretical and numerical studies of VLF triggered emissions. J Atmos Terrestrial Phys, 53: 351–368

  54. Omura Y, Katoh Y, Summers D. 2008. Theory and simulation of the generation of whistler-mode chorus. J Geophys Res, 113: A04223

  55. Omura Y, Hikishima M, Katoh Y, Summers D, Yagitani S. 2009. Nonlinear mechanisms of lower-band and upper-band VLF chorus emissions in the magnetosphere. J Geophys Res, 114: A07217

  56. O’Neil T M, Winfrey J H, Malmberg J H. 1971. Nonlinear interaction of a small cold beam and a plasma. Phys Fluids, 14: 1204–1212

  57. Parker S E, Lee W W. 1993. A fully nonlinear characteristic method for gyrokinetic simulation. Phys Fluids B-Plasma Phys, 5: 77–86

  58. Reeves G D, Spence H E, Henderson M G, Morley S K, Friedel 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, Niehof J T. 2013. Electron acceleration in the heart of the Van Allen radiation belts. Science, 341: 991–994

  59. Sagdeev R Z, Shapiro V D, Shevchenko V I. 1985. Mechanism of triggered emission in the magnetospheric plasma. Zh Eksp Teor Fiz, 89: 22–33

  60. Santolík O, Gurnett D A, Pickett J S, Parrot M, Cornilleau-Wehrlin N. 2004. A microscopic and nanoscopic view of storm-time chorus on 31 March 2001. Geophys Res Lett, 31: L02801

  61. Scarf F L, Gurnett D A, Kurth W S. 1979. Jupiter plasma wave observations: An initial Voyager 1 overview. Science, 204: 991–995

  62. Shprits Y Y, Menietti J D, Drozdov A Y, Horne R B, Woodfield E E, Groene J B, de Soria-Santacruz M, Averkamp T F, Garrett H, Paranicas C, Gurnett D A. 2018. Strong whistler mode waves observed in the vicinity of Jupiter’s moons. Nat Commun, 9: 3131

  63. Shue J H, Hsieh Y K, Tam S W Y, Wang K, Fu H S, Bortnik J, Tao X, Hsieh W C, Pi G. 2015. Local time distributions of repetition periods for rising tone lower band chorus waves in the magnetosphere. Geophys Res Lett, 42: 8294–8301

  64. Soto-Chavez A R, Wang G, Bhattacharjee A, Fu G Y, Smith H M. 2014. A model for falling-tone chorus. Geophys Res Lett, 41: 1838–1845

  65. Stix T H. 1992. Waves in Plasmas. Melville NY: American Institute of Physics Publishing

  66. Su Z, Zheng H, Wang S. 2009. Evolution of electron pitch angle distribution due to interactions with whistler mode chorus following sub-storm injections. J Geophys Res, 114: A08202

  67. Sudan R N, Ott E. 1971. Theory of triggered VLF emissions. J Geophys Res, 76: 4463–4476

  68. Tao X. 2014. A numerical study of chorus generation and the related variation of wave intensity using the DAWN code. J Geophys Res-Space Phys, 119: 3362–3372

  69. Tao X, Thorne R M, Li W, Ni B, Meredith N P, Horne R B. 2011. Evolution of electron pitch angle distributions following injection from the plasma sheet. J Geophys Res, 116: A04229

  70. Tao X, Li W, Bortnik J, Thorne R M, Angelopoulos V. 2012. Comparison between theory and observation of the frequency sweep rates of equatorial rising tone chorus. Geophys Res Lett, 39: L08106

  71. Tao X, Lu Q, Wang S, Dai L. 2014. Effects of magnetic field configuration on the day-night asymmetry of chorus occurrence rate: A numerical study. Geophys Res Lett, 41: 6577–6582

  72. Tao X, Zonca F, Chen L. 2017a. Investigations of the electron phase space dynamics in triggered whistler wave emissions using low noise Sf method. Plasma Phys Control Fusion, 59: 094001

  73. Tao X, Zonca F, Chen L. 2017b. Identify the nonlinear wave-particle interaction regime in rising tone chorus generation. Geophys Res Lett, 44: 3441–3446

  74. Taubenschuss U, Khotyaintsev Y V, Santolík O, Vaivads A, Cully C M, Contel O L, Angelopoulos V. 2014. Wave normal angles of whistler mode chorus rising and falling tones. J Geophys Res-Space Phys, 119: 9567–9578

  75. Teng S, Tao X, Li W, Qi Y, Gao X, Dai L, Lu Q, Wang S. 2018. A statistical study of the spatial distribution and source-region size of chorus waves using Van Allen Probes data. Ann Geophys, 36: 867–878

  76. Thorne R M, Ni B, Tao X, Horne R B, Meredith N P. 2010. Scattering by chorus waves as the dominant cause of diffuse auroral precipitation. Nature, 467: 943–946

  77. Thorne R M, Li W, Ni B, Ma Q, Bortnik J, Chen L, Baker D N, Spence H E, Reeves G D, Henderson M G, Kletzing C A, Kurth W S, Hospodarsky G B, Blake J B, Fennell J F, Claudepierre S G, Kanekal S G. 2013. Rapid local acceleration of relativistic radiation-belt electrons by magnetospheric chorus. Nature, 504: 411–414

  78. Trakhtengerts V Y. 1995. Magnetosphere cyclotron maser: Backward wave oscillator generation regime. J Geophys Res, 100: 17205–17210

  79. Tsurutani B T, Smith E J. 1974. Postmidnight chorus: A substorm phenomenon. J Geophys Res, 79: 118–127

  80. Vomvoridis J L, Denavit J. 1979. Test particle correlation by a whistler wave in a nonuniform magnetic field. Phys Fluids, 22: 367–377

  81. Vomvoridis J L, Denavit J. 1980. Nonlinear evolution of a monochromatic whistler wave in a nonuniform magnetic field. Phys Fluids, 23: 174–183

  82. Vomvoridis J L, Crystal T L, Denavit J. 1982. Theory and computer simulations of magnetospheric very low frequency emissions. J Geophys Res, 87: 1473–1489

  83. Watt C E J, Degeling A W, Rankin R, Murphy K R, Rae I J, Singer H J. 2011. Ultralow-frequency modulation of whistler-mode wave growth. J Geophys Res, 116: A10209

  84. Zonca F, Chen L, Briguglio S, Fogaccia G, Vlad G, Wang X. 2015. Nonlinear dynamics of phase space zonal structures and energetic particle physics in fusion plasmas. New J Phys, 17: 013052

  85. Zonca F, Tao X, Chen L. 2017. Nonlinear wave-particle dynamics in chorus excitation. Belfast: 44th EPS Conference on Plasma Physics

  86. Zonca F, Tao X, Chen L. 2019. A theoretical framework of chorus excitation. to be submitted to Geophysical Research Letter

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This work was supported by the National Natural Science Foundation of China (Grant Nos. 41631071, 41674174, and 41474142), and the Fundamental Research Funds for the Central Universities.

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Correspondence to Xin Tao.

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Tao, X., Zonca, F., Chen, L. et al. Theoretical and numerical studies of chorus waves: A review. Sci. China Earth Sci. 63, 78–92 (2020) doi:10.1007/s11430-019-9384-6

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  • Chorus waves
  • Frequency chirping
  • Triggered emissions