Skip to main content
Log in

Theoretical and numerical studies of chorus waves: A review

  • Review
  • Published:
Science China Earth Sciences Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

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

    Google Scholar 

  • 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: https://doi.org/10.1029/2012GM001324

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • 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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • 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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • 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

    Google Scholar 

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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • 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

    Google Scholar 

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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • 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

    Google Scholar 

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

    Google Scholar 

  • 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

    Google Scholar 

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

    Google Scholar 

  • 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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

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

    Google Scholar 

  • 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

    Google Scholar 

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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Thorne R M, Li W, Ni B, Ma Q, Bortnik J, Chen L, Baker D N, Spence H E, Reeves G D, Henderson M G, 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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

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

    Google Scholar 

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

Download references

Acknowledgements

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.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xin Tao.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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). https://doi.org/10.1007/s11430-019-9384-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11430-019-9384-6

Keywords

Navigation