Skip to main content
SpringerLink
Log in

3D MHD simulation of the double-gradient instability of the magnetotail current sheet

  • Article
  • Published:
Science China Technological Sciences Aims and scope Submit manuscript

Abstract

Flapping motion of the current sheet (CS) is an important physical process in the Earth’s magnetotail. The magnetic double-gradient model, which includes both the instability and wave modes, offers a reasonable explanation for the exciting and propagation of the flapping wave. In this paper, we apply an advanced numerical magnetohydrodynamic (MHD) scheme (conservation element and solution element (CESE)-MHD) to simulate the magnetic double-gradient instability in an idealized current sheet that mimics the magnetotail configuration. We initialize the simulations with a numerically relaxed magnetotail equilibrium, in which the normal component of the magnetic field has a tailward gradient. It is confirmed in our simulation that the instability develops in the current layer. The growth rate of the instability yielded from the simulation is very close to the prediction of theory, with a relative deviation of only ten percent. The results demonstrate that the CESE-MHD scheme is very powerful in numerical study of the double-gradient mechanism of the CS flapping mode, and can be used for further investigations of the flapping motion in more realistic CS configurations.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Lui A T Y, Meng C I, Akasofu S I. Wavy nature of the magnetotail neutral sheet. Geophys Res Lett, 1978, 5: 279–282

    Article  Google Scholar 

  2. Speiser T W, Ness N F. The neutral sheet in the geomagnetic tail: Its motion, equivalent currents, and field line connection through it. J Geo-phys Res, 1967, 72: 131–141

    Article  Google Scholar 

  3. Zhang T L, BaumjohannW, Nakamura R, et al. A wavy twisted neutral sheet observed by CLUSTER. Geophys Res Lett, 2002, 29: 1–4

    Google Scholar 

  4. Runov A, Sergeev V A, Baumjohann W, et al. Electric current and magnetic field geometry in flapping magnetotail current sheets. Ann Geophys, 2005, 23: 1391–1403

    Article  Google Scholar 

  5. Sergeev V A, Sormakov D A, Apatenkov S V, et al. Survey of large-amplitude flapping motions in the midtail current sheet. Ann Geophys, 2006, 24: 2015–2024

    Article  Google Scholar 

  6. Petrukovich A A, Zhang T, Baumjohann W, et al. Oscillatory mag-netic flux tube slippage in the plasma sheet. Ann Geophys, 2006, 24: 1695–1704

    Article  Google Scholar 

  7. Wei X H, Cai C L, Cao J B, et al. Flapping motions of the magnetotail current sheet excited by nonadiabatic ions. Geophys Res Lett, 2015, 42: 4731–4735

    Article  Google Scholar 

  8. Sergeev V, Runov A, Baumjohann W, et al. Current sheet flapping mo-tion and structure observed by Cluster. Geophys Res Lett, 2003, 30: 1327

    Google Scholar 

  9. Sergeev V, Runov A, Baumjohann W, et al. Orientation and propaga-tion of current sheet oscillations. Geophys Res Lett, 2004, 31: L05807

    Article  Google Scholar 

  10. Shen C, Rong Z J, Li X, et al. Magnetic configurations of the tilted current sheets in magnetotail. Ann Geophys, 2008, 26: 3525–3543

    Article  Google Scholar 

  11. Toichi T, Miyazaki T. Flapping motions of the tail plasma sheet induced by the interplanetary magnetic field variations. Planet Space Sci, 1976, 24: 147–159

    Article  Google Scholar 

  12. Forsyth C, Lester M, Fear R C, et al. Solar wind and substorm excita-tion of the wavy current sheet. Ann Geophys, 2009, 27: 2457–2474

    Article  Google Scholar 

  13. Malova H V, Zelenyi L M, Popov V Y, et al. Asymmetric thin current sheets in the Earth’s magnetotail. Geophys Res Lett, 2007, 34: L16108

    Article  Google Scholar 

  14. Daughton W. Kinetic theory of the drift kink instability in a current sheet. J Geophys Res, 1998, 103: 29429–29443

    Article  Google Scholar 

  15. Daughton W. Two-fluid theory of the drift kink instability. J Geophys Res, 1999, 104: 28701–28707

    Article  Google Scholar 

  16. Zelenyi L M, Artemyev A V, Petrukovich A A, et al. Low frequency eigenmodes of thin anisotropic current sheets and Cluster observations. Ann Geophys, 2009, 27: 861–868

    Article  Google Scholar 

  17. Karimabadi H W, Daughton W, Pritchett P L, et al. Ion-ion kink insta-bility in the magnetotail: 1. Linear theory. J Geophys Res, 2003, 108: 1400

    Article  Google Scholar 

  18. Karimabadi H, Pritchett P L, Daughton W, et al. Ion-ion kink instabil-ity in the magnetotail: 2. Three-dimensional full particle and hybrid simulations and comparison with observations. J Geophys Res, 2003, 108: 1401

    Article  Google Scholar 

  19. Sitnov M I, Swisdak M, Drake J F, et al. A model of the bifurcated cur-rent sheet: 2. Flapping motions. Geophys Res Lett, 2004, 31: L09805

    Article  Google Scholar 

  20. Ricci P, Lapenta G, Brackbill J U. Structure of the magnetotail current: Kinetic simulation and comparison with satellite observations. Geo-phys Res Lett, 2004, 31: L06801

    Article  Google Scholar 

  21. Cao J, Duan J, Du A, et al. Characteristics of middle-to low-latitude Pi2 excited by bursty bulk flows. J Geophys Res, 2008, 113: A07S15

    Google Scholar 

  22. Cao J B, Ma Y D, Parks G, et al. Joint observations by Cluster satel-lites of bursty bulk flows in the magnetotail. J Geophys Res, 2006, 111: A04206

    Article  Google Scholar 

  23. Ma Y D, Cao J B, Nakamura R, et al. Statistical analysis of earthward flow bursts in the inner plasma sheet during substorms. J Geophys Res, 2009, 114: A07215

    Google Scholar 

  24. Erkaev N V, Semenov V S, Kubyshkin I V, et al. MHD model of the flapping motions in the magnetotail current sheet. J Geophys Res, 2009, 114: A03206

    Article  Google Scholar 

  25. Duan A Y, Cao J B, Ma Y D, et al. Cluster observations of large-scale southward movement and dawnward-duskward flapping of Earth’s magnetotail current sheet. Sci China Tech Sci, 2013, 56: 194–204

    Article  Google Scholar 

  26. Golovchanskaya I V, Maltsev Y P. On the identification of plasma sheet flapping waves observed by Cluster. Geophys Res Lett, 2005, 32: L02102

    Article  Google Scholar 

  27. Erkaev N V, Semenov V S, Biernat H K. Magnetic double-gradient in-stability and flapping waves in a current sheet. Phys Rev Lett, 2007, 99: 235003

    Article  Google Scholar 

  28. Sun W, Fu S, Shi Q, et al. THEMIS observation of a magnetotail cur-rent sheet flapping wave. Chin Sci Bull, 2014, 59: 154–161

    Article  Google Scholar 

  29. Erkaev N V, Semenov V S, Biernat H K. Magnetic double gradient mechanism for flapping oscillations of a current sheet. Geophys Res Lett, 2008, 35: L02111

    Article  Google Scholar 

  30. Korovinskiy D B, Divin A, Erkaev N V, et al. MHD modeling of the double-gradient (kink) magnetic instability. J Geophys Res Space Phys, 2013, 118: 1146–1158

    Article  Google Scholar 

  31. Pritchett P L, Coroniti F V. A kinetic ballooning/interchange instability in the magnetotail. J Geophys Res, 2010, 115: A06301

    Google Scholar 

  32. Feng X, Hu Y, Wei F. Modeling the resistive MHD by the cese method. Sol Phys, 2006, 235: 235–257

    Article  Google Scholar 

  33. Feng X, Zhou Y, Wu S T. A novel numerical implementation for solar wind modeling by the modified conservation element/solution element method. Astrophys J, 2007, 655: 1110–1126

    Article  Google Scholar 

  34. Jiang C W, Feng X S, Zhang J, et al. AMR simulations of magnetohy-drodynamic problems by the CESE method in curvilinear coordinates. Sol Phys, 2010, 267: 463–491

    Article  Google Scholar 

  35. Jiang CW, Feng X S, Wu S T, et al. Magnetohydrodynamic simulation of a sigmoid eruption of active region 11283. Astrophys J, 2013, 771: L30

    Article  Google Scholar 

  36. Jiang C W, Wu S T, Feng X S, et al. Formation and eruption of an ac-tive region sigmoid. I. A study by nonlinear force-free field modeling. Astrophys J, 2014, 780: 55

    Article  Google Scholar 

  37. Jiang C W, Wu S T, Feng X S, et al. Data-driven magnetohydrodynamic modelling of a flux-emerging active region leading to solar eruption. Nat Commun, 2016, 7: 11522

    Article  Google Scholar 

  38. Feng X, Yang L, Xiang C, et al. Three-dimensional solar WIND modeling from the Sun to Earth by a SIP-CESE MHD model with a sixcomponent grid. Astrophys J, 2010, 723: 300–319

    Article  Google Scholar 

  39. Feng X, Zhang S, Xiang C, et al. A hybrid solar wind model of the CESE+HLL method with a Yin-Yang overset grid and an AMR grid. Astrophys J, 2011, 734: 50

    Article  Google Scholar 

  40. Feng X, Jiang C, Xiang C, et al. A data-driven model for the global coronal evolution. Astrophys J, 2012, 758: 62

    Article  Google Scholar 

  41. Feng X, Yang L, Xiang C, et al. Validation of the 3D AMR SIP-CESE solar wind model for four carrington rotations. Sol Phys, 2012, 279: 207–229

    Article  Google Scholar 

  42. Feng X, Xiang C, Zhong D, et al. SIP-CESE MHD model of solar wind with adaptive mesh refinement of hexahedral meshes. Comput Phys Commun, 2014, 185: 1965–1980

    Article  MathSciNet  Google Scholar 

  43. Feng X, Ma X, Xiang C. Data-driven modeling of the solar wind from 1 R s to 1 AU. J Geophys Res Space Phys, 2015, 120: 10159–10174

    Article  Google Scholar 

  44. Jiang C W, Cui S X, Feng X S. Solving the Euler and Navier-Stokes equations by the AMR-CESE method. Comput Fluids, 2012, 54: 105–117

    Article  MathSciNet  MATH  Google Scholar 

  45. Birn J, Sommer R, Schindler K. Open and closed magnetospheric tail configurations and their stability. Astrophys Space Sci, 1975, 35: 389–402

    Article  Google Scholar 

  46. Schindler K. A self-consistent theory of the tail of the magnetosphere. In: Earth’s Magnetospheric Processes. Dordrecht: Springer, 1972. 1836–1841

    Google Scholar 

  47. Schindler K. Physics of Space Plasma Activity. Cambridge: Cambridge University Press, 2010

    Google Scholar 

  48. Hesse M, Birn J. Three-dimensional magnetotail equilibria by numerical relaxation techniques. J Geophys Res, 1993, 98: 3973–3982

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Key Laboratory of Computational Geodynamics, University of Chinese Academy of Sciences, Beijing, 100049, China

    AiYing Duan & Huai Zhang

  2. State Key Laboratory of Space Weather, Chinese Academy of Sciences, Beijing, 100190, China

    AiYing Duan

  3. School of Space and Environment, Beihang University, Beijing, 100191, China

    HaoYu Lu

Authors
  1. AiYing Duan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Huai Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. HaoYu Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to AiYing Duan or Huai Zhang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Duan, A., Zhang, H. & Lu, H. 3D MHD simulation of the double-gradient instability of the magnetotail current sheet. Sci. China Technol. Sci. 61, 1364–1371 (2018). https://doi.org/10.1007/s11431-017-9158-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11431-017-9158-7

Keywords

Search

Navigation