Space Science Reviews

, Volume 95, Issue 1–2, pp 293–307

Avalanching and Self-Organised Criticality, a paradigm for geomagnetic activity?

  • Sandra Chapman
  • Nicholas Watkins
Article

Abstract

The characterization of global energy storage and release in the coupled solar wind-magnetosphere system remains one of the fundamental problems of space physics. Recently, it has been realised that a new paradigm in physics, that of Self Organised Criticality (SOC) may encapsulate the mixing and merging of flux on many scales in the magnetotail prompting bursty energy release and reconfiguration. SOC is consistent with qualitative measures such as power-law power spectra and bursty bulk flows and with more quantitative tests such as power law burst distributions in auroral indices and auroral optical activity. Here, we present a careful classification of the broad range of systems that fall under the general description of `SOC'. We argue that some, but not all, of these are consistent with our current understanding of the magnetosphere. We discuss the observed low dimensionality of the dynamic magnetosphere in terms of both SOC model properties, and observables. Observations of burst statistics are highlighted; we show that these are currently suggestive but not sufficient to confirm SOC and in particular we find that auroral indices are not effective at distinguishing the internal dynamics of the magnetosphere from that of the intermittent solar wind driver. This may also elucidate the paradox of predictability and complexity of the coupled solar wind-magnetosphere system.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Angelopoulos, V., Coroniti, F. V., Kennel, C. F., Kivelson, M. G., Walker, R. J., Russell, C. T., McPherron, K. L., Sanchez, E., Meng, C. I., Baumjohann, W., Reeves, G. D., Belian, R. D., Sato, N., Friis-Christensen, E., Sutcliffe, P. R., Yumoto, K. and Harris, T.: 1996, J. Geophys. Res. 101, 4967.Google Scholar
  2. Bak, P., Tang, C. and Weisenfeld, K.: 1987, ‘Self-Organized Criticality: An Explanation of 1/f noise’ Phys. Rev. Lett. 50, 381.Google Scholar
  3. Bohr, T., Jensen, M., Paladin, G. and Vulpiani, A.: 1998, Dynamical Systems Approach to Turbulence, Cambridge University Press, p. 350.Google Scholar
  4. Bofetta, G., Carbone, V., Giuliani, P., Veltri, P. and Vulpiani, A.: 1999, ‘Power Laws in Solar Flares: Self-Organized Criticality or Turbulence?’ Phys. Rev. Lett. 83, 4662.Google Scholar
  5. Borovsky, J. E., Nemzek, R. J. and Belian, R. D.: 1993, ‘The Occurence Rate of Magnetospheric-Substorm Onsets: Random and Periodic Substorms’ J. Geophys. Res. 98, 3807.Google Scholar
  6. Chang, T. S.: 1992, ‘Low-Dimensional Behaviour and Symmetry Breaking of Stochastic Systems Near Criticality — Can These Effects Be Observed in Space and in the Laboratory ?’ IEEE Trans. Plasma Sci. 20, 691.Google Scholar
  7. Chang, T. S.: 1999, ‘Self-Organized Criticality, Multi-Fractal Spectra, Sporadic Localized Reconnections and Intermittent Turbulence in the Magnetotail’ Phys. Plasmas 6, 4137.Google Scholar
  8. Chapman, S. C.: 2000, ‘Inverse cascade Avalanche Model with Limit Cycle Exhibiting Period Doubling, Intermittency and Self Similarity’ Phys. Rev. E, 62, 1905.Google Scholar
  9. Chapman, S. C., Watkins, N. W., Dendy, R. O., Helander, P. and Rowlands, G.: 1998, ‘A Simple Avalanche Model as an Analogue for Magnetospheric Activity’ Geophys. Res. Lett. 25, 2397.Google Scholar
  10. Chapman, S. C., Dendy, R. O. and Rowlands, G.: 1999, ‘A Sandpile Model with Dual Scaling Regimes for Laboratory, Space and Astrophysical Plasmas’ Phys. Plasmas 6, 4169.Google Scholar
  11. Christensen, K., Olami, Z. and Bak, P.: 1992, ‘Deterministic 1/f Noise in Nonconservative Models of Models of Self-Organized Criticality’ Phys. Rev. Lett. 68, 2417.Google Scholar
  12. Consolini, G.: 1997, ‘Sandpile Cellular Automata and Magnetospheric Dynamics’ in S. Aiello, N. Iucci, G. Sironi, A. Treves and U. Villante (eds), Proc. vol. 58, ‘Cosmic Physics in the Year 2000’, SIF, Bologna, Italy.Google Scholar
  13. Consolini, G.: 1999, ‘Avalanches, Scaling and Criticality in Magnetospheric Dynamics’ Phys. Rev. Lett., submitted.Google Scholar
  14. Consolini, G. and de Michelis, P.: 2000, ‘A Revised Forest-Fire Automaton for the Nonlinear Dynamics of the Earth's Magnetotail’ J. Atmospheric Solar Terrest. Phys., in press.Google Scholar
  15. Dendy, R. O. and Helander, P.: 1997, ‘Sandpiles, Silos and Tokamak Phenomenology: a Brief Review’ Plasma Phys. Controlled Fusion 39, 1947.Google Scholar
  16. Einaudi, G. and Velli, M.: 1999, ‘The Distribution of Flares, Statistics of Magneto-hydrodynamic Turbulence and Coronal Heating’ Phys. Plasmas 6, 4146.Google Scholar
  17. Freeman, M. P., Watkins, N. W. and Riley, D. J.: 2000a, ‘Evidence for a Solar Wind Origin of the Power Law Burst Lifetime Distribution of the AE Indices’ Geophys. Res. Lett. 27, 1087.Google Scholar
  18. Freeman, M. P., Watkins, N. W. and Riley, D. J.: 2000b, ‘An SOC-Like Avalanche Distribution Observed in an MHD Turbulent Cascade in the Solar Wind’ Phys. Rev. E, submitted.Google Scholar
  19. Frette, V., Christensen, K., Malthe-Sorenssen, A., Feder, J., Jossang, T. and Meakin, P.: 1996, ‘Avalanche Dynamics in a Pile of Rice’ Nature 379, 49.Google Scholar
  20. Hoshino, M., Nishida, A., Yamamoto, T. and Kokubun, S.: 1994, ‘Turbulent Magnetic Field in the Distant Magnetotail: Botom-Up Process of Plasmoid Formation’ Geophys. Res. Lett. 21, 2935.Google Scholar
  21. Huang, K.: 1987., Statistical Mechanics, second ed., Wiley, New York.Google Scholar
  22. Jensen, H. J.: 1998 Self-Organized Criticality: Emergent Complex: Behaviour in Physical and Biological Systems, Cambridge University Press, Cambridge, p. 153.Google Scholar
  23. Kaneko, K.: 1993, Theory and Applications of Coupled Map Lattices, Wiley, New York.Google Scholar
  24. Klimas, A. J., Vassiliadis, D., Baker, D. N. and Roberts, D. A.: 1996, ‘The Organised Nonlinear Dynamics of the Magnetosphere’ J. Geophys. Res. 101, 13089.Google Scholar
  25. Klimas, A. J., Valdivia, J. A., Vassiliadis, D., Baker, D. N., Hesse, M. and Takalo, J.: 2000, ‘The Role of Self-Organized Criticality in the Substorm Phenomenon and Its Relation to Localized Reconnection in the Magnetospheric Plasma Sheet’ J. Geophys. Res., submitted.Google Scholar
  26. Krommes, J. A.: 2000, ‘Renormalized Dissipation in the Nonconservatively Forced Burgers Equation’ Phys. Plasmas 7, 1064.Google Scholar
  27. Lewis, Z. V.: 1991, ‘On the Apparent Randomness of Substorm Onsets’ Geophys. Res. Lett. 18, 1627.Google Scholar
  28. Lu, E. T.: 1995, ‘Avalanches in Continuum Dissipative Systems’ Phys. Rev. Lett. 74, 2511.Google Scholar
  29. Lui, A. T. Y., Lopez, R. E., Krimigis, S. M., McEntire, R.W., Zanetti, L. J. and Potemra, T. A.: 1988, ‘A Case Study of Magnetotail Current Sheet Disruption and Diversion’ Geophys. Res. Lett. 15, 721.Google Scholar
  30. Lui, A. T. Y., Chapman, S. C., Liou, K., Newell, P. T., Meng, C. I., Brittnacher, M. and Parks, G. K.: 2000, ‘Is the Dynamic Magnetosphere an Avalanching System?’ Geophys. Res. Lett. 27, 911.Google Scholar
  31. Sharma, A. S.: 1995, ‘Assessing the Magnetosphere's Nonlinear Behaviour: Its Dimension is Low, Its Predictability High’ Rev. Geophys. Suppl. Series 33 (1), 645.Google Scholar
  32. Sitnov, M. I., Sharma, A. S., Papadopoulos, K., Vassiliadis, D., Valdivia, J. A., Klimas, A. J. and Baker, D. N.: 2000, ‘Phase Transition-Like Behavior of the Magnetosphere During Substorms’ J. Geophys. Res. 105(12), 955.Google Scholar
  33. Smith, A. J., Freeman, M. P. and Reeves, C. D.: 1996, ‘Postmidnight VLF Chorus Events, a Substorm Signature Observed at the Ground Near L=4’ J. Geophys. Res. 101, 24641.Google Scholar
  34. Takalo, J., Timonen, J. and Koskinen, H.: 1993, ‘Correlation Dimension and Affinity of ae Data and Bicolored Noise’ Geophys. Res. Lett. 20, 1527.Google Scholar
  35. Takalo, J., Timonen, J., Klimas, A., Valdivia, J. and Vassiliadis, D.: 1999, ‘Nonlinear Energy Dissipation in a Cellular Automaton Magnetotail Field Model’ Geophys. Res. Lett. 26, 1813.Google Scholar
  36. Tam, W. Y., Chang, T. S., Chapman, S. C. and Watkins, N. W.: 2000, ‘Analytical Determination of Power Law Index for the Chapman et al. Sandpile (FSOC) Analog for Magnetospheric Activity-Renormalization Group Analysis’ Geophys. Res. Lett. 27, 1367.Google Scholar
  37. Tsurutani, B., Sugiura, M., Iyemori, T., Goldstein, B. E., Gonzalez, W. D., Akasofu, S.-I. and Smith, E.J.: 1990, ‘The Nonlinear Response of AE to the IMF B s driver: A spectral brea at 5 hours’ Geophys. Res. Lett. 17, 279.Google Scholar
  38. Turcotte, D. L.: 1999, ‘Self-Organized Criticality’ Rep. Prog. Phys. 62, 1.Google Scholar
  39. Uritsky, V. M. and Semenov, V. S.: 1998, ‘A Sandpile Model for Global Statistics of Reconnection Events in the Magnetotail’ Proc. International Workshop on ‘The Solar Wind-Magnetosphere System 3’, 23–25 September, Graz Austria.Google Scholar
  40. Uritsky, V. M. and Pudovkin, M.: 1998, ‘Low Frequency 1/f-like Fluctuations of the AE-Index as a Possible Manifestation of Self-Organised Criticality in the Magnetosphere’ Ann. Geophys. 10, 1580.Google Scholar
  41. Vassiliadis, D., Anastasiadis, A., Georgioulis, M. and Vlahos, L.: 1998, ‘Derivation of Fine Cellular Automata Models from a Subset of the Magnetohydrodynamic Equations’ Astrophys. J. 509, L53.Google Scholar
  42. Watkins, N. W., Freeman, M. P., Chapman, S. C. and Dendy, R. O.: 2000, ‘Testing the SOC Hypothesis for the Magnetosphere’ J. Astron. Solar Terrest. Phys., in press.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Sandra Chapman
    • 1
  • Nicholas Watkins
    • 2
  1. 1.University of WarwickCoventryU.K
  2. 2.British Antarctic Survey (NERC)CambridgeU.K

Personalised recommendations