Space Science Reviews

, Volume 107, Issue 1–2, pp 425–445 | Cite as

Complexity, Forced and/or Self-Organized Criticality, and Topological Phase Transitions in Space Plasmas

  • Tom Chang
  • Sunny W.Y. Tam
  • Cheng-Chin Wu
  • Giuseppe Consolini


The first definitive observation that provided convincing evidence indicating certain turbulent space plasma processes are in states of ‘complexity’ was the discovery of the apparent power-law probability distribution of solar flare intensities. Recent statistical studies of complexity in space plasmas came from the AE index, UVI auroral imagery, and in-situ measurements related to the dynamics of the plasma sheet in the Earth's magnetotail and the auroral zone.

In this review, we describe a theory of dynamical ‘complexity’ for space plasma systems far from equilibrium. We demonstrate that the sporadic and localized interactions of magnetic coherent structures are the origin of ‘complexity’ in space plasmas. Such interactions generate the anomalous diffusion, transport, acceleration, and evolution of the macroscopic states of the overall dynamical systems.

Several illustrative examples are considered. These include: the dynamical multi- and cross-scale interactions of the macro-and kinetic coherent structures in a sheared magnetic field geometry, the preferential acceleration of the bursty bulk flows in the plasma sheet, and the onset of ‘fluctuation induced nonlinear instabilities’ that can lead to magnetic reconfigurations. The technique of dynamical renormalization group is introduced and applied to the study of two-dimensional intermittent MHD fluctuations and an analogous modified forest-fire model exhibiting forced and/or self-organized criticality [FSOC] and other types of topological phase transitions.

complexity magnetotail plasma sheet 


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  1. Angelopoulos, V., Coroniti, F. V., Kennel, C. F., Kivelson, M. G., Walker, R. J., Russell, C. T., McPherron, R. L., Sanchez, E., Meng, C. I., Baumjohann, W., Reeves, G. D., Belian, R. D., Sato, N., Fris-Christensen, E., Sutcliffe, P. R., Yumoto, K. and Harris, T.: 1996, ‘Multi-point analysis of a BBF event on April 11, 1985’, J.Geophys.Res. 101, 4967.CrossRefADSGoogle Scholar
  2. Angelopoulos, V., Mukai, T. and Kokubun, S.: 1999, ‘Evidence for Intermittency in Earth's Plasma Sheet and Implications for Self-organized Criticality’, Physics of Plasmas 6, 4161.CrossRefADSGoogle Scholar
  3. Bak, P., Chen, K. and Tang, C.: 1990, ‘A Forest-fire Model and Some Thoughts on Turbulence’, Phys.Lett. A147, 297.ADSGoogle Scholar
  4. Castaing, B., Gagne, Y. and Hopfinger, E.J.: 1990, ‘Velocity Probability Density Functions of High Reynolds Number Turbulence’, Physica D 46, 177.zbMATHCrossRefADSGoogle Scholar
  5. Chang, T. and Stanley, H. E.: 1973, ‘Renormalization-group Verification of Crossover with Respect to Lattice Anisotropy Parameter’, Phys.Rev. B8, 1178.ADSGoogle Scholar
  6. Chang, T., Hankey, A. and Stanley, H. E.: 1973a, ‘Double-power Scaling Functions Near Tricritical Points’, Phys.Rev. B7, 4263.ADSGoogle Scholar
  7. Chang, T., Hankey, A. and Stanley, H. E.: 1973b, ‘Generalized Scaling Hypothesis in Multicomponent Systems. I. Classification of Critical Points by Order and Scaling at Tricritical Points’, Phys.Rev. B8, 346.ADSGoogle Scholar
  8. Chang, T., Nicoll, J. F. and Young, J. E.: 1978, ‘A Closed-form Differential Renormalization-group Generator for Critical Dynamics’, Phys.Lett. 67A, 287.MathSciNetADSGoogle Scholar
  9. Chang, T.: 1992, ‘Low-dimensional Behavior and Symmetry Breaking of Stochastic Systems near Criticality-Can these Effects be Observed in Space and in the Laboratory?’, IEEE Trans.on Plasma Science 20, 691.CrossRefADSGoogle Scholar
  10. Chang, T., Vvedensky, D. D. and Nicoll, J. F.: 1992, ‘Differential Renormalization-group Generators for Static and Dynamic Critical Phenomena’, Physics Reports 217, 279.MathSciNetCrossRefADSGoogle Scholar
  11. Chang, T.: 1998a, ‘Sporadic, Localized Reconnections and Multiscale Intermittent Turbulence in the Magnetotail’, in J. L. Horwitz, D. L. Gallagher and W. K. Peterson (eds), Geospace Mass and Energy Flow, American Geophysical, Union, Washington, D. C., AGU Geophysical Monograph 104, p. 193.Google Scholar
  12. Chang, T.: 1998b, ‘Multiscale Intermittent Turbulence in the Magnetotail’, in Y. Kamide et al. (eds), Proc.4th Intern.Conf.on Substorms, Kluwer Academic Publishers, Dordrecht and Terra Scientific Publishing Company, Tokyo, p. 431.Google Scholar
  13. Chang, T.: 1998c, ‘Self-organized Criticality, Multi-fractal Spectra, and Intermittent Merging of Coherent Structures in the Magnetotail’, in J. Büchner et al. (eds), Astrophysics and Space Science, Kluwer Academic Publishers, Dordrecht, the Netherlands, v. 264, p. 303.Google Scholar
  14. Chang, T.: 1999, ‘Self-organized Criticality, Multi-fractal Spectra, Sporadic Localized Reconnections and Intermittent Turbulence in the Magnetotail’, Physics of Plasmas 6, 4137.CrossRefADSGoogle Scholar
  15. Chang, T.: 2001, ‘Colloid-like Behavior and Topological Phase Transitions in Space Plasmas: Intermittent Low Frequency Turbulence in the Auroral zone’, Physica Scripta T89, 80.CrossRefADSGoogle Scholar
  16. Chang, T.: 2002, ‘"Complexity” Induced Plasma Turbulence in Coronal Holes and the Solar Wind’, in Solar Wind 10(in press).Google Scholar
  17. Chang, T. and Wu, C. C.: 2002, ‘“Complexity” and Anomalous Transport in Space Plasmas’, Physics of Plasmas 9, 3679.CrossRefADSGoogle Scholar
  18. Chang, T., Wu, C. C. and Angelopoulos, V.: 2002, ‘Preferential Acceleration of Coherent Magnetic Structures and Bursty Bulk Flows in Earth's Magnetotail’, Physica Scripta T98, 48.CrossRefADSGoogle Scholar
  19. Chapman, S. C., Watkins, N.W., Dendy, R. G., Helander, P. and Rowlands, G.: 1998, ‘A Simple Avalanche Model as an Analogue for Magnetospheric Activity’, Geophys.Res.Lett. 25, 2397.CrossRefADSGoogle Scholar
  20. Consolini, G.: 1997, ‘Sandpile Cellular Automata and Magnetospheric Dynamics’, in S. Aiello, N. Lucci, G. Sironi, A. Treves and U. Villante (eds), Cosmic Physics in the Year 2000, Soc. Ital. di Fis., Bologna, Italy, pp. 123-126.Google Scholar
  21. Consolini, G. and Chang, T.: 2001, ‘Magnetic Field Topology and Criticality in Geotail Dynamics: Relevance to Substorm Phenomena’, Space Sci.Rev. 95, 309.CrossRefADSGoogle Scholar
  22. Consolini, G.: 2002, ‘Self-organized Criticality: A New Paradigm for the Magnetotail Dynamics’, Fractals 10, 275.Google Scholar
  23. Drossel, B. and Schwabl, F.: 1992, ‘Self-organized Critical Forest-fire Model’, Phys.Rev.Lett. 69, 1629.CrossRefADSGoogle Scholar
  24. Fairfield, D. H., Mukai, T., Brittnacher, M., Reeves, G. D., Kokubun, S., Parks, G. K., Nagai, T., Matsumoto, H., Hashimoto, K., Gurnett, D. A. and Yamamoto, T.: 1999, ‘Earthward Flow Bursts in the Inner Magnetotail and Their Relation to Auroral Brightenings, AKR Intensifications, Geosynchronous Particle Injections and Magnetic Activity’, J.Geophys.Res. 104, 355-370.CrossRefADSGoogle Scholar
  25. Farge, M., Holschneider, M. and Colonna, J. F.: 1990, ‘Wavelet Analysis of Coherent Two Dimensional Turbulent Flows’, in H. K. Moffat (ed.), Topological Fluid Mechanics, Cambridge University Press, Cambridge, p. 765.Google Scholar
  26. Germany, G. A., Parks, G. K., Ranganath, H., Elsen, R., Richards, P. G., Swift, W., Spann, J. F. and Brittnacher, M.: 1998, ‘Analysis of Auroral Morphology: Substorm Precursor and Onset on January 10, 1997’, Geophys.Res.Lett. 25, 3043-3046.CrossRefADSGoogle Scholar
  27. Gil, L. and Sornette, D.: 1996, ‘Laudau-Ginzburg Theory of Self-organized Criticality’, Phys.Rev.Lett. 76, 3991.CrossRefADSGoogle Scholar
  28. Ieda, A., Fairfield, D. H., Mukai, T., Saito, Y., Kokubun, S., Liou, K., Meng, C.-I., Parks, G. K. and Brittnacher, M. J.: 2001, ‘Plasmoid Ejection and Auroral Brightenings’, J.Geophys.Res. 106, 3845-3857.CrossRefADSGoogle Scholar
  29. Loreto, V., Pietronero, L., Vespignani, A. and Zapperi, S.: 1995, ‘Renormalization Group Approach to the Critical Behavior of the Forest-fire Model’, Phys.Rev.Lett. 75, 465.CrossRefADSGoogle Scholar
  30. Lu, E. T.: 1995, ‘Avalanches in Continuum Driven Dissipative Systems’, Phys.Rev.Lett. 74, 2511-2514.CrossRefADSGoogle Scholar
  31. Lui, A. T. Y.: 1996, ‘Current Disruptions in the Earth's Magnetosphere: Observations and Models’, J.Geophys.Res. 101, 4899.CrossRefADSGoogle Scholar
  32. Lui, A. T. Y.: 1998, ‘Plasma Sheet Behavior Associated with Auroral Breakups’, in Y. Kamide (ed.), Proc.4th Intern.Conf.on Substorms, Kluwer Academic Publishers, Dordrecht and Terra Scientific Publishing Company, Tokyo, p. 183.Google Scholar
  33. Lui, A. T. Y., Chapman, S. C., Liou, K., Newell, P. T., Meng, C. I., Brittnacher, M. and Parks, G. D.: 2000, ‘Is the Dynamic Magnetosphere an Avalanching System?’, Geophys.Res.Lett. 27, 911-914.CrossRefADSGoogle Scholar
  34. Lyons, L. R., Nagai, T., Blanchard, G. T., Samson, J. C. Yamamoto, T., Mukai, T., Nishida, A. and Kokubun, S.: 1999, ‘Association Between Geotail Plasma Flows and Auroral Poleward Boundary Intensifications Observed by CANOPUS Photometers’, J.Geophys.Res. 104, 4485-4500.CrossRefADSGoogle Scholar
  35. Matthaeus, W. H. and Goldstein, M. L.: 1986, ‘Low-frequency 1/f Noise in the Interplanetary Magnetic Field’, Phys.Rev.Lett. 57, 495.CrossRefADSGoogle Scholar
  36. Nagai, T., Fujimoto, M., Saito, Y., Machida, S. et al.: 1998, ‘Structure and Dynamics of Magnetic Reconnection for Substorm Onsets with Geotail Observations’, J.Geophys.Res. 103, 4419.CrossRefADSGoogle Scholar
  37. Nakamura, R., Baumjohann, W., Brittnacher, M., Sergeev, V. A., Kubyshkina, M., Mukai, T. and Liou, K.: 2001a, ‘Flow Bursts and Auroral Activations: Onset Timing and Foot Point Location’, J.Geophys.Res. 106, 10777-10789.CrossRefADSGoogle Scholar
  38. Nakamura, R., Baumjohann, W., Schodel, R., Brittnacher, M., Sergeev, V. A., Kubyshkina, M., Mukai, T. and Liou, K.: 2001b, ‘Earthward Flow Bursts, Auroral Streamers, and Small Expansions’, J.Geophys.Res. 106, 10791-10802.CrossRefADSGoogle Scholar
  39. Newell, P. T., Liou, K., Sotirelis, T. and Meng, C. I.: 2001, ‘Polar Ultraviolet Imager Observations of Global Auroral Power as a Function of Polar Cap Size and Magnetotail Stretching’, J.Geophys.Res. 106, 5895-5905.CrossRefADSGoogle Scholar
  40. Nicoll, J. F., Chang, T. and Stanley, H. E.: 1974, ‘Nonlinear Solutions of Renormalization-group Equations’, Phys.Rev.Lett. 32, 1446.MathSciNetCrossRefADSGoogle Scholar
  41. Nicoll, J. F., Chang, T. and Stanley, H. E.: 1976, ‘Nonlinear Crossover Between Critical and Tricritical Behavior’, Phys.Rev.Lett. 36, 113.CrossRefADSGoogle Scholar
  42. Sergeev, V. A., Liou, K., Meng, C. I., Newell, P. T., Brittnacher, M., Parks, G. and Reeves, G. D.: 1999, ‘Development of Auroral Streamers in Association with Localized Impulsive Injections to the Inner Magnetotail’, Geophys.Res.Lett. 26, 417-420.CrossRefADSGoogle Scholar
  43. Tam, S. W. Y., Chang, T., Consolini, G. and de Michelis, P.: 2000, ‘Renormalization-group Description and Comparison with Simulation Results for Forest-fire Models-Possible Near-criticality Phenomenon in the Dynamics of Space Plasmas’, Trans. Amer. Geophys. Union, EOS 81, SM62A-04.Google Scholar
  44. Uritsky, V. M., Klimas, A. J., Vassiliadis, D., Chua, D. and Parks, G. D.: 2002, ‘Scale-free Statistics of Spatiotemporal Auroral Emissions as Depicted by POLAR UVI Images: The Dynamic Magnetosphere is an Avalanching System’, J.Geophys.Res. (in press).Google Scholar
  45. Wu, C. C. and Chang, T.: 2000a, ‘2D MHD Simulation of the Emergence and Merging of Coherent Structures’, Geophys.Res.Lett. 27, 863.CrossRefADSGoogle Scholar
  46. Wu, C. C. and Chang, T.: 2000b, ‘Dynamical Evolution of Coherent Structures in Intermittent Two-dimensional MHD Turbulence’, IEEE Trans.on Plasma Science 28, 1938.CrossRefGoogle Scholar
  47. Wu, C. C. and Chang, T.: 2001, ‘Further Study of the Dynamics of Two-dimensional MHD Coherent Structures-A Large Scale Simulation’, J.Atmos.Sci.Terrest.Phys. 63, 1447.CrossRefADSGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Tom Chang
    • 1
  • Sunny W.Y. Tam
    • 1
  • Cheng-Chin Wu
    • 2
  • Giuseppe Consolini
    • 3
  1. 1.Center for Space ResearchMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Department of Physics and AstronomyUniversity of CaliforniaLos AngelesUSA
  3. 3.Istituto di Fisica dello Spazio InterplanetarioConsiglio Nazionale delle RicercheRomeItaly

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