Solar Flare Phenomena As Phase Transition Caused By Frustration Of Current Percolation

  • L. A. Pustil’nik

Abstract

We present analysis of flare process as ”phase transition” phenomena caused by frustration of current percolation in turbulent current sheet. We show that numerous plasma instabilities in the sheet will form random resistors network with ”bad resistors”-turbulent domains and ”good resistors”-normal plasma domains. We show that current percolation in random inhomogeneous turbulent current sheet like to another percolated systems is able to produce phase transition with drastic change of global properties of system as whole (conductivity, heat-conductivity, elasticity,) on the threshold value of critical density of ”bad” elements (p = pc). Another property of solar flares, what may be understood on the base of percolation approach is observed universal power dependence of frequency of flares and microflares (elementary events-spikes) on their amplitude: NWW-k. It may be explained as natural sequence of universal power dependence of clusters’ masses in percolated systems on their sizes. The slope of resulted spectra is determined by the fractal dimension of clusters and depends on feedback between current propagation and turbulence generation. We show that percolation approach allow to explain phenomena of preflare bursts-precursors observed in radio and hard X-ray. It may be understood as results of pre-catastrophic lose of elasticity of system to small disturbance on the percolation threshold, with formation of short life nuclear of ”new phase”.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Broadbent S.R. and Hammersley J.M., 1957, Proceed. Camb. Phylos. Soc., 53, 629.MathSciNetADSMATHCrossRefGoogle Scholar
  2. Buchner J., (1988), ‚this issue Crosby N., Aschwanden M., Dennis B., 1993, Solar Phys, 143, 275.Google Scholar
  3. Epstein, A.J., 1987, in Handbook of Conducting Polymers, Vol.2, T.A. Skotheim (ed.)., 1041.Google Scholar
  4. Feder J., Fractals, 1988, (Plenum Press).Google Scholar
  5. Furth H., Rosenbluth M., Killen J., 1963, Phys. Fluids, 6, 459.ADSCrossRefGoogle Scholar
  6. Gershberg R.E., Shahovskaya N.I., 1983, Astroph. and Space Science, 95, 2, 235.ADSCrossRefGoogle Scholar
  7. Kirkpatrick S., 1973, Reviews of Modern Physics, 45, 4, 574.ADSCrossRefGoogle Scholar
  8. Kruskal M., Shwarzschild M., 1954, M. Proceed. Roy. Soc, 223A, 348.ADSCrossRefGoogle Scholar
  9. Kurochka L., 1987, Astromicheskii Zhurnal, (Soviet Astronomy), 64, 2, 443.ADSGoogle Scholar
  10. Lu E., hamilton, R.J., 1991, Atrophys. J., 380, L.89.ADSCrossRefGoogle Scholar
  11. Mikhailovskii A.B., 1975, Theory of Plasma Instabilities, (Moscow, Atomizdat), V.1, 155, Instabilities in Inhomogeneous Plasma, Consulants Bureau, N-Y.Google Scholar
  12. Poston T., Stewart L, 1978, Catastrophe Theory and Its Application, Surveys and references works in mathematics, Pitman, London.Google Scholar
  13. Pustil’nik L., 1978, Astronomicheskii Zhurnal, (Soviet Atronomy), 55, 607.ADSGoogle Scholar
  14. Pustil’nik L., 1980, Astronomicheskii Zhurnal, (Soviet Atronomy), 57, 601.ADSGoogle Scholar
  15. Pustil’nik L., 1997, Astrophysics and Space Science, 252, 325.ADSMATHCrossRefGoogle Scholar
  16. Rammal R., Tannous C., Breton P., Tremblay A.M.S., 1985, Phys. Rev. Lett., 54, 1718.ADSCrossRefGoogle Scholar
  17. Shimuzu T., PASJ, 1995, 47, 251.ADSGoogle Scholar
  18. Seiden P.S., Wentzel D.G., 1996, Ap. J., 522.Google Scholar
  19. Shibata, K., 1997, Proc. of Workshop on Solar Flares and Related Disturbances, T.Sakurai, E.. sagawa and M.Akioka (eds), Hiraiso/CRL.Google Scholar
  20. Shklovskii B.I., Efros A.L., 1984, Electronic Propeties of Doped Semiconductors, (Heidelberg, Springer Verlag, 1984)Google Scholar
  21. Stanley H.E., 1971; Introduction to Phase Transition and critical Phenomena, (Oxford, OUP).Google Scholar
  22. Stauffer D., Aharony A., 1992, Introduction to Percolation Theory, Taylor&Francis, London.Google Scholar
  23. Srelniker Ya., 1998, private communication.Google Scholar
  24. Tajima T., Shibata K., 1997, Plasma Astrophysics, Addison-Wesley.Google Scholar
  25. Tappin, 1991, Astron.&Astrophys. Suppl. Series, 87, 1991.Google Scholar
  26. UenN, S., Mineshige, S., Neogoro, H., Shibata, K., Hudson, H.F., 1997, Astrophys. J., 484, 920.ADSCrossRefGoogle Scholar
  27. Vedernikov, N.F., Mukimov, K.M., Sigal, G.P., 1991, Superconductivity (Sverhprovodi-most: fizika, chimiya, technika (russian)), 7, 316.Google Scholar
  28. Vilmer N., Trotted G., in ”Coronal Physics from Radio and Space Observations”, (Lecture Notes in Physics), Springer, 28.Google Scholar
  29. Zelenyi, L.M., Milovanov A.V., Gaetano Z., 1998, this issue.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  • L. A. Pustil’nik
    • 1
  1. 1.Israel Cosmic Ray Center, Tel-Aviv Univ.Sea of Galilee Astrop. Obs., Jordan Valley CollegeIsrael

Personalised recommendations