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Solar Physics

, Volume 88, Issue 1–2, pp 163–177 | Cite as

The stability of coronal loops: Finite-length and pressure-profile limits

  • G. Einaudi
  • G. Van Hoven
Article

Abstract

Results are described from a quickly converging, necessary-and-sufficient, MHD-stability test for coronal-loop models. The primary stabilizing influence arises from magnetic line tying at the photosphere, and this end conditions requires a series expansion of possible loop excitations. The stability boundary is shown to quickly approach a limit as the number of terms increases, providing a critical length for the loop in proportion to its transverse magnetic scale. Several models of force-free-field profiles are tested and the stability behavior of a localized current channel, embedded in an external current-free region, is shown to be superior to that of other, broader, current profiles. Pressure-gradient effects, leading to increased or decreased stability, are shown to be amplified by line tying. Long loops must either conduct low net current, or exhibit an axial-field reversal coexisting with a low-pressure core. The limits on stability depend on the magnetic aspect ratio, the plasma-to-magnetic pressure ratio, and the field orientation at the loop edge. Applications of these results to the structure of coronal loops are described.

Keywords

Pressure Ratio Stability Boundary Current Channel Coronal Loop Critical Length 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Bernstein, I. B., Frieman, E. A., Kruskal, M. D., and Kulsrud, R. M.: 1958, Proc. Roy. Soc. A244, 17.Google Scholar
  2. Chiuderi, C. and Einaudi, G.: 1981, Solar Phys. 73, 89.Google Scholar
  3. Chiuderi, C., Giachetti, R., and Van Hoven, G.: 1977, Solar Phys. 54, 107.Google Scholar
  4. Chiuderi, C., Einaudi, G., Ma, S. S., and Van Hoven, G.: 1980, J. Plasma Phys. 24, 39.Google Scholar
  5. Christiansen, J. P. and Roberts, K. V.: 1978, Nucl. Fusion 18, 181.Google Scholar
  6. Einaudi, G. and Van Hoven, G.: 1981, Phys. Fluids 24, 1092.Google Scholar
  7. Einaudi, G., Torricelli-Ciamponi, G., and Chiuderi, C.: 1983, submitted to Solar Phys. Google Scholar
  8. Giachetti, R., Van Hoven, G., and Chiuderi, C.: 1977, Solar Phys. 55, 371.Google Scholar
  9. Goedbloed, J. P.: 1971, Physica 53, 501.Google Scholar
  10. Gold, T. and Hoyle, F.: 1960, Monthly Notices Roy. Astron. Soc. 120, 89.Google Scholar
  11. Hood, A. W. and Priest, E. R.: 1979, Solar Phys. 64, 303.Google Scholar
  12. Hood, A. W. and Priest, E. R.: 1981, Geophys. Astrophys. Fluid Dynamics 17, 297.Google Scholar
  13. Hood, A. W., Priest, E. R., and Einaudi, G.: 1982, Geophys. Astrophys. Fluid Dynamics 20, 247.Google Scholar
  14. Kruskal, M. D., Johnson, J. L., Gottlieb, M. B., and Goldman, L. M.: 1958, Phys. Fluids 1, 421.Google Scholar
  15. Newcomb, W. A.: 1960, Ann. Phys. 10, 232.Google Scholar
  16. Raadu, M. A.: 1972, Solar Phys. 22, 425.Google Scholar
  17. Ray, A. and Van Hoven, G.: 1982, Phys. Fluids 25, 1355.Google Scholar
  18. Shafranov, V. D.: 1957, J. Nucl., Energy II 5, 86.Google Scholar
  19. Van Hoven, G.: 1981, in E. R. Priest (ed.), Solar Flare Magnetohydrodynamics, Gordon and Breach, New York, p. 217.Google Scholar
  20. Van Hoven, G., Chiuderi, C., and Giachetti, R.: 1977, Astrophys. J. 213, 869.Google Scholar
  21. Van Hoven, G., Ma, S. S., and Einaudi, G.: 1981, Astron. Astrophys. 97, 232.Google Scholar
  22. Voslamber, D. and Callebaut, D. K.: 1962, Phys. Rev. 128, 2016.Google Scholar

Copyright information

© D. Reidel Publishing Company 1983

Authors and Affiliations

  • G. Einaudi
    • 1
    • 2
  • G. Van Hoven
    • 3
  1. 1.Scuola Normale SuperiorePisaItaly
  2. 2.University of CaliforniaIrvineUSA
  3. 3.University of CaliforniaIrvineUSA

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