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The linear and nonlinear instabilities of force-free magnetic fields of perfectly conducting fluid cylinder have been analyzed. Indeed, the instability of force-free magnetized flows poses a challenge to our physical understanding and mathematical skills. Equilibrium state is studied by taking Lundquist field (1951) and it is found that the fluid kinetic pressure is non-uniform. Normal mode analysis is utilized for investigating the linear perturbation technique while in nonlinear ones an iteration procedure (see Radwan (1989)) is used. The stability criterion is discussed analytically and numerically and the unstable domains are identified. Surprising results are obtained due to Lundquist Bessel model effect. The second order perturbation equations are derived and solved. Upon applying appropriate conditions, the coefficients control nonlinear theory are identified in general and in the case in which the force-free tenuous field is unperturbed in the linear analysis. Second order analysis does not alter in a direct way the unstable domains. However, it gives corrections and domain of validity for the linear analysis, since no linear theory can predict its domain of validity.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
203--221
Opis fizyczny
Bibliogr. 26 poz.
Twórcy
autor
- Mathematics Department, Faculty of Science, Qatar University
Bibliografia
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- 8. Radwan, A. E., Astrophys. Space Sei. 191, 307 (1992).
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- 13. Uberiori, C. and Somasunderam, K., Plasma Phys. 22, 747 (1980).
- 14. Drazin. P. G. and Reid, W., "Hydrodynamic Stability". (Cambridge University Press, London (1981). See also Banks, W. H., Drazin, P. G. and Zatureka, M. B, J. Fluid Mech. 186. 559 (1988).____, Fluid Dynamics Res. 4, 151 (1988).
- 15. Cheng, L. Y., Phys. Fluids 28, 2614 (1985).
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- 17. Lin, S. P. and Lain, Z., Phys. Fluids Al, 490 (1989).
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- 19. Boyd, T. J. and Sanderson, J. J., "Plasma Dynamics (London 1969).
- 20. Abramovitz, M. and Stegun, I. "Handbook of Mathematical Functions” (Dover, New York, 1981).
- 21. Callebaut, D. K., Simon Stevin, 45, 1 (1971).
- 22. Radwan, A. E., Int. J. Eng. Sei., 36, 87 (1998).
- 23. Radwan, A. E., Saad M. Sileem and Amaal A. Ashour, Ind. J. Maths. 43 (2001) in press.
- 24. Radwan, A. E., J. Magn. Matrs. 78, 85 (1989a).
- 25. Radwan, A. E., J. Magn. Matrs. 79, 17 (1989b).
- 26. Shem, V. and Hussain, F., Phys. Fluids A5, 2183 (1993).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD7-0033-0087