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## Open Physics

2009 | 7 | 1 | 130-134
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### Topological constraints on solar loop plasma instabilities and Alfvén waves

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EN
Inhomogeneous plasmas-solar instabilities-are investigated by using the techniques of classical differential geometry for curves, where the Frenet torsion and curvature describe completely the motion of a curve. In our case, the Frenet frame changes in time and also depends upon the other coordinates, taking into account the inhomogeneity of the plasma. The exponential perturbation method, so commonly used to describe cosmological perturbations, is applied to the magnetohydrodynamic (MHD) plasma equations to find modes describing Alfvén wave propagation in the medium of planar loops. Stability is investigated in the imaginary axis of the spectra of complex frequencies ω, i.e. $$\Im$$
m (ω) ≠ 0. A pratical guide for experimental solar physicists is given by computing the twist of force-free solar loops, which generalizes the Parker formula relating the twist to the Frenet torsion. In our expression the twist of the solar loops also depends on the abnormality of the normal vector of the frame.
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130-134
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published
1 - 3 - 2009
online
8 - 1 - 2009
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• Departamento de Física Teórica - IF - Universidade do Estado do Rio de Janeiro-UERJ Rua São Francisco Xavier, 524 Cep, 20550-003, Maracanã, Rio de Janeiro, RJ, Brasil, garcia@dft.if.uerj.br
References
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• [4] J. Thiffeault, A.H. Boozer, arXiv:nlin/0209042v1
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• [7] L.C. Garcia de Andrade, Phys. Scripta 73 (2006)
• [8] M. Lopez Fuentes et al., Astron. Astrophys. 397, 305 (2003) http://dx.doi.org/10.1051/0004-6361:20021487[Crossref]
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• [10] E.N. Parker, Spontaneous Current Sheets in Magnetic fields (Oxford, 1994)
• [11] L.C. Garcia de Andrade, Astrophys. Space Sci. (in press)
• [12] S. Childress, A. Gilbert, Twist, Stretch and Fold: The Fast Dynamo (Springer, 1995) [WoS]
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