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Title: On the relationship between equilibrium bifurcations and ideal MHD instabilities for line-tied coronal loops
Authors: Neukirch, T.
Romeou, Z.
Keywords: Corona, structures
Flares, relation to magnetic field
Instabilities
Magnetohydrodynamics
Free cylindrical equilibria
Solar eruptive processes
Kink instability
Numerical simulations
Stability analysis
Onset conditions
Magnetic-fields
Current layers
Current sheets
Evolution
QB Astronomy
Issue Date: Jan-2010
Citation: Neukirch , T & Romeou , Z 2010 , ' On the relationship between equilibrium bifurcations and ideal MHD instabilities for line-tied coronal loops ' Solar Physics , vol 261 , no. 1 , pp. 87-106 .
Abstract: For axisymmetric models for coronal loops the relationship between the bifurcation points of magnetohydrodynamic (MHD) equilibrium sequences and the points of linear ideal MHD instability is investigated, imposing line-tied boundary conditions. Using a well-studied example based on the Gold -aEuro parts per thousand Hoyle equilibrium, it is demonstrated that if the equilibrium sequence is calculated using the Grad -aEuro parts per thousand Shafranov equation, the instability corresponds to the second bifurcation point and not the first bifurcation point, because the equilibrium boundary conditions allow for modes which are excluded from the linear ideal stability analysis. This is shown by calculating the bifurcating equilibrium branches and comparing the spatial structure of the solutions close to the bifurcation point with the spatial structure of the unstable mode. If the equilibrium sequence is calculated using Euler potentials, the first bifurcation point of the Grad -aEuro parts per thousand Shafranov case is not found, and the first bifurcation point of the Euler potential description coincides with the ideal instability threshold. An explanation of this results in terms of linear bifurcation theory is given and the implications for the use of MHD equilibrium bifurcations to explain eruptive phenomena is briefly discussed.
Version: Postprint
Status: Peer reviewed
URI: http://hdl.handle.net/10023/2268
DOI: http://dx.doi.org/10.1007/s11207-009-9480-0
ISSN: 0038-0938
Type: Journal article
Rights: This is an author version of an article published in Solar Physics, (c) Springer Science+Business Media B.V 2009. The original publication is available at www.springerlink.com
Appears in Collections:University of St Andrews Research
Applied Mathematics Research



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