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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 linetied boundary conditions. Using a wellstudied 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.
Original language  English 

Pages (fromto)  87106 
Number of pages  20 
Journal  Solar Physics 
Volume  261 
Issue number  1 
Early online date  15 Dec 2009 
DOIs  
Publication status  Published  Jan 2010 
Keywords
 Corona, structures
 Flares, relation to magnetic field
 Instabilities
 Magnetohydrodynamics
 Free cylindrical equilibria
 Solar eruptive processes
 Kink instability
 Numerical simulations
 Stability analysis
 Onset conditions
 Magneticfields
 Current layers
 Current sheets
 Evolution
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 2 Finished


Solar&Magnetospheric Plasma Theory PP/E1: Solar and Magnetospheric Plasma Theory
Neukirch, T., Hood, A. W., Parnell, C. E., Priest, E., Roberts, B. & Wright, A. N.
1/04/07 → 31/03/12
Project: Standard