On the Relationship between Equilibrium Bifurcations and Ideal MHD Instabilities for Line-Tied Coronal Loops}
Thomas Neukirch Submitted: 2009-10-30 09:12
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
Using a well-studied example based on the Gold-Hoyle equilibrium, it is demonstrated
that if the equilibrium sequence is calculated using the Grad-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-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.
Authors: Neukirch, T., Romeou, Z.
Publication Status: Solar Physics, accepted
Last Modified: 2009-11-01 07:42