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On the application of numerical continuation methods to solar
magnetostatic equilibria
Zaharenia Romeou
(St.Andrews)
Sequences of magnetostatic equilibria have long served as a useful
tool to model the quasistatic pre-eruptive energy storage phase of
coronal eruptive phenomena. The eruption onset would then be
identified with a bifurcation or catastrophe point in the solution
diagram. From the more fundamental viewpoint of dynamical systems,it
would also be important if we first studied and understood the
possible stationary states and their bifurcation properties. For the
resulting highly non-linear partial differential equations, and for a
given set of boundary conditions, multiple solutions (or none at all)
may exist. Such problems can in general be solved only
numerically. The most appropriate numerical algorithms for these cases
are continuation methods since they calculate complete solution
branches and detect bifurcation points.
We present here a numerical continuation code which uses
finite-element discretization to allow for flexibility in the grid
structure. The code also employs a sufficient linear stability
criterion to investigate the stability of each calculated solution of
the non-linear magnetohydrostatic (MHS) equations. Some preliminary
results for simple MHS equilibria will be presented and potential
future application will be discussed.
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