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**Session 19 - Solar Flares.**

*Oral session, Monday, June 10*

*Wisconsin Center, *

## [19.02] Non-Equilibrium in Line-Tied Coronal Magnetic Fields

*C. S. Ng, A. Bhattacharjee (University of Iowa)*
Parker's model of nonequilibrium and topological dissipation
[E. N. Parker, ApJ 174, 499, 1972] is revisited. Within the
framework of ideal reduced MHD equations, it is shown that
there can be at most one smooth magnetostatic equilibrium for
each continuous footpoint mapping between the two plates with
the line-tied boundary condition.
This implies that for a given amount of footpoint driving, if
a coronal equilibrium becomes unstable, magnetic non-equilibrium
and current sheets (tangential discontinuities) can be realized.
The special case of island coalescence is considered analytically
and numerically. Stability of an equilibrium containing current
layers is also studied. Numerical results suggest that such an
equilibrium becomes more unstable as the current increases.
This is consistent with the tendency for the formation of true
tangential discontinuities.
This work is supported by NSF and AFOSR.

**Program
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