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**Session 36 - Solar Activity.**

*Display session, Tuesday, June 11*

*Tripp Commons, *

## [36.09] Quasi-modes as dissipative MHD eigenmodes : results for 1-dimensional equilibrium states

*W. J. Tirry, M. Goossens (KUL)*
Quasi-modes which are important for understanding the MHD wave behavior of
solar and astrophysical magnetic plasmas are computed as eigenmodes of the
linear dissipative MHD equations. This eigenmode computation is carried out
with a simple numerical scheme which is based on analytical solutions to the
dissipative MHD equations in the quasi-singular resonance layer.
Non-uniformity in magnetic field and plasma density gives rise to a continuous
spectrum of resonant frequencies. Global discrete eigenmodes with
characteristic frequencies lying within the range of the continuous spectrum
may couple to localised resonant Alfvén waves. In ideal MHD these modes
are not eigenmodes of the Hermitian ideal MHD operator, but are found as a
temporal dominant global exponentially decaying response to an initial
perturbation. In dissipative MHD they are really eigenmodes with damping
becoming independent of the dissipation mechanism in the limit of vanishing dissipation.
An analytical solution of these global modes is found in the dissipative
layer around the resonant Alfvénic position. Using the analytical solution
to cross the quasi-singular resonance layer the required numerical effort of the
eigenvalue scheme is
limited to the integration of the ideal MHD equations in regions away from
any singularity. The presented scheme allows for a straightforward
parametric study. The method is checked with known ideal
quasi-mode frequencies found for a 1-D box model for the Earth's magnetosphere
(Zhu amp; Kivelson 1988). The agreement is excellent. The dependence of the
oscillation frequency on the wavenumbers for a 1-D slab model for coronal loops
found by Ofman, Davila, amp; Steinolfson (1995) is also easily recovered.

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