Statistics – Computation
Scientific paper
May 1996
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996aas...188.3609t&link_type=abstract
American Astronomical Society, 188th AAS Meeting, #36.09; Bulletin of the American Astronomical Society, Vol. 28, p.874
Statistics
Computation
Scientific paper
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 Alfven 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 Alfvenic 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 & 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, & Steinolfson (1995) is also easily recovered.
Goossens Marcel
Tirry W. J.
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