Astronomy and Astrophysics – Astrophysics
Scientific paper
Jun 1999
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999a%26a...346..303v&link_type=abstract
Astronomy and Astrophysics, v.346, p.303-312 (1999)
Astronomy and Astrophysics
Astrophysics
17
Magnetohydrodynamics (Mhd), Plasmas, Sun: Corona, Sun: Magnetic Fields
Scientific paper
A WKB method to determine approximations to the critical length for the onset of ideal MHD instabilities with high poloidal mode numbers m in one-dimensional force-free cylindrical models of line-tied coronal loops is presented, extending the work of Hood et al. (\cite{wkb}) and Van der Linden & Hood (\cite{vh98}). Qualitatively, the procedure is similar to the one used in these two papers and pioneered by Connor et al. (\cite{CHT}). It is found, however, that the scalings for sheared force-free equilibria are different from those in the other cases, so that significant modifications to the method are necessary. The WKB method developed only requires solving a simple ordinary differential equation rather than the original set of complicated two-dimensional partial differential equations. For all force-free sheared equilibria we find that for large m the marginal stability length behaves like lc~ ml0+l2/m compared to lc~ ml0+l1 for the unsheared case investigated in Hood et al. (\cite{wkb}). Thus, it appears that in the force-free (or nearly force-free) case the m=1 mode is always the first to become unstable. The WKB results are complemented with numerical solutions of the full equations and for sufficiently large values of the wave number m excellent agreement is found. The combination of the results and methods described in this paper, together with those in Van der Linden & Hood (\cite{vh98}) provide all the tools necessary to perform a complete stability assessment of any one-dimensional cylindrically-symmetric equilibrium model for a coronal loop.
Hood Alan William
van der Linden Ronald A. M.
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