EDP Sciences
Free access
Volume 433, Number 1, April I 2005
Page(s) 335 - 347
Section The Sun
DOI http://dx.doi.org/10.1051/0004-6361:20042008

A&A 433, 335-347 (2005)
DOI: 10.1051/0004-6361:20042008

Extrapolation of a nonlinear force-free field containing a highly twisted magnetic loop

G. Valori1, B. Kliem1 and R. Keppens2

1  Astrophysical Institute Potsdam, An der Sternwarte 16, 14482 Potsdam, Germany
    e-mail: gvalori@aip.de
2  FOM-Institute for Plasma Physics Rijnhuizen, PO Box 1207, 3430 BE Nieuwegein, The Netherlands

(Received 14 September 2004 / Accepted 6 November 2004 )

The stress-and-relax method for the extrapolation of nonlinear force-free coronal magnetic fields from photospheric vector magnetograms is formulated and implemented in a manner analogous to the evolutionary extrapolation method. The technique is applied to a numerically constructed force-free equilibrium that has a simple bipolar structure of the normal field component in the bottom (magnetogram) plane but contains a highly twisted loop and a shear (current) layer, with a smooth but strong variation of the force-free parameter $\alpha$ in the magnetogram. A standard linear force-free extrapolation of this magnetogram, using the so-called $\alpha_\mathrm{best}$ value, is found to fail in reproducing the twisted loop (or flux rope) and the shear layer; it yields a loop pair instead and the shear is not concentrated in a layer. With the nonlinear extrapolation technique, the given equilibrium is readily reconstructed to a high degree of accuracy if the magnetogram is sufficiently resolved. A parametric study quantifies the requirements on the resolution for a successful nonlinear extrapolation. Permitting magnetic reconnection by a controlled use of resistivity improved the extrapolation at a resolution comparable to the smallest structures in the magnetogram.

Key words: magnetic fields -- magnetohydrodynamics (MHD) -- methods: numerical -- Sun: corona

© ESO 2005

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