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Computing nonlinear force-free fields in spherical geometry

Thomas Wiegelmann
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Abstract

We describe a newly developed code for the extrapolation of nonlinear force-free coronal magnetic fields in spherical coordinates. The program uses measured vector magnetograms on the solar photosphere as input and solves the force-free equations in the solar corona. The method is based on an optimization principle and the heritage of the newly developed code is a corresponding method in Cartesian geometry. We test the newly developed code with the help of a semi-analytic solution and rate the quality of our reconstruction qualitatively by magnetic field line plots and quantitatively with a number of comparison metrics. We find that we can reconstruct the original test field with high accuracy. The method is fast if the computation is limited to low co-latitudes (say $30^\circ \leq θ\leq 150^\circ$), but becomes significantly slower if the polar regions are included.

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Thomas Wiegelmann. 2006-12-05. Computing nonlinear force-free fields in spherical geometry. https://doi.org/10.1007/s11207-006-0266-3

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