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

Abstract

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 α in the magnetogram. A standard linear force-free extrapolation of this magnetogram, using the so-called 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.