Nonlinear force-free modeling of the solar coronal magnetic field

Abstract

The coronal magnetic field is an important quantity because the magnetic field dominates the structure of the solar corona. Unfortunately direct measurements of coronal magnetic fields are usually not available. The photospheric magnetic field is measured routinely with vector magnetographs. These photospheric measurements are extrapolated into the solar corona. The extrapolated coronal magnetic field depends on assumptions regarding the coronal plasma, e.g. force-freeness. Force-free means that all non-magnetic forces like pressure gradients and gravity are neglected. This approach is well justified in the solar corona due to the low plasma beta. One has to take care, however, about ambiguities, noise and non-magnetic forces in the photosphere, where the magnetic field vector is measured. Here we review different numerical methods for a nonlinear force-free coronal magnetic field extrapolation: Grad-Rubin codes, upward integration method, MHD-relaxation, optimization and the boundary element approach. We briefly discuss the main features of the different methods and concentrate mainly on recently developed new codes.

33 pages, 3 figures, Review article

References in corpus (10)

• Optimization code with weighting function for the reconstruction of coronal magnetic fields
• Preprocessing of vector magnetograph data for a non-linear force-free magnetic field reconstruction
• The "Yin-Yang Grid": An Overset Grid in Spherical Geometry
• Adaptive mesh refinement for conservative systems: multi-dimensional efficiency evaluation
• Comparing magnetic field extrapolations with measurements of magnetic loops
• Including stereoscopic information in the reconstruction of coronal magnetic fields
• Magnetic modelling and tomography: First steps towards a consistent reconstruction of the solar corona
• How to use magnetic field information for coronal loop identification?
• Computing nonlinear force free coronal magnetic fields
• Inversion of coronal Zeeman and Hanle Observations to reconstruct the coronal magnetic field

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