At the Sun, the strongest magnetic fields are routinely detected at dark sunspots. The magnitude of the field is typically about 3000 G, with only a few exceptions that reported the magnetic field in excess of 5000 G. Given that the magnetic field decreases with height in the solar atmosphere, no coronal magnetic field above ∼2000 G was ever reported. Here, we present imaging microwave observations of anomalously strong magnetic field of about 4000 G at the base of the corona in solar active region NOAA 12673 on 06 September 2017. Combining the photospheric vector measurements of the magnetic field and the coronal probing, we created and validated a nonlinear force-free field coronal model, with which we quantify the record-breaking coronal magnetic field at various coronal heights.

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Quantifying coronal magnetic field remains a central problem in solar physics. Nowadays the coronal magnetic field is often modelled using nonlinear force-free field (NLFFF) reconstructions, whose accuracy has not yet been comprehensively assessed. Here we perform a detailed casting of the NLFFF reconstruction tools, such as π-disambiguation, photospheric field preprocessing, and volume reconstruction methods using a 3D snapshot of the publicly available fullfledged radiative MHD model. Specifically, from the MHD model we know the magnetic field vector in the entire 3D domain, which enables us to perform "voxel-by-voxel" comparison of the restored and the true magnetic field in the 3D model volume. Our tests show that the available π-disambiguation methods often fail at the quiet sun areas dominated by small-scale magnetic elements, while they work well at the AR photosphere and (even better) chromosphere. The preprocessing of the photospheric magnetic field, although does produce a more force-free boundary condition, also results in some effective 'elevation' of the magnetic field components. This 'elevation' height is different for the longitudinal and transverse components, which results in a systematic error in absolute heights in the reconstructed magnetic data cube. The extrapolations performed starting from actual AR photospheric magnetogram are free from this systematic error, while have other metrics comparable with those for extrapolations from the preprocessed magnetograms. This finding favors the use of extrapolations from the original photospheric magnetogram without preprocessing. Our tests further suggest that extrapolations from a force-free chromospheric boundary produce measurably better results, than those from the photospheric boundary.

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