Abstract
The solar atmosphere being magnetic in nature, the understanding of the structure and evolution of the magnetic field in different regions of the solar atmosphere has been an important task over the past decades. This task has been made complicated by the difficulties to measure the magnetic field in the corona, while it is currently known with a good accuracy in the photosphere and/or chromosphere. Thus, to determine the coronal magnetic field, a mathematical method has been developed based on the observed magnetic field. This is the so-called magnetic field extrapolation technique. This technique relies on two crucial points: i) the physical assumption leading to the system of differential equations to be solved, ii) the choice and quality of the associated boundary conditions. In this review, I summarise the physical assumptions currently in use and the findings at different scales in the solar atmosphere. I concentrate the discussion on the extrapolation techniques applied to solar magnetic data and the comparison with observations in a broad range of wavelengths (from hard X-rays to radio emission).
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Acknowledgements
I would like to thank Steve Tomczyk and Marc DeRosa for inviting me to contribute to the “Coronal Magnetism – Connecting Models to Data and the Corona to the Earth” workshop held in Boulder (2012). I also thank Michael Thompson for his hospitality at HAO (Boulder) during the workshop.
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Invited Review
Coronal Magnetometry
Guest Editors: S. Tomczyk, J. Zhang, and T.S. Bastian
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Régnier, S. Magnetic Field Extrapolations into the Corona: Success and Future Improvements. Sol Phys 288, 481–505 (2013). https://doi.org/10.1007/s11207-013-0367-8
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DOI: https://doi.org/10.1007/s11207-013-0367-8