Solar Physics

, Volume 289, Issue 12, pp 4453–4480 | Cite as

Validation and Benchmarking of a Practical Free Magnetic Energy and Relative Magnetic Helicity Budget Calculation in Solar Magnetic Structures

  • K. Moraitis
  • K. Tziotziou
  • M. K. Georgoulis
  • V. Archontis


In earlier works we introduced and tested a nonlinear force-free (NLFF) method designed to self-consistently calculate the coronal free magnetic energy and the relative magnetic helicity budgets of observed solar magnetic structures. In principle, the method requires only a single, photospheric or low-chromospheric, vector magnetogram of a quiet-Sun patch or an active region and performs calculations without three-dimensional magnetic and velocity-field information. In this work we strictly validate this method using three-dimensional coronal magnetic fields. Benchmarking employs both synthetic, three-dimensional magnetohydrodynamic simulations and nonlinear force-free field extrapolations of the active-region solar corona. Our time-efficient NLFF method provides budgets that differ from those of more demanding semi-analytical methods by a factor of approximately three, at most. This difference is expected to come from the physical concept and the construction of the method. Temporal correlations show more discrepancies that are, however, soundly improved for more complex, massive active regions, reaching correlation coefficients on the order of, or exceeding, 0.9. In conclusion, we argue that our NLFF method can be reliably used for a routine and fast calculation of the free magnetic energy and relative magnetic helicity budgets in targeted parts of the solar magnetized corona. As explained in this article and in previous works, this is an asset that can lead to valuable insight into the physics and triggering of solar eruptions.


Helicity, magnetic Magnetic fields, corona Active regions, magnetic fields Magnetohydrodynamics 



This research has been carried out in the framework of the research projects hosted by the RCAAM of the Academy of Athens. The observations used are courtesy of NASA/SDO and the HMI science team. We thank X. Sun and Y. Liu for the magnetic-field extrapolations of NOAA AR 11158. The simulations were performed on the STFC and SRIF funded UKMHD cluster, at the University of St Andrews. MKG is a Marie Curie Fellow. VA acknowledges support by EU (IEF-272549 grant). This work was supported from the EU’s Seventh Framework Programme under grant agreement no. PIRG07-GA-2010-268245. It has been also co-financed by the European Union (European Social Fund – ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) – Research Funding Program: Thales. Investing in knowledge society through the European Social Fund.


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • K. Moraitis
    • 1
  • K. Tziotziou
    • 1
  • M. K. Georgoulis
    • 1
  • V. Archontis
    • 2
  1. 1.Research Center for Astronomy and Applied Mathematics (RCAAM)Academy of AthensAthensGreece
  2. 2.School of Mathematics and StatisticsSt. Andrews UniversitySt. AndrewsUK

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