2007/06/27 by M. K. Georgoulis, Manolis K. Georgoulis, Barry J. LaBonte +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Classical mechanics #Computational physics #Geomagnetism and Paleomagnetism Studies #Helicity #Ionosphere and magnetosphere dynamics #Magnetic energy #Magnetic field #Magnetic helicity #Magnetization #Magnetohydrodynamics #Physics #Quantum electrodynamics #Quantum mechanics #Solar and Space Plasma Dynamics #astro-ph
paper · pdf · doi:10.1086/521417
44 pages, 8 figures, 2 tables. The Astrophysical Journal, in press
arxiv created 2007/06/27 · openalex publication_date 2007/12/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We self-consistently derive the magnetic energy and relative magnetic helicity budgets of a three-dimensional linear force-free magnetic structure rooted in a lower boundary plane. For the potential magnetic energy we derive a general expression that gives results practically equivalent to those of the magnetic virial theorem. All magnetic energy and helicity budgets are formulated in terms of surface integrals applied to the lower boundary, thus avoiding computationally intensive three-dimensional magnetic field extrapolations. We analytically and numerically connect our derivations with classical expressions for the magnetic energy and helicity, thus presenting a unified treatment of the energy/helicity budgets in the constant-alpha approximation that is lacking so far. Applying our derivations to photospheric vector magnetograms of an eruptive and a noneruptive solar active region, we find that the most profound quantitative difference between these regions lies in the estimated free magnetic energy and relative magnetic helicity budgets. If this result is verified with a large number of active regions, it will advance our understanding of solar eruptive phenomena. We also find that the constant-alpha approximation gives rise to large uncertainties in the calculation of the free magnetic energy and the relative magnetic helicity. Therefore, care must be exercised when this approximation is applied to photospheric magnetic field observations. Despite its shortcomings, the constant-alpha approximation is adopted here because this study will form the basis of a comprehensive nonlinear force-free description of the energetics and helicity in the active region solar corona, which is our ultimate objective.