Separable Solutions of Force-Free Spheres and Applications to Solar Active Regions

摘要: We present a systematic study of the force-free field equation for simple axisymmetric configurations in spherical geometry and apply it to solar active regions. The condition separability solutions radial angular variables leads two classes solutions: linear nonlinear fields (NLFF). have studied these extended power law index irreducible rational form n = p/q, which is allowed all cases odd p q > even p, where poloidal flux ψ∝1/r{sup n} B∝1/r {sup n+2}. simulate photospheric vector magnetograms obtained using spectropolarimeter on board Hinode. effectiveness our search strategy first demonstrated test inputs dipolar, axisymmetric, nonaxisymmetric fields. Using best fit, we build three-dimensional calculate energy relative helicity with independent methods, are agreement. analyzed five AR 10930 spanning period three days during X-class flares occurred found free region before aftermore » flare; analysis indicates peak quantities flare events, consistent other results. also single-polarity regions 10923 10933, showed very good fits potential This method provides useful reconstruction NLFF input numerical techniques.« less