Constructing the Coronal Magnetic Field: by Correlating Parameterized Magnetic Field Lines with Observed Coronal Plasma Structures
The reconstruction of the coronal magnetic field is carried out using a perturbation procedure. A set of magnetic field lines generated from magnetogram data is parameterized and then deformed by varying the parameterized values. The coronal fluxtubes associated with this field are adjusted until the correlation between the field lines and the observed coronal loops is maximized. A mathematical formulation is described which ensures (1) that the normal component of the photospheric field remains unchanged, (2) that the field is given in the entire corona, (3) that the field remains divergence free, and (4) that electrical currents are introduced into the field. It is demonstrated that a simple radial parameterization of a potential field, comprising a radial stretching of the field, can provide a match for a simple bipolar active region, AR 7999, which crossed the central meridian on 1996 Nov 26. At a coronal height of 30 km, the resulting magnetic field is a non-force free magnetic field with the maximum Lorentz force being on the order of 2.6 x 10(exp -9) dyn resulting from an electric current density of $0.13 mu A/ sq m. This scheme is an important tool in generating a magnetic field solution consistent with the coronal flux tube observations and the observed photospheric magnetic field.