Parametric Transformation Analysis

Because twisted coronal features are important proxies for predicting solar eruptive events, and, yet not clearly understood, we present new results to resolve the complex, non-potential magnetic field configurations of active regions. This research uses free-form deformation mathematics to generate the associated coronal magnetic field. We use a parametric representation of the magnetic field lines such that the field lines can be manipulated to match the structure of EUV and SXR coronal loops. The objective is to derive sigmoidal magnetic field solutions which allows the beta greater than 1 regions to be included, aligned and non-aligned electric currents to be calculated, and the Lorentz force to be determined. The advantage of our technique is that the solution is independent of the unknown upper and side boundary conditions, allows non-vanishing magnetic forces, and provides a global magnetic field solution, which contains high- and low-beta regimes and is consistent with all the coronal images of the region. We show that the mathematical description is unique and physical.