Efficient and Automated Inversions of Magnetically-Sensitive Forbidden Coronal Lines: CLEDB -- The Coronal Line Emission DataBase Magnetic Field Inversion Algorithm

We present CLEDB, a "single point inversion" algorithm for inferring magnetic parameters using I,Q,U, and V Stokes parameters of forbidden magnetic dipole lines formed in the solar corona. We select lines of interest and construct databases of Stokes parameters for combinations of plasma thermal and magnetic configurations. The size and complexity of such databases are drastically reduced by taking advantage of symmetries. Using wavelength-integrated line profiles, each of which might be decomposed beforehand into several line-of-sight components, we search for nearest matches to observed Stokes parameters computed for the elongation corresponding to the observed region. The method is intended to be applied to two or more lines observed simultaneously. The solutions initially yield magnetic orientation, thermal properties, and the spatial position of the emitting plasma in three dimensions. Multiple possible solutions for each observation are returned, including irreducible degeneracies, where usually sets of two solutions are compatible with the two input I,Q,U, and V measurements. In solving for the scattering geometry, this method avoids an additional degeneracy pointed out by Dima & Schad (2020). The magnetic field strength is separately derived from the simple ratio of observed to database Stokes V data, after the thermal properties and scattering geometry solutions have been determined.