A practical approach to coronal magnetic field extrapolation based on the principle of minimum dissipation rate

We present a newly developed approach to solar coronalmagnetic field extrapolation from vector magnetograms, based on the principle of minimum dissipation rate (MDR). The MDR system was derived from a variational problem that ismore suitable for an open and externally driven system, like the solar corona. The resultingmagnetic field equation is more general than force-free. Its solution can be expressed as the superposition of two linear (constant-a) force-free fields (LFFFs) with distinct parameters, and one potential field. Thus, the original extrapolation problem is decomposed into three LFFF extrapolations, utilizing boundary data. The full MDR-based approach requires two layers of vector magnetograph measurements on the solar surface, while a slightly modified practical approach only requires one.We test both approaches against three-dimensional MHD simulation data in a finite volume. Both yield quantitatively good results. The errors in the magnetic energy estimate are within a few percent. In particular, the main features of relatively strong perpendicular current density structures, representative of the non-force-freeness of the solution, are well recovered.