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The solar active region magnetic field and energetics

Abstract Motivated by increasingly more advanced solar observations, we recently develop a method of coronal magnetic field extrapolation, especially for an active region (sunspot region). Based on a more complex variational principle, the principle of minimum (energy) dissipation rate (MDR), we adopt and solve a more complex equation governing the coronal magnetic field that is non-force-free in general. We employ the vector magnetograms from multiple instruments, including Hinode, NSO, and HSOS, and particularly observations at both photospheric and chromospheric levels for one active region. We discuss our results in the context of quantitative characterization of active region magnetic energy and magnetic topology. These quantitative analyses aid in better understanding and developing prediction capability of the solar activity that is largely driven by the solar magnetic field.