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Description
We present the first part of a project on the global energetics of solar flares and coronal mass ejections that includes about 400 M- and X-class flares observed with Atmospheric Imaging Assembly (AIA) and Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO). We calculate the potential (E_p_), the nonpotential (E_np_) or free energies (E_free_=E_np_-E_p_), and the flare-dissipated magnetic energies (E_diss_). We calculate these magnetic parameters using two different NLFFF codes: the COR-NLFFF code uses the line-of-sight magnetic field component B_z_ from HMI to define the potential field, and the two-dimensional (2D) coordinates of automatically detected coronal loops in six coronal wavelengths from AIA to measure the helical twist of coronal loops caused by vertical currents, while the PHOT-NLFFF code extrapolates the photospheric three-dimensional (3D) vector fields. We find agreement between the two codes in the measurement of free energies and dissipated energies within a factor of <~3. The size distributions of magnetic parameters exhibit powerlaw slopes that are approximately consistent with the fractal-diffusive self-organized criticality model. The magnetic parameters exhibit scaling laws for the nonpotential energy, E_np_{propto}E_p_^1.02^, for the free energy, E_free_{propto}E_p_^1.7^ and E_free_{propto}B_{phi}_^1.0^L^1.5^, for the dissipated energy, E_diss_{propto}E_p_^1.6^ and E_diss_{propto}E_free_^0.9^ , and the energy dissipation volume, V{propto}E_diss_^1.2^. The potential energies vary in the range of E_p_=1x10^31^-4x10^33^erg, while the free energy has a ratio of E_free_/E_p_{approx}1%-25%. The Poynting flux amounts to F_flare_{approx}5x10^8^-10^10^erg/cm2/s during flares, which averages to F_AR_{approx}6x10^6^erg/cm2/s during the entire observation period and is comparable with the coronal heating rate requirement in active regions.
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