Magnetic energy, Eq. (16), normalized to the energy of the corresponding potential field (black lines, zoom of Fig. 2), and energy associated to the nonsolenoidal part of BJ, normalized to the energy of Btest (red lines, equal to EJ,ns/E in the notation of Eq. (8)), as a function of the amplitude δ of the nonsolenoidal term, Eq. (14). Two models for the divergence are shown according to Eq. (15). Each panel shows the results of a test field: a) the potential field of a double dipole, BDD; b) the TD model, BTD; c) the MHD model, BMHD; d) the NLFFF model of the nonpreprocessed magnetogram of AR 11158, BEx1; e) the NLFFF model of the preprocessed magnetogram of AR 11024, BEx2PP; f) the NLFFF model of the nonpreprocessed magnetogram of AR 11024, BEx2. The black dash-dotted line at E/Ep = 1 marks the value below which the solution is unphysical. A large change of scale of both axes is present between the top and the bottom rows.
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