Abstract
It seems that the potential and linear force-free magnetic fields are inadequate to represent the observed magnetic events occurring in different regions of the solar corona. To reconstruct the nonlinear force-free fields from the solar surface magnetograms, various analytical and numerical methods have already been examined by different authors. Here, using the Lagrange multiplier technique, a constrained optimization approach for reconstructing force-free magnetic fields is proposed. In the optimization procedure the solenoidal property is considered as a constraint on the initial non-force-free field. In the Wheatland et al. (2000) method as an unconstrained optimization, both solenoidal and force-free conditions are fulfilled approximately. In contrast, the constrained optimization method, up to numerical precision, leads us to a nearly force-free magnetic field with exactly zero divergence. The solutions are obtained and tested by the Low and Lou (1990) semi-analytic solution.
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