reconstructing a helical magnetic field in the solar corona using lagrange multiplier technique

We aim to reconstruct a nonlinear force-free magnetic field by minimizing the global departure of an initial field from a force-free and solenoidal state in the presence of helicity to obtain an appropriate representation of the magnetic field compatible with the solar coronal condition. following the wheatland et al method we modify their functional to include the magnetic helicity using the lagrange multiplier technique. we reconstruct the magnetic field by minimizing the new functional in a computational box whose lower side coincides with the artificial magnetogram on the photosphere while the lateral and top sides extends up to the corona and by assuming appropriate boundary conditions for the lagrange multiplier. the artificial magnetogram is obtained by low and lou semi-analytical solutions. a potential field as well as a suitable ansatz is used for the initial input magnetic filed and lagrange multiplier for the iteration procedure, respectively. the results obtained by different optimization methods are in agreement with those obtained by our approach.