Non-force-free extrapolation of solar coronal magnetic field using vector magnetograms

We report our recent improvement in non-force-free extrapolation of coronal magnetic field, using vector magnetograms. Based on the principle of minimum (energy) dissipation rate (MDR), a generally non-force-free magnetic field solution is expressed as the superposition of one potential field and two (constant-αconstant-α) linear force-free fields, with distinct αα parameters. With a known potential field, the system is reduced to a second-order one that can be solved using one single-layer vector magnetogram. We devise an iteration procedure to determine the potential field, by achieving satisfactory agreement between the MDR-model computed and measured transverse magnetic field vectors on the bottom boundary. We illustrate this approach by applying it to real magnetograph measurement of solar active region AR 10953. We show that the results are satisfactory as judged from the quantitative magnetic field measurement, and the behavior of the derived Lorentz force.