Progress in Solar Magnetic Field Extrapolation

Solar magnetic field is the predominant factor of the solar activities.Precise measurements of solar magnetic fields so far are still confined to the thin layer of solar photosphere.In order to understand the nature of the coronal magnetic fields, it becomes necessary to extrapolate the coronal magnetic fields based on theoretical models using observed photospheric magnetograms as boundary conditions.Taking force-free assumptions, three kinds of models are currently being used the potential field (or current-free field)model, the linear force-free field (or constant-αforce-free field)model, and the non-linear force-free (NLFF)field (or non-constant-αforce-free field)model.Methods of extrapolations based on these three models are introduced, with specific examples given and their astrophysical applications mentioned.Progress and problems in the extrapolation methods are also briefly addressed.