On the current state of the development of the magneto-hydro-static extrapolation method

Modeling the three-dimensional (3D) magnetic fields of the solar active region in multiple layers is very important. The main approach is to extrapolate the magnetic field from magnetograms measured in the photosphere. A basic assumption of the modeling in the past several decades was to completely neglect all plasma effects and to perform the so-called force-free field (FFF) extrapolations. While the force-free assumption is well justified in the solar corona, it is not the case in the photosphere and chromosphere. A magneto-hydro-static (MHS) equilibrium which takes into account plasma forces, such as pressure gradient and gravitational force, is considered to be more appropriate to describe the lower atmosphere and has been developing rapidly during the past several years. In this talk, I am going to review various MHS modeling methods, including tests of these methods with known reference models and applications to real data. Recent developments of the MHS modeling will also be presented.