Modeling Magnetic Fields in the Solar Atmosphere
Anna Malanushenko

The Sun's ever-evolving magnetic field has a major influence on space weather. Coronal mass ejections, as well as solar flares, are believed to be a manifestation of major energy release in the solar atmosphere. The modeling of magnetic equilibria is crucial for understanding where, when and how the stored magnetic energy may be released. This modeling is, however, as challenging as it is important. In this talk, I will outline basic concepts of modeling the magnetic equilibria, and major difficulties arising for the modelers. Then, I will describe the tools I have developed with colleagues at Lockheed Martin Advanced Technology Center and Sydney Institute for Astronomy. The tools I describe solve the problem in a principally new way. They do not use full vector of magnetic field at the solar surface, where low-beta assumption can not be made. Instead, they draw information about currents directly from the region of interest: from the rarefied low-beta solar corona. The coronal loops, seen in Extreme Ultraviolet, or EUV, are believed to outline the magnetic field lines. Our modeling tools use loops to evaluate the three-dimensional distribution of currents along sparse set of trajectories in space. These trajectories are used as volume constraints for the magnetic field model, which is made to match the observed loops, while obeying the equilibrium equations as closely as possible. I will talk about validations of this model on test cases. I will then demonstrate the successful application of this tool to modeling actual coronal magnetic field, before and after a major eruptive event, and discuss what we can learn from the modeling.