Modeling Solar Magnetic Field In The Solar Corona From The View Of Magnetic Helicity

Modeling Solar magnetic field in the corona is very important to understand the solar eruption and heating mechanism. However, the direct measurements of solar magnetic field in the solar corona is still taking a great challenge not only in the high accurate measurements of solar polarization signal, but also in the inversion approach for the Optic-thin condition of corona atmosphere. Existence and uniqueness in the force-free/Non-force-free extrapolation in the solar corona is still unknown. Magnetic helicity, as a topological invariant, has become a key factor in exploring the generation of magnetic fields within the Sun, solar eruptions, and energy transfer processes in interplanetary. We firstly give a short review of modelling magnetic helicity in the solar corona from the observation to simulation. Then we introduce a new method by calculating the potential current in a magnetic-helicity-conservation-decomposed approach to derive the magnetic helicity/energy equivalence of three-dimension magnetic field only based on the photospheric vector magnetogram. We testify our method by using the given magnetic field of Low and Lou (1990) and the difference is very small. Even though, the Lorentz force caused from the calculated magnetic field well explained the strong shearing movements of polarity inversion line (PIL) in the newly emerging active region of NOAA11158. Finally, we apply our method to the observation data and it is also successfully found that the weak/strong loss ratio of magnetic helicity in the solar confined/eruptive solar events.