Solar Magnetic Helicity

Helicities is topologically a measure of the structural complexity of the corresponding fields. The magnetic helicity can be separated into two kinds. One is the self helicity, which relates to the magnetic flux tubes twisted themselves. This helicity may be used to analyze the twisted magnetic flux loops. Another one is the mutual helicity, which relates to the different magnetic flux tubes linked to each other. The magnetic helicity Hm and current helicity Hc can be written in the form Hm=∫vhmd x=∫vA•Bd x and Hc=∫vhcd x=∫vB•▽×Bd x where A is the magnetic potential, B is the magnetic field and hc is defined as current helicity density. It is known that most of the magnetic helicity in the solar atmosphere concentrates in the solar active regions. Since the operation of the Huairou Solar Observing Station of the CAS National Astronomical Observatories took off in 1984, a series of vector magnetograms of solar active regions have been observed by the Solar Magnetic Field Telescope. Hence, we have seized a chance to study the magnetic helicity of solar active regions systematically (Figure 1). The synthetic analysis of magnetic helicity in solar active regions is important for understanding the basic topology of magnetic field in solar atmosphere and the relationship with solar flare-coronal mass ejections process (cf. Bao et al., 1999; Deng et al., 2001; Liu and Zhang, 2002; Zhang et Solar Magnetic Helicity