Multiple flux rope events at the high-latitude magnetopause on January 26, 2001: Current density calculating

A systematic comparison is carried out for three Methods of current density calculating based on simultaneous magnetic field measurements of four-spacecraft Cluster mission. Analytically and numerically demonstrated that within the linear approximation, all these methods lead to the exactly the same results. As a case study, the current density of multiple flux rope events at the high-latitude magnetopause on January 26, 2001 is investigated. It is showed that an intense current flows inside the ropes with the current density reaching as high as about 10^-8 A/m² . The current inside rope is valuable for the small relative calculating error. It is also found that the directory of current is almost parallel the axis of flux rope gotten by magnetic minimum variance analysis (MVA). It is supposed the current MVA method is useful and simply for the rope axis orientation.