Study on the Curvature and Gradient of the Magnetic Field in Earth's Cusp Region Based on the Magnetic Curvature Analysis Method

This paper uses the multiple-point magnetic measurements from the Cluster mission to investigate the curvature and gradient of the magnetic field as well as their relations with the current density inside the cusp region under different interplanetary magnetic field (IMF) conditions. From two event studies, it is shown that the curvature radius of magnetic field line is on average 5.13 R_E under southward IMF and 19.75 R_E under northward IMF condition. The directional angle of curvature is more distributed in a wider range under southward condition. The gradient of the magnetic field strength B is larger with a larger standard deviation under southward IMF condition. These results imply that the cusp region has more complicated magnetic structures under southward IMF condition. Through the correlation analysis between the magnetic field parameters and the current density, it is found that the magnetic gradient has a strong relation with total current density j_t and perpendicular current density j_⊥ when the ratio of parallel component j_// to j_t decreases, possibly due to gradient B drift. Furthermore, we present a statistical study on the 19 cusp crossing events from July 2003 to September 2003. The results from the statistical study are consistent with the event studies.