Empirical model of the Earth's cusp at low-altitudes

The Earth's cusp is a critical "window" for the solar wind plasma to enterthe low-altitude magnetosphere and ionosphere. However, the overall configuration of cusp has not been established. Based on the simulation of two successive substorms on 8 March 2008, we propose a 2D model of low-altitude (1.1 R_E) cusp modulated by the interplanetary magnetic field (IMF) B_Y and B_Z. This model is constructed from curve fitting of low-altitude cusp with an elliptic function controlled by the cusp center and width, which is dependent on IMF B_Y and B_Z. The plasma thermal pressure P_T derived from the simulation data is used to extract the cusp center on the sphere surface with a radius of 6 R_E. The cusp center is defined as where P_T reaches the maximum, and the cusp boundary is identified as where P_T decreases to 68% of that at the cusp center. After the high-altitude cusp has been determined, the low-altitude (0.1 R_E altitude in the ionosphere) cusp can be obtained from mapping the high-altitude cusp along the magnetic field lines. The coordinate system of the low-altitude cusp used throughout this paper is the magnetic coordinate. The low-altitude cusp extracted from simulations is fitted with the elliptic function controlled by cusp location and width. The cusp geomagnetic latitude (MLAT) increases gradually with northward IMF B_Z but decreases significantly with southward IMF B_Z. The local magnetic time (MLT) is nearly 12 when B_Y = 0, corresponding to the observation results. When IMF B_Y is duskward (dawnward), the cusp center will locate at the post-noon (pre-noon) sector in the northern hemisphere. The MLAT width decreases as IMF B_Z swings from north to south, and the MLT width is the opposite. This model is validated by comparing with observations from DMSP satellites during this concerning time interval. Based on this 2D model of low-altitude cusp, the 3D cusp could be obtained further, which would help to space weather prediction.