The numerical results from a physics-based global magnetohydrodynamic (MHD) model are used to examine the effect of the interplanetary magnetic field (IMF), solar wind dynamic pressure, and dipole tilt angle on the size and shape of the magnetopause. The subsolar magnetopause is identified using the plasma velocity and density, the cusps are identified using the thermal pressure, and the whole shape of the magnetopause is determined with the three-dimensional streamlines traced through the simulation domain. The magnetopause surface obtained from the simulations is fitted with a three-dimensional surface function controlled by ten configuration parameters, which provide a description of the subsolar magnetopause, the cusp geometry, the flaring angle, the azimuthal asymmetry, the north-south asymmetry, and the twisting angle of the magnetopause. Effects of the IMF, solar wind dynamic pressure, and dipole tilt angle on the configuration parameters are analyzed and fitted by relatively simple functions. It is found that the solar wind dynamic pressure mainly affects the magnetopause size; the IMF mainly controls the magnetopause flaring angle, azimuthal asymmetry, and twisting angle; and the dipole tilt angle mainly affects the magnetopause north-south asymmetry and the cusp geometry. The model is validated by comparing with available empirical models and observational results, and it is demonstrated that the new model can describe the magnetopause for typical solar wind conditions.

In the analysis of in-situ space plasma and field data, an establishment of the coordinate system and the frame of reference, helps us greatly simplify a given problem and provides the framework that enables a clear understanding of physical processes by ordering the experimental data. For example, one of the most important tasks of space data analysis is to compare the data with simulations and theory, which is facilitated by an appropriate choice of coordinate system and reference frame. While in simulations and theoretical work the establishment of the coordinate system (generally based on the dimensionality or dimension number of the field quantities being studied) and the reference frame (normally moving with the structure of interest) is often straightforward, in space data analysis these are not defined a priori, and need to be deduced from an analysis of the data itself. Although various ways of building a dimensionality-based (D-based) coordinate system (i.e., one that takes account of the dimensionality, e.g., 1-D, 2-D, or 3-D, of the observed system/field), and a reference frame moving along with the structure have been used in space plasma data analysis for several decades, in recent years some noteworthy approaches have been proposed. In this paper, we will review the past and recent approaches in space data analysis for the determination of a structure's dimensionality and the building of D-based coordinate system and a proper moving frame, from which one can directly compare with simulations and theory. Along with the determination of such coordinate systems and proper frame, the variant axis/normal of 1-D (or planar) structures, and the invariant axis of 2-D structures are determined and the proper frame velocity for moving structures is found. These are found

The soft X-ray emissions from the Earth's magnetosheath and cusp regions are simulated under different solar wind conditions, based on the PPMLR-MHD code. The X-ray images observed by a hypothetical telescope are presented, and the basic responses of the magnetopause and cusp regions are discernable in these images. From certain viewing geometries, the magnetopause position in the equatorial plane, as well as the latitudinal scales and azimuthal extent of cusp can be directly extracted from the X-ray images. With these reconstructed positions, the issues we are able to analyze include but are not limited to the compression of magnetopause and widening of the cusp after an enhancement of solar wind flux, as well as the erosion of the magnetopause and equatorward motion of cusp after the southward turning of the interplanetary magnetic field. Hence, the X-ray imaging is an appropriate technique to study the large-scale motion of magnetopause and cusps in response to solar wind variations.Recently, a novel approach was proposed to remotely detect the large-scale magnetopause: soft X-ray imaging (Branduardi-Raymont et al., 2012Collier et al., 2012;Sibeck et al., 2018;Walsh et al., 2016). The basic mechanism for soft X-ray emissions in the magnetosheath and cusp regions is the solar wind charge exchange (SWCX) process. On the one hand, heavy ions in high charge states, such as O 7+ , exist in the ambient solar wind. On the other hand, neutral atoms and molecules, such as the hydrogen, are ubiquitous in the geospace environment due to the Earth's exosphere. When they encounter and interact with each other, an electron can be transferred from the neutral to the ion. As a result of capturing the electron, the solar wind ion is in an electronically excited state, and then emits one or more photons in the extreme ultraviolet or soft X-ray bands while decaying to the lower-energy state. In the magnetosheath, the density of the highly charged ions is enhanced as the solar wind slows down after the bow shock. The solar wind cannot directly penetrate the magnetopause, and thus, the plasma with solar wind origin is quite tenuous inside the magnetosphere. This leads to a sharp boundary at the magnetopause in terms of the soft X-ray emissivity. The cusps are special regions on the magnetopause. The solar wind plasma can enter directly, and thus, the X-ray emissivity is expected to be higher inside of the cusps. With different solar wind fluxes and/or interplanetary magnetic fields (IMF), the X-ray emissivity in the magnetosheath and cusps can be