Determination of the Configurations of Boundaries in Space

• Published in: Journal of geophysical research. Space physics 2020-09, Vol.125 (9), p.n/a
• Main Authors: Shen, Chao, Zeng, Gang, Zhang, Chi, Rong, Zhaojin, Dunlop, M., Russell, C. T., Escoubet, C. Philippe, Ren, Nian
• Format: Article
• Language: English
• Subjects: Aerospace environments; Boundaries; Boundary layers; bow shocks; Configurations; curvatures of the surfaces; dipolarization fronts; Earth bow shock; Fronts; geometry of surfaces; Magnetopause; Magnetotails; normal of a surface; Parabolic bodies; Plasmapause; Space plasmas; Spacecraft
• ISSN: 2169-9380; 2169-9402
• DOI: 10.1029/2020JA028163

This research aims to determine the geometrical configurations of boundary surfaces in the space environment, based on multiple spacecraft measurements. To achieve this, the Normal Field Analysis (NFA) method is presented here. With multipoint observations, the three‐dimensional gradient of the normal of boundary layers can be obtained, and the principal curvatures and principal directions of the surfaces can be deduced. The correctness of the method is then verified. Two initial applications have been carried out. The first is to determine the geometrical features of the Earth's bow shock where it is found that, with a one‐dimensional approximation, the surface of the bow shock has a rotational conicoid shape with eccentricity about 0.82, consistent with previous studies. Second, the method is also used to analyze two magnetotail dipolarization fronts showing that the dipolarization fronts are hyperbolic paraboloids or saddle surfaces with negative Gaussian curvatures. The south‐north scale of the dipolarization fronts is about 0.835–3.98 RE, and the dawn‐dusk/azimuthal scale is about 1.58–1.92 RE, confirming previous studies. The method presented can also be applied to investigate the geometries of the magnetopause, plasmapause, and other boundaries. Plain Language Summary Boundary layers commonly exist in space plasma environments and play important roles in the dynamical evolution of physical processes in space. In this research, we have presented an efficient method for determining the geometry of boundary surfaces, based on Cluster and MMS multispacecraft measurements. From multipoint measurements of the normal to boundaries, the gradient of the normal is obtained, and the principal curvatures of the surface can be deduced. Initial applications have been made for the determination of the geometrical features of the Earth's bow shock and magnetotail dipolarization fronts, confirming the efficiency of the new method. The method presented can also be applied to investigate other boundaries such as the magnetopause and plasmapause. Key Points Non‐Euclid geometry is used for determining the local geometrical features of the boundary surfaces based on multiple‐point measurements The method is successfully applied to deduce the average configuration of the Earth's bow shock, as well as its curvature This method can quantitatively obtain the geometrical features of the magnetotail dipolarization fronts