Determination of the Configurations of Boundaries in Space

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 R-E, and the dawn-dusk/azimuthal scale is about 1.58-1.92 R-E, confirming previous studies. The method presented can also be applied to investigate the geometries of the magnetopause, plasmapause, and other boundaries.