Topological configurations of the magnetic field play key roles in the dynamics of space plasmas. This study presents a novel algorithm that can estimate the quadratic magnetic gradient as well as the complete geometrical features of magnetic field lines, based on magnetic field and current density measurements by a multiple spacecraft constellation at four or more points. The explicit estimators for the linear and quadratic gradients, the apparent velocity of the magnetic structure and the curvature and torsion of the magnetic field lines can be obtained with well‐predicted accuracies. The feasibility and accuracy of the method have been verified with two demonstrations. The algorithm has been successfully applied to exhibit the geometrical structure of a flux rope. This algorithm has wide applications for studying a variety of magnetic configurations in space plasmas.

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.

Geometrical invariants of magnetic field gradient tensors are used to classify the topological structures of a magnetic field. This study presents a statistical analysis on the geometrical invariants of magnetic field gradient based on high-quality data measured by magnetospheric multiscale mission in turbulent magnetosheath. The method for the classification of velocity field topologies cannot be applied to magnetic field with strong intensity directly because the magnetic field cannot be transformed to zero by selecting a co-moving reference frame in which the velocity is zero. During a strong magnetic field, flux ropes and tubes are the most possible magnetic structures. Statistics in the plane formed by geometrical invariants show that about 23% are force-free structures comprised of 20.5% flux tubes and 79.5% flux ropes. The remaining actively evolved structures are comprised of 30% flux tubes and 70% flux ropes. Moreover, the conditional average of current density and Lorentz force decomposition in geometrical invariants plane are investigated. The results show that flux ropes carried more current density than flux tubes for the same geometrical invariants, and flux ropes tend to associate with magnetic pressure force and flux tubes tend to associate with magnetic tension.

This research explores the relationship between the temperatures of the solar corona and planetary magnetosheaths. Based on the second law of thermodynamics, the maximum temperature of the planetary magnetosheaths cannot exceed that of the solar corona. A theoretical investigation is presented into the expansion of the solar corona, the propagation of solar wind, and the compression of planetary magnetosheaths by bow shocks. The method used is general and fits the dynamics of multiple components, thermal anisotropy, and non‐Maxwellian plasmas in the steady state, and approximate formulas are obtained. The results indicate that, for the steady state, planetary magnetosheaths at the subsolar points in the solar system have approach peak mean temperatures. Second, a systematic statistical survey of the average temperature of the planetary magnetosheaths is presented and shows that the average plasma temperature of the subsolar point magnetosheaths of Earth and Saturn are 206 eV (2.39 MK) and 171 eV (1.98 MK), respectively, which are close to that of the corona. The statistical results are consistent with the theoretical estimations. These results are of significant use for estimating the thermal properties of the planetary magnetospheres.

We studied the thermal features of magnetized plasmas in the Martian subsolar magnetosheath using MAVEN’s observations from 2014 to 2019. Statistical analyses show that the average ion and electron temperature in the Martian subsolar magnetosheath are 210 and 31 eV, respectively, which are significantly lower than their counterparts in the subsolar magnetosheaths of Earth and Saturn which both have an inherent magnetosphere. However, the ratio ${\overline{T}}_i/{\overline{T}}_e$ in the Martian subsolar magnetosheath is about 6.8, which is very close to that of Earth and Saturn. We further investigated the relationship between $T_i/T_e$ and the bulk ion flow velocity $V_i$, as well as the relationship between the total plasma beta $\beta$ and $V_i$. Results show that the average value of $T_i/T_e$ when $V_i<300\mathrm{km}/\mathrm{s}$ is considerably higher than when $V_i>300\mathrm{km}/\mathrm{s}$. A value of $V_i$ closer to 250–300 km/s leads to a higher average value of the total plasma beta $\beta$. These results confirm the prediction of previous researchers, that there is not enough room for solar wind thermalization as the distance between the Martian bow shock and the so-called obstacle is of the order of a solar wind proton gyroradius.

Topological configurations of the magnetic field play key roles in the evolution of space plasmas. This paper presents a novel algorithm that can estimate the quadratic magnetic gradient as well as the complete geometrical features of magnetic field lines, based on magnetic field and current density measurements by a multiple spacecraft constellation at 4 or more points. The explicit estimators for the linear and quadratic gradients, the apparent velocity of the magnetic structure and the curvature and torsion of the magnetic field lines can be obtained with well predicted accuracies. The feasibility and accuracy of the method have been verified with thorough tests. The algorithm has been successfully applied to exhibit the geometrical structure of a flux rope. This algorithm has wide applications for uncovering a variety of magnetic configurations in space plasmas.