The coming 7 spacecraft Plasma Observatory and 9 spacecraft HelioSwarm will achieve 7–9 point magnetic measurements. In this study, a new algorithm is generated to calculate the linear and quadratic magnetic gradients from 7–9 point magnetic measurements so as to obtain the complete geometry of the magnetic structures observed. The tests have verified the feasibility of the method. The algorithm can thus be applied to the analysis of magnetic field data from Plasma Observatory and HelioSwarm.

Multiple spacecraft can operate jointly to detect quantities that are unattainable with a single spacecraft. Present constellations typically consist of four spacecraft, and it is established that a planar distribution of the spacecraft should be avoided. This study addresses the configuration problem for future missions of more spacecraft to measure physical gradients of higher orders. As for quadratic gradients, spacecraft must not be on any quadric surface, such as a sphere or cylinder.

In this paper, we propose a new explanation for shoulder-like formations based on the test particle model. The simulation reproduced three shoulders in a substorm case. The physical explanation of shoulder formation is not yet understood. The paper suggests that the physical mechanism of shoulder formation is the result of plasma extrusion in the predawn sector, caused by the outer plasmasphere drifting radially outward and rotating faster.