Determining the full magnetic field gradient from two spacecraft measurements under special constraints

In this exploration, it is revealed for the first time that the full magnetic field gradient and current density distribution can be derived from two spacecraft magnetic field measurements under the assumptions that the magnetic field is approximately stationary and force-free, conditions which are particularly relevant to low altitude regions of the Earth's magnetosphere and in the regions containing the field aligned current systems. The magnetic field gradients along the spacecraft line, spacecraft velocity direction and the normal direction can be defined so that the full magnetic field gradient tensor is determined, projected into any coordinate system. One test for an ideal situation has been made, which confirms the validity of this approach with very high accuracy. This method can be applied to the determination of the magnetic field gradient tensor and current density for the forthcoming multispacecraft Swarm mission.