On the effect of line current width and relative position on the multi-spacecraft curlometer technique

The response of the multi-spacecraft curlometer technique to variations in the size and relative position of infinitely long line currents with radially varying current density is systematically investigated for spacecraft in a regular tetrahedral formation. It is shown that, for line currents with a width less than the spacecraft separation, there is significant variation in the returned current with position of that current within the tetrahedron. For infinitely thin line currents, the curlometer tends to detect approximately 20% of the input current. For increasingly wide line currents there is less variation of the curlometer results with position of the current and the percentage of current magnitude detected increases. When the width of the current system is half the spacecraft separation, the curlometer tends to detect approximately 80% of the input current. These results are discussed in the context of multi-scale, multi-spacecraft missions.