Curlometer and gradient techniques: past and future applications - Dunlop, M. W.; Fu, H.-S.; Shen, C.; Tan, X.; Dong, X.-C.; Yang, Y.-Y.; Robert, P.; Escoubet, C. P. (Frontiers in Astronomy and Space Sciences, 2024)
We review the range of applications and use of multi spacecraft techniques, applicable to close formation arrays of spacecraft, focusing on spatial gradient based methods, and the curlometer in particular. The curlometer was originally applied to Cluster multi-spacecraft magnetic field data, but later was updated for different environments and measurement constraints such as the NASA MMS mission, small-scale formation of 4 spacecraft; the 3 spacecraft configurations of the NASA THEMIS mision, and derived 2-4 point measurements from the ESA Swarm mission. In general, spatial gradient based methods are adaptable to a range of multi-point and multi-scale arrays. We also review the range of other techniques based on the computation of magnetic field gradients and magnetic field topology in general, including: magnetic rotation analysis and various least squares approaches. We review Taylor expansion methodology (FOTE), in particular, which has also been applied to both Cluster and MMS constellations, as well as interpretation of simulations. Four-point estimates of magnetic gradients are limited by uncertainties in spacecraft separations and the magnetic field, as well as the presence of non-linear gradients and temporal evolution. Nevertheless, the techniques can be reliable in many magnetospheric regions where time stationarity is largely applicable, or when properties of the morphology can be assumed (for example, the expected orientation of underlying large-scale structure). Many magnetospheric regions have been investigated directly (illustrated here by the magnetopause, ring current and field-aligned currents at high and low altitudes), and options for variable numbers of spacecraft have been considered. The comparative use of plasma measurements and possible new methodology for arrays of spacecraft greater than four are also considered briefly.