Curlometer and gradient techniques: application to multiscale studies

We revisit the use of multi-spacecraft techniques in range of applications applicable to close formation arrays of spacecraft, focusing on the curlometer, in particular, for both large and small-scale structures. 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, with small-scale 4 spacecraft formations; the 3 spacecraft configurations of the NASA THEMIS magnetospheric mission, and derived 2-4-point measurements from the ESA Swarm mission. Spatial gradient-based methods are adaptable to a range of multi-point and multi-scale arrays and conjunctions of these, and other, missions can produce distributed, spatial coverage with large numbers of spacecraft. 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 (giving certain applicability limits which can be mitigated by supporting information on morphology. Many magnetospheric regions have been investigated directly (illustrated here by the magnetopause, ring current and field-aligned currents at high and low altitudes). In addition, the analysis can support investigations of transient and smaller-scale current structures (e.g. reconnected flux tubes, boundary layer sub-structure, or dipolarisation fronts) and energy transfer processes. We anticipate the use of complementary information from imminent missions such as SMILE and the new EISCAT-3D radar.