Curlometer technique and applications

We review the range of applications and use of the curlometer, initially developed to analyze electric current density using Cluster multi-spacecraft magnetic field data; but more recently adapted to other arrays of spacecraft flying in formation, such as MMS small-scale, 4-spacecraft configurations; THEMIS close constellations of 3-5 spacecraft, and Swarm 2-3 spacecraft configurations. The method (and associated methods based on spatial gradients) has been shown to be easily adaptable to other multi-point and multi-scale arrays. Although magnetic gradients require knowledge of spacecraft separations and the magnetic field, the structure of the electric current density (for example, its relative spatial scale), and any temporal evolution, limits measurement accuracy. Nevertheless, in many magnetospheric regions the curlometer is reliable (within certain limits), particularly under conditions of time stationarity, or with supporting information on morphology (for example, when the geometry of the large scale structure is expected). A number of large-scale regions have been investigated directly, such as: the cross-tail current sheet, ring current, the current layer at the magnetopause and field-aligned currents. 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. The method is able to provide estimates of single components of the vector current density, even if there are only two or three satellites flying in formation, within the current region, as can be the case when there is a highly irregular spacecraft configuration. The computation of magnetic field gradients and topology in general includes magnetic rotation analysis and various least squares approaches, as well as the curlometer, and indeed the combination with plasma measurements and the extension to larger arrays of spacecraft have recently been considered. We touch on these extensions and on new methodology accessing the properties of the underlying formulism.