Curlometer Technique and Applications

Abstract

We review the range of applications and use of the curlometer, initially developed to analyze 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. 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 covered, such as: the cross‐tail current sheet, ring current, the current layer at the magnetopause and field‐aligned currents. Transient and smaller scale current structures (e.g., reconnected flux tube 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 added inclusion of plasma measurements and the extension to larger arrays of spacecraft have recently been considered.

Ring current morphology from MMS observations

“…In fact, we have made a preliminary study of Cluster data selected from the 19 years of data (from 2001 to 2019) to check the overall context of the MMS epoch used here and show these results later in Figure 11. We note here that for Cluster data from 2015-16, corresponding to the MMS period, the RC densities show similar ordering to MMS (as in Figure 5 above), and the current density intensities broadly agree although slightly lower than MMS as would be expected from the larger separation scales of the Cluster configurations (Dunlop, 2021). Below, we therefore probe the morphology trends by averaging the binned median values over different ranges of MLT to obtain the trends of J⊥ (φ) as a function of L-shell (statistically) and, conversely, averaging the median values over different ranges of L to obtain trends of J⊥ (φ) as a function of MLT.…”

“…The current density is calculated here using the curlometer method (Dunlop et al 1988;Dunlop 2002;Dunlop et al 2021), based on a linear expression of Ampere's law, for regions of high conductivity, so that the current density normal to a plane composed of any three spacecraft can be expressed as…”

Joint Cluster/Ground‐Based Studies in the First 20 Years of the Cluster Mission

“…The potential for conjugate Cluster/Swarm/ground‐based observations has been discussed by Chulliat et al. (2017), and we highlight that conjugate Cluster/Swarm studies are discussed in another review in this special issue (Dunlop et al., 2021).…”

Simultaneous Mesoscale Polar Cusp Field‐Aligned Currents Measured on Mid‐ and Low‐Altitude Satellites

“…This indicates that the FACs can be assumed to be a large‐scale current sheet structure with their normal in the N direction. Due to the irregular tetrahedral shape of the four spacecraft such that the separation distance between the pairs C1, C2, and C3, C4 is much larger than the implied scale of the FACs (Figures 1a, 1b, and 1e), it follows that the four spacecraft curlometer method (Dunlop et al., 2002, 2021) is not accurate. Nevertheless, the distance between C3 and C4 in the northward direction ($${{\increment}R}_{N34}^{n}$$ ∼ 480 km) appears to be less than the main scale of the FACs in our case, so that the residual magnetic fields δ $${B}_{y}$$ of C3 and C4 both show similar trends and values, except with their profiles shifted by a time lag (Figure 1e).…”