Four‐point Cluster application of magnetic field analysis tools: The Curlometer

Abstract

For the first time, the Cluster spacecraft have collected 3‐D information on magnetic field structures at small to medium scales in the Earth's dayside magnetosphere. We focus here on the first application of the Curlometer (direct estimation of the electric current density from curl(B), using measured spatial gradients of the magnetic field) analysis technique. The applicability of this multipoint technique is tested, for selected events within the data set, in the context of various mission constraints (such as position, timing, and experimental accuracy). For the Curlometer, nonconstant spatial gradients over the spacecraft volume, time dependence, and measurement errors can degrade the quality of the estimate. The estimated divergence of the magnetic field can be used to monitor (indirectly) the effect of nonconstant gradients in the case of many magnetic field structures. For others, and at highly distorted spacecraft configurations, this test may not reflect the quality of the Curlometer well. The relative scales and relative geometry between the spacecraft array and the structures present, as well as measurement errors, all are critical to the quality of the calculation. We demonstrate that even when instrumental and other errors are known to contribute to the uncertainty in the estimate of the current, a number of current signatures within the magnetosphere can be plausibly determined in direction, if not absolute size. A number of examples show consistent currents at the magnetopause, both separate from, and nearby or in the cusp region. Field‐aligned currents near the polar cap boundary are also estimated reliably. We also demonstrate one example of an anomalous current arising from the effect of a highly distorted spacecraft configuration.

Cluster observations of continuous reconnection at the magnetopause under steady interplanetary magnetic field conditions

“…The MP current density at these MP crossings is of the order of 50 nA/m 2 which is rather typical (Dunlop et al, 2002). This translates to a differential electron-ion motion of 20 km/s, compared to the 200 km/s flow acceleration.…”

“…This implies an ion-electron differential motion of ∼20 km/s, which is small compared to the 200 km/s flow enhancements at the MP. Since this MP current density value is rather typical (Dunlop et al, 2002), the use of ions instead of electrons is unlikely to be the source for previous sub-Alfvénic flow cases.…”

“…2c). The current density is computed from ∇×B using magnetic field measurements from all 4 spacecraft (Dunlop et al, 2002).…”

Energy conversion regions as observed by Cluster in the plasma sheet

“…[29] The full current density vector, J, is calculated from r × B/m 0 (neglecting the displacement current) by using the curlometer method [Robert et al, 1998;Dunlop et al, 2002]. The size and shape of the Cluster tetrahedron affect the curlometer estimate, and current density structures smaller than the characteristic size of the tetrahedron cannot generally be resolved with the curlometer.…”

Statistical survey of day-side magnetospheric current flow using Cluster observations: Bow shock

“…25 Dunlop et al (2001) pointed out that high frequency fluctuations are likely to cause uncertainties within the Curlometer results and suggest an appropriate averaging in time before applying the Curlometer to magnetic field data. Regarding the bow shock crossing events examined in this study an averaging window of 30 s proved to be sufficient to damp highly fluctuating current signatures with spatial dimensions far below the tetrahedron size without altering current structures having dimensions of about 50 km and more along the spacecraft trajectory to a significant extent.…”