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Persistent URL http://purl.org/net/epubs/work/10773099
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Record Id 10773099
Title The Curlometer and other gradient based methods
Abstract The magnetic field measurements on the four Cluster spacecraft can be combined to produce a determination of the electric current density, j, point by point in time, from Ampere's law, i.e., through an estimate of the curl of the magnetic field, B, assuming the displacement current may be neglected (an assumption nearly always true in space plasmas). This combination of spatial gradients is named the Curlometer technique, first introduced by Dunlop et al. [1988], and first used on Cluster measurements by Dunlop et al. [2002b]. Although estimates of current density from single and dual spacecraft have been attempted in the past [e.g. van Allen and Adnan, 1992] (a simple 1-D current layer, sampled from an individual spacecraft, can at least give an estimate of the current magnitude), these estimates also depend on accurate knowledge of relative orientation and motion in order to obtain positions within a current layer (the finite region where the cur- rent density is distributed). The Curlometer technique independently estimates the current vector at each time in the data stream and can be understood in a number of different ways, as outlined in Chapters 12, 14, 15, and 16 of ISSI SR-001. In using the Curlometer, a clear understanding of the associated caveats is important, the main one being that only linear estimates of B and B can be made. Multi-spacecraft analysis also depends upon temporal behaviour, and most methods assume some degree of stationarity in their interpretation. The Curlometer is an important part of the analysis of spatial gradients as measured by four spacecraft, and this general problem was addressed in part in ISSI SR- 001. A number of additional methods have since been introduced which are also based on the use of spatial gradients and we also deal briefly with these below, or reference them. The four Cluster spacecraft fly in an evolving configuration, which repeats every or- bit (apart from minor perturbations), but which has been changed at intervals during the mission to cover a large range of spacecraft separation distances (100-10,000 km) at the magnetopause and in the magnetotail. The results presented here therefore have been con- firmed over a variety of spatial scales, and have been used in a number of different investigations, and below we list those papers that have used the technique in these circumstances. Through these studies, an understanding of the applicability of the method has developed. For example, the thickness of a planar current layer can be accurately estimated from its magnetic profile at each spacecraft and the corresponding boundary crossing times; the latter also giving a determination of boundary motion relative to the Cluster array, which scales the corresponding current profile through the current layer. The estimate of electric current density can be representative even when the configuration of Cluster spacecraft approaches the thickness of the current layer and minimum variance analysis on the Curlometer measurements can estimate the current normal. The other gradient methods can be used to calculate a number of other properties, such as the dimensionality of the structure.
Organisation SSTD , STFC , SSTD-SP
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Language English (EN)
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Book Chapter or Section In Multi-Spacecraft Analysis Methods Revisited. ISSI Science Report SR-008 edited by G. Paschmann and P.W. Daly, 17-26. Kluwer Academic Pub, 2008. 2008