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Calculating currents from four spacecraft

1 May 2011

Artist's impression of the Cluster quartet. (c) ESA

Ampere's law tells us that the curl of a magnetic field is proportional to current density. In order to measure the curl of a magnetic field in space, one needs to know approximate the variation of the magnetic field between four non-coplanar points. Such measurements are achieved by the Cluster quartet.

Whilst the overall magnetospheric shape is described by current sheets, many of the dynamic features of the magnetosphere are connected with smaller, field-aligned current systems. These can have a variety of shapes and sizes. In order to understand these current systems, it is necessary to model how Cluster might observe these current systems.

Forsyth et al. (2011) uses infinitely long, circular current tubes over across which the current density varied to investigate how Cluster might observe these current systems and how these observations vary with the relative size of the spacecraft quartet to the current system. Their results show that although currents smaller than the spacecraft quartet are detected, the current density determined varied with the position of the current system through the spacecraft tetrahedron. They also found that the standard indicator of the quality of the curlometer results indicated good values for the determination of the current even when currents were detected outside of the spacecraft tetrahedron. These results highlight the need for care and careful analysis when analysing currents in the magnetosphere.

Figure adapted from Forsyth et al. (2011) showing the current density determined by the curlometer for an infinitely long, infinitely thin current at different locations around the spacecraft tetrahedron
Figure adapted from Forsyth et al. (2011) showing the current density determined by the curlometer for an infinitely long, infinitely thin current at different locations around the spacecraft tetrahedron

For more information, see:

Forsyth, C and Lester, M and Fazakerley, AN and Owen, CJ and Walsh, AP (2011) On the effect of line current width and relative position on the multi-spacecraft curlometer technique. PLANET SPACE SCI , 59 (7) 598 - 605 doi:10.1016/j.pss.2009.12.007.

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