ESA Science & Technology11-Jul-2005 14:35:45

Science Results

Measurement of the electric current

Magnetic field measured on the four spacecraft (C1 in black, C2 in blue, C3 in green and C4 in red) on 26 January 2001. The electric current is plotted in the fourth panel (From Robert and Roux et al., 2003).

The prime scientific objective of Cluster is to derive physical quantities, such as the electric current density that can only be obtained by combining measurements from the four spacecraft. A first example where this has been achieved was obtained close to the external boundary of the Earth's magnetic field, in a Flux Transfer Event (FTE). A FTE is a magnetic flux tube that is connected, by magnetic reconnection, on one side to the Earth and on the other side to the solar wind. Never before have these currents been measured with such precision and without any assumption about the current structure. This new finding has important implications for modelling these structures, and how energy flows from the solar wind to the magnetosphere.

Cluster measured the magnetic field (B) in an FTE on 26 January 2001. The modulus of B, which was about 25 nT before and after the event (a typical value for the magnetosheath), exceeds 50 nT inside the structure, just after 11:31. This large increase is one of the characteristic signatures of FTE's observed in the magnetosheath. The distance between the various satellites was about 600 km, and the Cluster tetrahedron was almost regular, a situation which is favourable for calculating curl B. Variations in the modulus of B, between the various satellites is small, less than 10%, which indicates that the size of the FTE is much larger than the distance between the spacecraft, as required to estimate curl B. There are, however, relatively large variations in the angles q and f, which is indicative of a rotational discontinuity. The result of the calculation of curl B, from the 4 tri-axial magnetometers, via the "curlometer" method, is displayed. There are two maximums in the modulus of the current density that reaches 25 nAm-2 (at 11:31:10) and 55 nAm-2 (at 11:31:50). Thus the current density is not homogeneous inside the FTE. Notice that the parallel component of the current dominates, and that it is negative, which means that the current, inside the two current density sub-structures, is antiparallel to B. The last panel shows the ratio divB/CcurlB. This ratio sometimes reaches unity, but it is small (around 0.2), when the current density is large. Further analysis, not described here, shows that the FTE is a cylindrical tube moving along the direction of a nominal magnetopause, the axis of the tube is in the azimuth direction. Thus the curlometer method, applied to the 4 spacecraft shows that the FTE is a force-free structure with the current flowing along an "hollow" tube.

The electric current has also been measured in other places like the solar wind in the heliospheric current sheet, at the magnetopause (2nd figure), and in the magnetotail inside a "flux rope" (3rd figure). These results have been published in Dunlop et al., J. Geophys. Res., 2002 and Slavin at al., Geophys. Res. Lett, 2002.

Electric current along the Cluster orbit and projected in XY plane.
The model magnetopause is shown in green dashed line and the
current in red. It is clear that the current is tangent to the
magnetopause as expected from theoretical models. The bursty
behavior of the current is due to the motion of the magnetopause
(from Dunlop et al., J. Geophys. Res., 2002)

Electric current density determined using the 4 s/c curlometer
technique (black) and the single s/c Lepping-Burlaga model (colour)
is displayed. The curlometer current density determination with the
four spacecraft showed that the flux rope was not completely
force-free as assumed by the single s/c models, but rather that the
parallel current was less than the perpendicular current over most
of the forward portion of the rope (from Slavin at al., Geophys. Res.
Lett, 2002).

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