Cluster electric current density measurements within a magnetic flux rope in the plasma sheet

On August 22, 2001 all 4 Cluster spacecraft nearly simultaneously penetrated a magnetic flux rope in the tail. The flux rope encounter took place in the central plasma sheet, Beta(sub i) approx. 1-2, near the leading edge of a bursty bulk flow. The "time-of-flight" of the flux rope across the 4 spacecraft yielded V(sub x) approx. 700 km/s and a diameter of approx.1 R(sub e). The speed at which the flux rope moved over the spacecraft is in close agreement with the Cluster plasma measurements. The magnetic field profiles measured at each spacecraft were first modeled separately using the Lepping-Burlaga force-free flux rope model. The results indicated that the center of the flux rope passed northward (above) s/c 3, but southward (below) of s/c 1, 2 and 4. The peak electric currents along the central axis of the flux rope predicted by these single-s/c models were approx.15-19 nA/sq m. The 4-spacecraft Cluster magnetic field measurements provide a second means to determine the electric current density without any assumption regarding flux rope structure. The current profile determined using the curlometer technique was qualitatively similar to those determined by modeling the individual spacecraft magnetic field observations and yielded a peak current density of 17 nA/m2 near the central axis of the rope. However, the curlometer results also showed that the flux rope was not force-free with the component of the current density perpendicular to the magnetic field exceeding the parallel component over the forward half of the rope, perhaps due to the pressure gradients generated by the collision of the BBF with the inner magnetosphere. Hence, while the single-spacecraft models are very successful in fitting flux rope magnetic field and current variations, they do not provide a stringent test of the force-free condition.