The curlometer and other gradient measurements with Cluster

The four-spacecraft, magnetic field measurements on Cluster can produce an accurate determination of the electric current point by point in time (the Curlometer technique). For example, for planar events, the thickness of the current layer can be accurately estimated from its magnetic profile at each spacecraft and the corresponding boundary crossing times. The latter give a determination of boundary motion relative to the Cluster array. For a range of spacecraft separation distances, the estimate of electric current density can be representative even when the configuration of Cluster spacecraft approaches the thickness of the current layer. The magnitude of the current is often accurately represented and in principle can be tracked through any structure. Minimum variance analysis on the curlometer measurements can be used to estimate the normal to a current layer. Other methods exist which are based on estimation of the magnetic gradients, curvature, or temporal derivative. These methods can be used to calculate a number of other properties, such as the dimensionality of the structure and the corresponding velocity, the field curvature, or boundary normals, but have the commonality of providing a quantity at every moment in time, like the curlometer.