Precise Calculation of Current Densities Via Four Spinning Spacecraft in a Tetrahedron Configuration

In certain regions of the Earth's magnetosphere the divergence and the curl of the magnetic field are vanishingly small. Four spacecraft that fly across such a region in a tetrahedron configuration may not observe vanishingly small divergence and curl of the magnetic field. This can be due to errors in magnetometer calibration and spacecraft orientation. We present new equations that minimize the divergence and the curl of the magnetic field by adjusting orientation as well as certain calibration parameters of the magnetometers. Our equations are roughly an order of magnitude more compact than the previously published equations (Khurana et al, 1996) and their derivation is more transparent. We apply the technique using data from all four Cluster spacecraft in regions where the divergence and curl are vanishingly small to improve measurements of these quantities. We also show that the importance of interspacecraft calibration increases with smaller separations of the spacecraft.