Polynomial Reconstruction of the Reconnection Magnetic Field Observed by Multiple Spacecraft

We describe methods for polynomial reconstruction of the magnetic field close to a cluster of spacecraft and apply that to reconstruction of the magnetic field observed during a magnetic reconnection event on 10 August 2017 by the Magnetospheric Multiscale spacecraft. Four different models are described, which vary in complexity between a 12‐parameter linear model, which has only linear variation with respect to the spatial coordinates, and a 27‐parameter quadratic model, which has the full quadratic expansion except that the second derivative with respect to the Minimum Directional Derivative minimum gradient coordinate m has been neglected. In contrast to previous reconstruction techniques, these reconstructions can be found using only the magnetic field and current density measured at a single time by the cluster of spacecraft. The equations satisfying ∇·B=0 are satisfied exactly, while the equations specifying the model fields at the spacecraft locations are satisfied for most models in a best least squares sense. For this magnetotail event, the models have very small errors in magnetic field components (