Polynomial Reconstruction of the Reconnection Magnetic Field Observed by Multiple Spacecraft

Abstract

AbstractWe 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 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 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 ( 0.1 nT) at a distance from the nearest spacecraft on the order of the spacecraft separation, , here equal to 20.5 km. The magnetic structures found using the quadratic models are very time dependent, with a stretched field leading to plasmoid formation at one point in time.