A New Three-Dimensional Empirical Reconstruction Model Using a Stochastic Optimization Method

Abstract

Motivated by MMS mission observations near magnetic reconnection sites, we have developed a new empirical reconstruction (ER) model of the three-dimensional (3D) magnetic field and the associated plasma currents. Our approach combines both the measurements from a constellation of satellites and a set of physics-based equations as physical constraints to build spatially smooth distributions. This ER model directly minimizes the loss function that characterizes the model-measurement differences and the model departures from linear or nonlinear physical constraints using an efficient stochastic optimization method by which the effects of random measurement errors can be effectively included. Depending on the availability of the measured parameters and the adopted physical constraints on the reconstructed fields, the ER model could be either slightly over-determined or under-determined, yielding nearly identical reconstructed fields when solved by the stochastic optimization method. As a result, the ER model remains valid and operational even if the input measurements are incomplete. Two sets of new indices associated respectively with the model-measurement differences and the model departures are introduced to objectively measure the accuracy and quality of the reconstructed fields. While applying the reconstruction model to observations of an electron diffusion region (EDR) observed by NASA’s Magnetospheric Multiscale (MMS) mission, we examine the relative contributions of the errors in the plasma current density arising from random measurement errors and linear approximations made in application of the curlometer technique. It was found that the errors in the plasma current density calculated directly from the measured magnetic fields using a linear approximation were mostly contributed from the nonlinear configuration of the 3D magnetic fields.