Can we derive the current density from three point LEO measurements of the magnetic field perturbations?

Matthew Potter1, Jesper W Gjerloev2, Marc Muhleisen3, Matthew Michael Friel3, Polly Martin3, Guan Le4, Claudia Stolle5 and Hermann Luhr6, (1)Applied Physics Laboratory Johns Hopkins, Laurel, MD, United States, (2)Johns Hopkins University Applied Physics Laboratory, Laurel, United States, (3)Georgetown Day School, Washington DC, DC, United States, (4)NASA Goddard Space Flight Center, Greenbelt, MD, United States, (5)Leibniz Institute of Atmospheric Physics at the University of Rostock, Kühlungsborn, Germany, (6)Helmholtz Centre Potsdam GFZ German Research Centre for Geosciences, Potsdam, Germany
Abstract:
In this paper, we perform critical test of the well-known curlometer technique. The curlometer technique allows a derivation of the current density using measurements of the magnetic field at spatially separated points. At LEO altitudes this generally three dimensionally problem is simplified to a two dimensions by the fact that the current is almost solely flowing along the magnetic field lines. Strictly speaking the current density is derived from integration around a closed loop but in the curlometer technique this integration is simplified to a summation over just three points. In this paper we present a critical analysis of when and to what extend this approximation is valid. We show some simple theoretical considerations, results from a series of simulations, and finally apply the knowledge to ESA SWARM measurements.
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