We present a reconstruction technique to solve the steady resistive MHD equations in two dimensions with initial inputs of field and plasma data from a single space- craft as it passes through a coherent structure in space. At least two components of directly measured electric fields (the spacecraft spin-plane components) are required for the reconstruction, to produce two-dimensional (2-D) field and plasma maps of the cross section of the structure. For con- venience, the resistivity tensor η is assumed diagonal in the reconstruction coordinates, which allows its values to be es- timated from Ohm’s law, E+v×B=η·j. In the present paper, all three components of the electric field are used. We benchmark our numerical code by use of an exact, axi- symmetric solution of the resistive MHD equations and then apply it to synthetic data from a 3-D, resistive, MHD numer- ical simulation of reconnection in the geomagnetic tail, in a phase of the event where time dependence and deviations from 2-D are both weak. The resistivity used in the simu- lation is time-independent and localized around the recon- nection site in an ellipsoidal region. For the magnetic field, plasma density, and pressure, we find very good agreement between the reconstruction results and the simulation, but the electric field and plasma velocity are not predicted with the same high accuracy.
Teh, W L.; Sonnerup, B U.; Birn, J; and Denton, R E., "Resistive MHD reconstruction of two-dimensional coherent structures in space" (2010). Open Dartmouth: Faculty Open Access Articles. 441.