Grad-Shafranov reconstruction: An overview

Grad-Shafranov reconstruction is a data analysis tool for the reconstruction of two-dimensional (2-D) coherent field and flow structures from data collected as the structures move past an observing platform. To date, the method has been applied with good success to reconstruct magnetohydrostatic structures in Earth's magnetopause, in the solar wind, and in the geomagnetic tail, as the structures move past one or more observing spacecraft. However, with suitable modification, the reconstruction method can be extended to other applications, three of which are presented here: 2-D magneto-hydrodynamic structures in which dynamically important field-aligned flow is present, 2-D flow transverse to the magnetic field in the magnetospheric low-latitude boundary layer, and 2-D ordinary gasdynamic/hydrodynamic flow. We develop the fundamental equations required in the reconstructions, both for isotropic pressure and, in Appendix A, for the case where the pressures parallel and perpendicular to the magnetic field are described by the double-polytropic laws. Applications to actual or simulated data are discussed but not included in the present paper.