Reconstruction of two-dimensional coherent MHD structures in a space plasma: The theory

摘要

We develop basic theory for the reconstruction of two-dimensional, time-stationary, ideal, compressible MHD structures in a space plasma from data taken by a single spacecraft as the structures move past it. The MHD equations are solved as a spatial initial-value problem in a manner similar to that used in so-called Grad-Shafranov (GS) reconstruction (e.g., Sonnerup et al., 2006), the difference being that our new method can deal with general structures, not just those governed by a GS-like equation. The approach described here represents a first step toward reconstruction of 2D steady state reconnection configurations, viewed in a frame moving with the X-line: Resistive, electron pressure, and Hall terms are still missing in Ohm's law but resistive and Hall effects can, we argue, ultimately be included. A numerical algorithm to perform the integration has been developed. It is tested by generation of synthetic data from a virtual spacecraft moving through an exact, analytical, axisymmetric solution of the MHD equations; these data are then used for the reconstruction. The exact solution involves isentropic plasma flow at an angle to the magnetic field. In addition to pressure and density, all three magnetic field and flow components are activated in the solution, i.e., they all vary with radius. Results show that the new method works with acceptable accuracy in a rectangular region surrounding the spacecraft path, with the two long sides of the rectangle parallel to the path. As is the case for GS reconstruction, the length of the short sides is limited by spatially growing numerical instability inherent in this type of integration procedure. Applications to actual spacecraft (Cluster) data will be reported separately.