Reconstruction of two-dimensional coherent structures in ideal and resistive Hall MHD: The theory

Abstract

We demonstrate that it is possible, in principle, to use data from a single spacecraft to produce reconstructions of two-dimensional, time-independent field and plasma structures in space, in circumstances where the Hall effect is important. Such reconstruction generates maps, in a limited region around the spacecraft path, of magnetic and electric fields, of flow field and current distributions, as well as of the various other plasma parameters that characterize the configuration. It is similar to recent work applicable to ideal MHD, but requires additionally that at least two components (usually the spacecraft spin-plane components) of the electric field have been directly measured. Principal emphasis is on ideal Hall MHD. For this case we have developed and benchmarked a numerical code by use of an exact axisymmetric solution in which the Hall effect is significant. The case where electrical resistivity is present as well, for example, in resistive-dispersive shocks, is discussed briefly to illustrate that reconstruction is possible in this case also. A principal target of Hall reconstruction, without or with resistivity, is the ion diffusion region around a reconnection site; applications to actual observed structures will be presented elsewhere.