A new technique for determining orientation and motion of a 2-D, non-planar magnetopause

For a four-point mission like Cluster, the differences in position and time when the satellites detect the magnetopause or any other discontinuity, can be used to infer the discontinuity local orientation, thickness and motion. This timing technique, commonly assuming a planar geometry, offers an independent check for various single-spacecraft techniques. In the present paper we propose an extension of the timing method, capable of determining in a self-consistent way the macroscopic parameters of a two-dimensional, non-planar discontinuity. Such a configuration can be produced by a local bulge or indentation in the magnetopause, or by a large amplitude wave traveling on this surface, and is recognized in Cluster data when the single spacecraft techniques provide different individual normals contained roughly in the same plane. The model we adopted for the magnetopause assumes a layer of constant thickness of either cylindrical or parabolic shape, which has one or two degrees of freedom for the motion in the plane of the individual normals. The method was further improved by incorporating in a self-consistent way the requirement of minimum magnetic field variance along the magnetopause normal. An additional assumption, required in a previously proposed non-planar technique, i.e. that the non-planarity has negligible effects on the minimum variance analysis, is thus avoided. We applied the method to a magnetopause transition for which the various planar techniques provided inconsistent results. By contrast, the solutions obtained from the different implementations of the new 2-D method were consistent and stable, indicating a convex shape for the magnetopause. These solutions perform better than the planar solutions from the normal magnetic field variance perspective. The magnetopause dynamics and the presence of a non-zero normal magnetic field component in the analyzed event are discussed.