Multi-Spacecraft Discontinuity Analysis: Orientation and Motion

In this chapter we discuss the shape, orientation, and motion of discontinuities in the magnetic field, as sampled by an array of closely separated spacecraft. Our central purpose is to introduce an established analysis method, designed to determine these properties. We describe the use of the technique and its application to simulated as well as real data. We first discuss the methodology adopted and then briefly present the application to both planar and non-planar event models in situations of linearly accelerating motion. The ability of the analysis to distinguish between non-constant motion and surface curvature is discussed. It is stressed that this chapter concentrates on the analysis of magnetic field data alone, since methods which incorporate multi-instrument data are predominantly limited to single spacecraft techniques at the present time (see, for example, Chapters 8 and9). Discontinuity analysisis used generically to describe the set of multi-spacecraft magnetometer analysis methods, which are best used in situations when the dominant, or most interesting, event scale length is much shorter than the spacecraft separation distances (the boundary structure is thin). As we discuss below, for such events where the spatial sampling is well below the effective Nyquist sampling rate, one first seeks parameters describing macroscopic properties of the event. As a secondary aim, one can assess the possibility of a more detailed analysis of structure. In ordering the data set, the analysis relies on an interpretation of the spatial content in the individual time series of each spacecraft in terms of its variance, and via the solenoidality of the field [ Sonnerup and Cahill , 1967]. The thin boundary regime allows this coordination, within each spacecraft data set, to be made independently from comparisons across the spacecraft array. Additionally, boundary structure here is typically assumed to be quasi-static in its own frame, but moving with respect to the spacecraft (we refer to this as “the degree of stationarity”). Thus, macroscopic analysis requires two things: firstly, a limit on the degree of time dependence in the data to be useful, and secondly, that the data can be characterised in terms of a “thin boundary”. It is interesting to note in passing that an opposing data regime occurs when the event scale length of variation is well in excess of the spacecraft separations. Direct differencing of inter-spacecraft measurements can then usefully approximate the differential changes in the field locally between spacecraft. In other words, the spatial content in the time series