Orientation and motion of current layers: Minimization of the Faraday residue

A simple analytical solution is presented for a minimization problem encountered by Terasawa et al. [1996] in analyzing electromagnetic (EM) field and plasma data, series acquired by a spacecraft traversing a one-dimensional (1D) current layer. Their analysis was developed to infer the direction of spatial variation, n, and velocity, u(n), along n of a 1D EM structure such as the bowshock, the magnetopause, or the geotail current sheet. We show that the optimization procedure of Terasawa et al., which involved a numerical search, in fact reduces to solving a 3 x 3 eigenproblem for a certain matrix Q defined in terms of the data. ii step-by-step outline is given of the operations needed to predict n and un in this manner from an actual data set. Statistical estimates of uncertainty are given. Two magnetopause crossings by the spacecraft AMPTE/IRM are used to illustrate the procedure and to compare the results with those obtained by other methods.