Generalized coherences between vector data on two spacecraft

This paper describes some methods to analyze relations between vector-valued time series in a plasma environment. Specifically, we study the propagation between ACE, a spacecraft located at the first Lagrange point; and wind, a spacecraft whose complex orbit includes both Earth and L₁. Propagation in an inhomogeneous magnetoplasma, in near-field conditions, and at frequencies below the plasma cutoff frequency makes analytic (or even numerical) solutions extremely difficult. Thus, a major goal is to measure the wavelength as a function of frequency and hence infer the dispersion relations. A major problem is that both spacecraft measure B, but in a plasma, this is insufficient to determine the direction of propagation and polarization properties of the wave. Thus a new method of determining propagation properties is required. We propose to examine the angular offsets between apparent directions derived from principle components of B as a function of frequency on both spacecraft and from the canonical coherences between the two spacecraft. The principle components for both spacecraft and the canonical coherences between the two vector-valued magnetic fields can be efficiently computed by using three singular-value-decompositions (SVD\´s) at each frequency. The goal is to do three-dimensional "beamforming" from a pair of moving vector sensors in an uncertain propagation environment.