Use of an array of satellites as a wave telescope

Abstract

The four‐satellite array of the Cluster mission will allow the separation of spatial and temporal variations in the Earth's magnetosphere and magnetosheath and in the solar wind. We are using a general linear filter formulation to construct a mathematical formalism to determine not only the frequency spectra but also directional distribution and mode separation in a general wave field. This formalism is completely model independent and requires knowledge of the basic dispersion and polarization properties of the participating waves only. The four‐satellite array combined with a suitable formalism is called a wave telescope. We show that at a given frequency the transmission properties expressed by a transmission function can be shaped by 72 independent parameters for a three‐component vector output of the wave telescope filter. Considering the periodicity of the transmission function in wave vector k space, we are led to the concept of an elementary cell in k space given by the geometric properties of the array such that outside the elementary cell the k ‐ vectors are subject to spatial aliasing analogously to aliasing in time at frequencies above the Nyquist frequency. We show that for MHD waves the fast mode is particularly benign as far as spatial aliasing is concerned. The aliasing properties of other wave modes are also discussed. As an example a filter is constructed which suppresses waves propagating in the magnetic field direction but allows passage of waves propagating antiparallel to the magnetic field.