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.

Low-frequency waves in the Earth's magnetosheath: present status

“…The application of more modern techniques (e.g., Dudok de Wit et al, 1995) and the multipoint measurements of Cluster should greatly advance this area. Several multipoint analysis techniques have been developed recently (Glassmeier et al, 1995;Neubauer and Glassmeier, 1990;Pinion and Lefeuvre, 1991;Pinion, 1993;vom Stein et al, 1993).…”

Review article: Wave analysis methods for space plasma experiment

“…Multi-spacecraft methods can be applied to multi-probe data analysis such as the timing analysis to measure the phase speed or the wave telescope technique or k-filtering technique to measure the fluctuation energy in the wavevectorfrequency domain (Neubauer and Glassmeier, 1990;Pinçon and Lefeuvre, 1991;Motschmann et al, 1996;Glassmeier et al, 2001). spin plane; and 3-D domain if the probes are in the spin plane and along the spin axis.…”

Wave vector analysis methods using multi-point measurements

“…The idea to use multiple spacecraft as a plasma wave array experiment was originally raised by Musmann et al (1974) before the concept of the Cluster mission was developed. The idea of the array experiment using multi-spacecraft was further developed for the Cluster mission (Neubauer and Glassmeier, 1990;Pinçon and Lefeuvre, 1991;Motschmann et al, 1996;Glassmeier et al, 2001), applying the projection methods earlier used in seismic wave studies (Capon, 1969;Harjes and Henger, 1973).…”

“…The position vectors satisfy the condition i r i = 0. In the case of four sensors (L = 4) like the Cluster mission, the solution can be given as a linear combination of the reciprocal vectors of the spacecraft positions κ i (Neubauer and Glassmeier, 1990;Chanteur, 1998),…”