Wavelength and direction filtering by magnetic measurements at satellite arrays: Generalized minimum variance analysis

Abstract

The main goal of the Cluster mission, consisting of four identical spacecraft, is the spatial resolution of plasma structures. For the determination of the wave vectors of a wave field from four positions, classical Fourier analysis is inappropriate. We develop a generalized minimum variance technique which gives a high wave vector resolution though the spatial grid is restricted to only a few sampling positions. This technique uses the amplitude and phase information of the magnetic field from the four satellite positions and determines the optimum wave field corresponding to the measured data. The components of the magnetic field are assumed to be normally distributed. The divergence-free nature of the magnetic field is used as a constraint. Using the magnetic data measured at four positions allows up to seven different wave vectors at one frequency to be uniquely resolved.

Statistical analysis of ground based magnetic field measurements with the field line resonance detector

“…(4) to adapt the basis functions of the wave telescope. A detailed derivation of the wave telescope technique has already been done by Motschmann et al (1996). In order to make differences between both techniques understandable we will repeat some of the computations of the mentioned work and use similar symbols.…”

“…This equation is the result of a Lagrangian minimization of the spectral energy density P with the constraint, that the spectral energy corresponding to the wave of wave vector k and frequency ω is preserved (for further details see Motschmann et al, 1996). The structure of the phase compensation matrix H is irrelevant for this minimization procedure.…”

“…Pillai (1989) proved the wave telescope to be a generalized minimum variance technique. Pinçon and Lefeuvre (1991) expanded the method to include multidimensional (vectorial) observables and Motschmann et al (1996) further developed it in order to apply it to multipoint satellite measurements (e.g. Glassmeier et al, 2001;Narita et al, 2003;Constantinescu et al, 2007).…”

Propagation pattern of low frequency waves in the terrestrial magnetosheath

“…In the wave analysis procedure dominant frequencies are first identified in the frequency spectra using Cluster magnetic field data , and then wave vectors at those frequencies are identified. We make use of the wave telescope method Motschmann et al, 1996;Pinçon and Lefeuvre, 1991) which was developed particularly for the multi-spacecraft mission. The Doppler shift of the frequencies is then corrected and the plasma frame frequencies are determined using the relation ω pl =ω sc −k·v f l , where ω pl denotes the plasma frame frequency, ω sc the spacecraft frame frequency, k the wave vector, and v f l the plasma flow velocity.…”

“…In the case of the foreshock or the solar wind, in contrast, the ambient field can be well approximated by a homogeneous field and the wave propagation pattern can be relatively easily configured and sketched (Narita et al, 2004). The bent magnetic field may cause an asymmetry in the wave propagation pattern in the magnetosheath, for instance, between the plane containing the bent field and the one perpendicular to it, but it is not clear how similar or how different the propagation pattern is around the symmetry axis of the magnetosheath.…”