Reconstruction Test of Turbulence Power Spectra in 3D Wavenumber Space with at Most 9 Virtual Spacecraft Measurements

Abstract

The k filtering/wave telescope method has been successfully applied to the 4 spacecraft measurements from Cluster II and MMS, revealing the four dimensional power spectral density (PSD, ω, k). As the number of spacecraft within a constellation increases, the geometry becomes more complicated, and it is harder to find the first Brillouin like zone, since we cannot use known formulas to calculate the geometry of the zone. To our knowledge, a quantitative study on the aliasing effects as well as the geometry of the first Brillouin like zone for the constellation with more than 4 spacecraft has not been proposed yet. Herewith we provide a method to estimate and compare the geometry of the first Brillouin like zone in multispacecraft constellations. The corresponding array of reciprocal lattice in the wavevector space forms the Brillouin zone. We set the preset PSDs conforming to the "slab only" and "slab + 2D" patterns as the benchmark, and compare them with the reconstructed PSDs using 4, 5, and 9 virtual spacecraft. Our results validate the estimation of the Brillouin like zones. The method may provide a constraint of aliasing effects. Our proposed method may be useful for the design and analysis of future exploration sessions with multispacecraft constellation.