Extending the wave telescope technique to larger numbers of spacecraft obtaining robust spatial power spectra

The wave telescope is an analysis technique for multi-point spacecraft data that estimates power spectra in reciprocal position space (k-space). It has been used to reveal the spatial properties of waves and fluctuations in space plasmas. Originally designed as an analysis tool for 4 spacecraft constellations, new multi-scale missions such as HelioSwarm or Plasma Observatory require extension of the technique to larger numbers of spacecraft, which introduces spatial aliasing effects that can largely inhibit physical interpretation and analysis of obtained power spectra. We present a comprehensive algorithm — the extended wave telescope — on how to obtain evaluable power spectra in k-space applying the wave telescope to spacecraft configurations with larger numbers of spacecraft (typically n>4). We complement the steps presented in Schulz et al. (2023) by showing how spacecraft position errors can be included into the calculation of the spatial Nyquist limit (SNL, the upper detection limit in k-space due to aliasing) as well as how to dampen remaining aliasing artifacts within the SNL. We test our implementation of the algorithm on a global hybrid-Vlasov simulation Vlasiator of Earth’s magnetospheric environment, probing the foreshock and magnetosheath with virtual spacecraft. We find good agreement between the virtual spacecraft’s and real-word multi-spacecraft observations. This highlights the success of our methodology of applying the wave telescope to spacecraft constellations with n>4 and also demonstrates the capabilities of Vlasiator in simulating the local near Earth space environment. We conclude that the presented algorithm is well-suited for application on future multi-scale spacecraft mission data.