On the Conditions of Aliasing Effects in Constellations with More than Four Spacecraft

TL;DR

This paper introduces a method to analyze aliasing effects and the geometry of the first-Brillouin-like zone in multi-spacecraft constellations exceeding four spacecraft, aiding in the design of future space exploration missions.

Contribution

It provides a quantitative approach to estimate and compare the Brillouin-like zones in complex multi-spacecraft configurations, which was previously not well-studied.

Findings

Validated the estimation method against benchmark PSD patterns.

Compared the geometry of Brillouin zones for 4, 5, and 9 spacecraft.

The method constrains aliasing effects in multi-spacecraft measurements.

Abstract

The k-filtering/wave telescope method has been successfully applied to the four-spacecraft measurements from Cluster II and MMS, revealing the four-dimensional power spectral density $\textrm{PSD}(\omega, \mathbf k)$. 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 multi-spacecraft 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 validates 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 multi-spacecraft constellation.