Data-driven Uncertainty Quantification of the Wave Telescope Technique: General Equations and Demonstration Using HelioSwarm

The upcoming NASA mission HelioSwarm will use nine spacecraft to make the first simultaneous multipoint measurements of space plasmas spanning multiple scales. Using the wave telescope technique, HelioSwarm's measurements will allow for both the calculation of the power in wavevector and frequency space and the characterization of the associated dispersion relations of waves present in the plasma at MHD and ion-kinetic scales. This technique has been applied to the four-spacecraft Cluster and Magnetospheric Multiscale missions, and its effectiveness has previously been characterized in a handful of case studies. We expand this uncertainty quantification analysis to arbitrary configurations of four through nine spacecraft for three-dimensional plane waves. We use Bayesian inference to learn equations that approximate the error in reconstructing the wavevector as a function of relative wavevector magnitude, spacecraft configuration shape, and number of spacecraft. We demonstrate the application of these equations to data drawn from a nine-spacecraft configuration to both improve the accuracy of the technique, as well as expand the magnitudes of wavevectors that can be characterized.