Multipoint Turbulence Analysis with Helioswarm

Exploration of plasma dynamics in space, including turbulence, is entering a new era of multi-satellite constellation measurements that will determine fundamental properties with unprecedented precision. Familiar but imprecise approximations will need to be abandoned and replaced with more advanced approaches. We present a preparatory study of the evaluation of second- and third-order statistics, using simultaneous measurements at many points. Here, for specificity, the orbital configuration of the NASA Helioswarm mission is employed in conjunction with three-dimensional magnetohydrodynamics numerical simulations of turbulence. The Helioswarm 9-spacecraft constellation flies virtually through the turbulence to compare results with the exact numerical statistics. We demonstrate novel increment-based techniques for the computation of (1) the multidimensional spectra and (2) the turbulent energy flux. This latter increment-space estimate of the cascade rate, based on the third-order Yaglom-Politano-Pouquet theory, uses numerous increment-space tetrahedra. Our investigation reveals that Helioswarm will provide crucial information on the nature of astrophysical turbulence.