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
