Applicability of Bispectral Analysis to Causality Determination within and between Ensembles of Unstable Plasma Waves

Abstract

Turbulence implies nonlinear wave–wave coupling, and determining cause and effect of either is important to understand mixing responsible for enhanced number, momentum, or energy (NME) transport. To explain the identification of parent and daughter modes via a look-up table, we sketch the framework of bispectral analysis without repeating the mathematical formalism of earlier bispectrum researchers. We then apply this technique to a test signal and plasma fluctuation data from the WVU-Q machine, where the inhomogeneous energy density-driven spectrum exhibited a degree of coupling to lower frequencies that was absent in the case of the related, single-eigenmode, current-driven spectrum.