Time-resolved biphase signatures of quadratic nonlinearity observed in coupled eigenmodes on the DIII-D tokamak*

We report the detection of quadratic coupling between toroidicity-induced Alfven eigenmodes (TAEs) on sub-millisecond time scales (~750 μs). Identification of phase-coherency between multiple TAEs and nonlinearly-generated modes is facilitated by wavelet-based bicoherence analysis of time-series from inductive coils, taken from 4 DIII-D shots heated by neutral beam injection (NBI). A three-point scan of beam power (3, 4, and 5MW) compares coupling in different regimes of fast-ion drive.

Characterization of nonlinear three-wave interaction is inferred by stationary bispectrum phase (biphase), and confirmed via band-pass filtering. Biphase dynamics associated with prominent bispectral features are well-resolved in time and consistent with intermittent quadratic coupling. Onset and duration of nonlinearity are correlated with enhanced amplitude of one or both contributing TAEs; coincident changes in amplitude are observed for modes at the sum and difference frequency.