Radial mode coupling saturation of a flute mode

The structure and properties of a centrifugal flute mode driven by E × B rotation of a plasma column have been studied experimentally and theoretically. This mode appears as a single mode (m = 1, k = 0). The bispectral analysis of the mode clearly indicates strong three-wave coupling in the narrow spectral width of the mode. The amplitudes of the individual frequencies across the plasma cross section are also tracked, giving the radial structure of different frequency amplitudes. Frequencies with self-similar radial structures are grouped together to belong to the same radial harmonic. Clearly, these radial harmonics contribute to the spectral width. These observations suggest that the nonlinear mode coupling between these radial harmonics is the saturation mechanism, as well as the underlying cause of anomalous transport. Prompted by the above observations a three-wave nonlinear coupling model using radial harmonics has been formulated. A proper treatment of two-dimensional (azimuthal and radial) nature of the polarization drift nonlinearity and the inclusion of damped radial harmonics to insure a steady-state have been done. The analysis reveals the generation of damped higher-order radial harmonics by the unstable fundamental radial harmonic, which is the saturation mechanism. The resulting root mean square fluctuation and levels of higher harmonic generation are in fair agreement with the experimental observations.