Nonlinear coupling of tearing fluctuations in the Madison Symmetric Torus*

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Abstract
Three‐wave, nonlinear, tearing mode coupling has been measured in the Madison Symmetric Torus (MST) reversed‐field pinch (RFP) [Fusion Technol. 19, 131 (1991)] using bispectral analysis of edge magnetic fluctuations resolved in ‘‘k‐space.’’ The strength of nonlinear three‐wave interactions satisfying the sum rules m1+m2=m3 and n1+n2=n3 is measured by the bicoherency. In the RFP, m=1, n∼2R/a (6 for MST) internally resonant modes are linearly unstable and grow to large amplitude. Large values of bicoherency occur for two m=1 modes coupled to an m=2 mode and the coupling of intermediate toroidal modes, e.g., n=6 and 7 coupled to n=13. These experimental bispectral features agree with predicted bispectral features derived from magnetohydrodynamic (MHD) computation. However, in the experiment, enhanced coupling occurs in the ‘‘crash’’ phase of a sawtooth oscillation concomitant with a broadened mode spectrum suggesting the onset of a nonlinear cascade.