Neoclassical Tearing Mode Seeding by Nonlinear Three-Wave Interactions in Tokamaks

We report the experimental observation of seed magnetic island formation by nonlinear three-wave coupling of magnetic island triplets. In this experiment, disruptive 2,1 islands are seeded by the coupling of 4,3 and 3,2 tearing modes to a central 1,1 sawtooth precursor. Three-wave interactions between these modes are conclusively identified by bispectral analysis, indicating fixed phase relationships in agreement with theory. This new observation of this seeding mechanism has important implications for future reactors that must operate in stable plasma equilibria, free of disruptive 2,1 islands.

Figure 1

(a) $q_{95}$, $l_i$, ${\beta }_N$, $q_{\min }$, and $D_{\alpha }$. (b) Cross power spectrogram of ${\tilde{B}}_{\theta }$ signals. (c) Frequency of $n=1$, 2, and 3 modes. Magnetic amplitude of (d) $n=2$ and 3 modes and (e) $n=1$ mode. Expanded view of (f) 1,1 and (g) 2,1 amplitudes.

Figure 2

(a) Bicoherence of ${\tilde{B}}_{\theta }$ at the time of 2,1 seeding. (b) Time trace of bicoherence between the $n=1$ and $n=2$ modes, $n=1$ amplitude, and differential rotation of $n=1$ and $n=3$ modes. (c) Spatial harmonics of ${\tilde{B}}_{\theta }$. (d) Cartoon of 2,1; 3,2; and 4,3 islands with phasing derived from (c).

Figure 3

$\delta W_1$ and ${\mathrm{\Delta }}_{22}^{\prime }$. Positive values reflect stable conditions.