Experimental Observation of Magnetic Island Heteroclinic Bifurcation in Tokamaks

We report empirical observations of magnetic island heteroclinic bifurcation for the first time. This behavior is observed in interacting coupled $2/1$ tearing modes in the core of a DIII-D tokamak plasma. Poincaré maps constrained by measured magnetic amplitudes and phasing show bifurcation from heteroclinic to homoclinic topology in the $2/1$ island as the $4/2$ relative amplitude ($R_{4/2}$) decreases. Initially, the local electron temperature peak in the $2/1$ island splits, consistent with two $O$ points. As $R_{4/2}$ decreases a single peak forms, consistent with one $O$ point. These call for developing tearing stability theory and control solutions for heteroclinic islands in tokamaks.

Figure 1

Cross-power (a) spectrogram and (b) spectrum ($t=2795\mathrm{ms}$) of magnetic probes. $2/1$, $4/2$, and $6/3$ (c) normalized frequencies and (d) magnetic amplitudes at the wall and $D_{\alpha }$ signal. (e) $R_{4/2}$ and $R_{6/3}$ at $q=2$ (lines are third order polynomial fits). (f) Helical FWHM of $\mathrm{\Delta }{T}_e$.

Figure 2

Poincaré maps in the (a) heteroclinic and (b) homoclinic phase. (c),(d) $T_e(R,\xi )$ maps at the corresponding times of (a),(b), respectively. (e),(f) Helical profiles of $T_e$ through the $O$ point marked with horizontal dashed lines in (c),(d), respectively. Vertical dashed lines mark the $O$ point locations from (a) and (b).

Figure 3

Helical FWHM of $\mathrm{\Delta }{T}_e$ peak with respect to $R_{4/2}$.