Axisymmetric instability in a non-circular tokamak: Experiment and theory

The stability of dee, inverse-dee and square-cross-section plasmas to axisymmetric modes has been investigated experimentally in Tokapole II, a tokamak with a four-null poloidal divertor. Experimental results are closely compared with predictions of two numerical stability codes: the PEST code (ideal MHD, linear stability) adapted to tokapole geometry and a code which follows the non-linear evolution of shapes similar to tokapole equilibria. Experimentally, there exists an optimal initial vertical position for the plasma for which both dees will experience a small oscillation with the restoring force provided by non-linear passive feedback. Slight vertical displacement of the initial position causes, however, both dees to be unstable to a non-rigid vertical motion. The central-magnetic-axis displacement grows exponentially with a growth time -10³ poloidal Alfvén times or on the order of the plasma L/R time. Contrarily, the square is always vertically stable. Experimental poloidal flux plots are produced directly from internal-magnetic-probe measurements. The PEST code, ignoring passive feedback, predicts all equilibria to be vertically unstable with the square having the slowest growth. With passive feedback, all are stable. Thus experiment and code agree that the square is the most stable shape, but experiment indicates that passive feedback is partially defeated by finite resistivity. In both code and experiment, square-like equilibria exhibit a relatively harmless horizontal instability.