Experimental Study of External Kink Instabilities in the Columbia High Beta Tokamak

Measurements of the internal and external magnetic structure of the plasma have provided a detailed characterization of long-wavelength current- and beta -limiting instabilities in the Columbia High Beta Tokamak (HBT). The instabilities are manifest as toroidally asymmetrical perturbations of the plasma magnetic field and exhibit the rapid growth rates, global displacements, and parametric dependencies predicted for external kink modes by ideal MHD theory. Fast formation techniques in HBT have enabled the production of plasmas with beta -values exceeding the Troyon limit for stability to ideal MHD external kink modes. Control of the relative magnitudes of the plasma current and the toroidal field has permitted observation of instabilities over a range 0.3 < q^* < 7. In toroidal Z-pinch operation (q^* < 1), the Kruskal-Shafranov stability condition is violated and m/n = 1/1 external kinks have been clearly observed. The instabilities were detected shortly (~2 mu s) after start-up, and invariably resulted in the termination of the discharge. Plasmas produced in tokamak operation (q^* > 1) often evolve such that q^* decreases and beta increases in value. At q^* ~ 2 (q(a) ~ 2.4), an abrupt transition from stability to instability was observed in many discharges. The magnetic perturbations were accompanied by large fluctuations in the line-integrated electron density and the loop voltage. Smaller-amplitude instabilities, exhibiting a more complex internal magnetic structure, were observed at higher values of q ^* near the Troyon beta -limit. In all cases, the mode growth occurred on an Alfven time scale. Ideal MHD stability analysis of numerically reconstructed equilibria that best represent the experimental measurements indicates that the plasmas were theoretically unstable to external kinks at the time the instabilities were observed. Qualitative similarities are evident between the measured and predicted perturbed internal magnetic field profiles, with the largest discrepancies occurring near the cooler (more resistive) inner edge of the plasma. The measured growth times agree well with theoretical calculations for q^ * < 1 unstable discharges, but instabilities occurring at q^* >= 1 grow faster than predicted.