Experimental and Theoretical Studies of a High-Beta Toroidal Pinch

Observations on various axisymmetric pinch systems operating above the Kruskal-Shafranov limit are in broad agreement with predictions. The experiment has five capacitor banks (2 MJ in all) which can be programmed in any sequence. Longitudinal currents and fields (Bz) up to 250 kA and 12 kG were used, with rise-times about 10 μs. The quartz torus, major diameter 2 m and bore 12 cm, was filled with deuterium between 10 and 50 mtorr pressure. Theoretically, unless the pressure gradient is positive, a pitch (rBz/Bθ) minimum is sufficient for instability. Stability is possible with total 6 up to 0.3-0.4 when the external Bz reverses. The inclusion of compressibility increases instability growth rates, and three characteristic eigenfunctions are computed, two of which are identified in the experiment. Estimates show that energy losses which can be neglected for power inputs of ≲ 25 eV/particle/μs, obtainable by compression, can become important at power inputs typical of resistive heating. In screw pinches temperatures up to 200 eV are obtained in the central core, which can remain grossly stable for 20 μs. The outer regions where most of the axial current flows are relatively cold, with a resistivity temperature of 5 eV, and always show radial magnetic field fluctuations. Stabilized z-pinches have resistivity and pressure balance temperatures about 10 eV with βθ = 0.3. In well-compressed plasmas a stable phase of up to 15 μs precedes non-localized pressure-driven instability which appears when the pressure gradient near the axis changes from positive to negative. Weakly compressed pinches become unstable in ≲ 1 μs to a localized mode expected from an outer pitch minimum. Applying reversed external Bz to weakly compressed pinches increases the stable time from ≲ 1 μs to 6 or 7 μs, while with compressed pinches the reversed field configuration lasts up to 15 μs, being limited by the same pressure-driven mode as before. (author)