An optimization of beta in the DIII‐D tokamak

Accurate equilibrium reconstruction and detailed stability analysis of a strongly shaped, double‐null, β_T=11% discharge shows that the plasma core is in the second stable regime to ideal ballooning modes. The equilibrium reconstruction using all the available data (coil currents, poloidal magnetic loops, motional Stark effect data, the kinetic pressure profile, the magnetic axis location, and the location of the two q=1 surfaces) shows a region of negative magnetic shear near the magnetic axis, an outer positive shear region, and a low shear region connecting the two. The inner negative shear region allows a large positive shear region near the boundary, even at low q (q₉₅=2.6), permitting a large outer region pressure gradient to be first regime stable. The inner region is in the second stable regime, consistent with the observed axial beta [β_T(0)=44%]. In the low shear region p′ vanishes, consistent with Mercier stability. This is one way to extend the ballooning limit in shaped plasmas while maintaining stability against external kinks. The n=1 analysis shows that the plasma is unstable to an ideal internal mode, consistent with the experimental observations of a saturated internal m/n=1/1 mode. The core plasma pressure, not being limited by ballooning stability, appears to be reaching a local equilibrium limit at the magnetic axis.