Synergism between cross-section and profile shaping in beta optimization of tokamak equilibria with negative central shear

Systematic stability studies of the negative central shear (NCS) configuration reveal a synergistic relationship between the gains in the ideal n = 1 magnetohydrodynamic (MHD) β limit from optimizing the profiles and from optimizing the shape. For a circular cross-section with highly peaked pressure profiles, βN = β/(I/aB) is limited to βN~2% (mT/MA). Small to moderate improvements in βN result either from broadening the pressure or from strong cross-section shaping. At fixed safety factor the latter translates to a much larger increase in β and the root mean square β denoted as β*. With both optimal profiles and strong shaping, however, the gain in all the relevant fusion performance parameters is dramatic, and β and β* can be increased by a factor of 5. The calculations show that stabilization from a nearby conducting wall greatly contributes to this large improvement, since coupling of the plasma to the wall is increased for the optimum profiles and cross-section. Moreover, the alignment of the bootstrap current density profile with the total current density profile is also optimized with broad pressure, strong cross-section shaping and high βN, thus minimizing steady state current drive requirements. Sensitivity studies using other profiles show some variation in the actual β limits, but the general trends remain robustly invariant.