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) beta limit from optimizing the profiles and from optimizing the shape. Fbr a circular cross-section with highly peaked pressure profiles, beta(N) = beta/(I/aB) is limited to beta(N) similar to 2% (mT/MA). Small to moderate improvements in PN 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 beta and the root mean square beta denoted as beta*. With both optimal profiles and strong shaping, however, the gain in all the relevant fusion performance parameters is dramatic, and beta and beta* 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 beta(N), thus minimizing steady state current drive requirements. Sensitivity studies using other profiles show some variation in the actual beta limits, but the general trends remain robustly invariant.