MAGNETOHYDRODYNAMIC BETA-LIMITS FOR TOKAMAKS WITH NEGATIVE CENTRAL SHEAR

Magnetohydrodynamic (MHD) operational limits are computed for tokamaks with negative central shear (NCS). Beta optimized profiles are genera ted, imposing stability to ideal n = 1, 2, 3 and infinity modes withou t a conducting wall. In addition, the profiles are constrained so that no negative current drive is needed to counterbalance the bootstrap c urrent in steady state operation. Under this last condition, the highe st stable values of both beta and beta(N) are found for high current a nd broad current profiles. Beta limits significantly above the semi-em pirical scaling beta(N) less than or equal to 4l; are found at low ind uctances, in particular for strong shaping. The broadness of useful cu rrent profiles is limited by the appearance of 'ravines', where the be ta limit falls drastically for q(a) below integer values. Low-n modes, in particular n = 1, limit the peaking of the pressure, and the optim al pressure peaking factors are in the range of 2.5 to 3. The beta lim it increases significantly when both elongation n and triangularity de lta are increased, but high elongation is not favourable at low triang ularity. At low-q operation with about 40% bootstrap fraction, a JET s haped cross-section, kappa = 1.6, delta = 0.3, gives a beta limit of 6.2% while stronger shaping, kappa = 2.0 and delta = 0.7, gives a limi t of 9.8%. At a bootstrap fraction of 65%, the corresponding beta lim its are rather low, about 2.3% for a JET shaped cross-section and 3.5% for kappa = 2.0, delta = 0.7.