On the energy confinement time in spherical tokamaks: implications for the design of pilot plants and fusion reactors

Experiments on NSTX and MAST have shown the thermal energy confinement time in spherical tokmaks (STs), tau(E,th), to have a stronger toroidal field and weaker plasma current dependence than in conventional large aspect ratio tokamaks. These scalings were derived for single machines both of which are similarly sized, consequently the NSTX and MAST scaling laws do not include a size dependence, and so cannot be used to extrapolate the performance of future STs. Using physics-based dimensional arguments we extend the NSTX scaling to include a size scaling. We also resolve a colinearity problem specific to NSTX data by assuming core transport is gyro-Bohm like. The resulting scaling has approximately zero beta dependence, a typical collisionality dependence, and a relatively weak safety factor dependence: B tau(E,th) proportional to rho(-3)(*)nu(-0.53)(*) * beta(-0.17) q(-0.35). With the exception of the safety factor, all exponents are consistent with recent experiments in large aspect ratio tokamaks. This apparent difference between STs and large aspect ratio tokamaks is consistent with MAST and NSTX results. We have considered the implications of the scaling for pilot plants and reactors and find it may be possible to develop more compact reactors based on the ST approach.