Reduced model for direct induction startup scenario development on MAST-U and NSTX-U

A reduced semi-empirical model using time-dependent axisymmetric vacuum field calculations is used to develop the prefill and feed-forward coil current targets required for reliable direct induction (DI) startup on the new MA-class spherical tokamaks, MAST-U and NSTX-U. The calculations are constrained by operational limits unique to each device, such as the geometry of the conductive elements and active coils, power supply specifications and coil heating and stress limits. The calculations are also constrained by semi-empirical models for sufficient breakdown, current drive, equilibrium and stability of the plasma developed from a shared database. A large database of DI startup on NSTX and NSTX-U is leveraged to quantify the requirements for achieving a reliable breakdown (I-p similar to 20 kA). It is observed that without preionization, STs access the large E/P regime at modest loop voltage (V-loop) where the electrons in the weakly ionized plasma are continually accelerating along the open field lines. This ensures a rapid (order millisecond) breakdown of the neutral gas, even without pre-ionization or high-quality field nulls. The timescale of the initial increase in I-p on NSTX is reproduced in the reduced model provided a mechanism for impeding the applied electric field is included. Most discharges that fail in the startup phase are due to an inconsistency in the evolution of the plasma current (I-p) and equilibrium field or loss of vertical stability during the burn-through phase. The requirements for the self-consistent evolution of the fields in the weakly and fully-ionized plasma states are derived from demonstrated DI startup on NSTX, NSTX-U and MAST. The predictive calculations completed for MAST-U and NSTX-U illustrate that the maximum I-p ramp rate (dI(p)/d(t)) in the early startup phase is limited by the voltage limits on the poloidal field coils on MAST-U and passive vertical stability on NSTX-U.