Discharge start-up and ramp-up development for NSTX-U and MAST-U

A collaborative modeling effort is underway to develop robust inductive start-up and ramp-up scenarios for NSTX-U and MAST-U. These complementary spherical tokamak devices aim to generate the physics basis for achieving steady-state, high-beta and high-confinement plasma discharges with a self-consistent solution for managing the divertor heat flux. High-performance discharges in these devices require sufficient plasma elongation ($\kappa \quad =$ 2.4 -- 2.8) to maximize the bootstrap and beam-driven current drive, increase MHD stability at high I$_{\mathrm{p}}$ and high $\beta_{\mathrm{N}}$, and realize advanced divertor geometries such as the snowflake and super-X. Achieving the target elongation on NSTX-U is enabled by an L-H transition in the current ramp-up that slows the current diffusion and maintains a low internal inductance (l$_{\mathrm{i}}$ $\le $ 0.8). Modeling focuses on developing scenarios that achieve a suitable field null for breakdown and discharge conditions conducive to an early L-H transition while maintaining vertical and MHD stability, with appropriate margin for variation in experimental conditions. The toroidal currents induced in conducting structures and the specifications of the real-time control and power supply systems are unique constraints for the two devices.