Assessing the effect of error field penetration during plasma current ramp-up in the DIII-D tokamak

Abstract: This work provides evidence that established error field penetration threshold scalings remain applicable during plasma current ramp-up. In dedicated DIII-D experiments with imposed $n=1$ perturbations during extended $I_p$ ramps, an apparent empirical threshold is found between $2$ and $3$~kA of applied 3D coil current, above which MHD modes are seeded. The imposed perturbation couples to the rational surfaces present during the ramp, seeding near the $q=4$ surface and penetrating as an $m/n=3/1$ mode by the end of the perturbation phase. To interpret these observations, multi-machine penetration threshold scalings are combined with equilibrium-based overlap metrics from the GPEC code, including the in-situ error fields of the device. This modeling reproduces the observed onset in the amplitude scan and classifies mode seeding across a database of 12 ramp-up discharges spanning a range of plasma currents and densities. Across this database, the seeding appears to be controlled primarily by the applied 3D coil current rather than by the plasma current or its ramp rate. Accounting for the in-situ error fields is found to be important for reliable prediction. These results are consistent with the robustness of scaling-based penetration metrics when coupled to detailed 3D field modeling under transient ramp-up conditions, and suggest the importance of accounting for in-situ error fields when assessing additional externally induced perturbations. This work is motivated by future tokamaks in which transient, non-axisymmetric error fields can arise during startup, for example from runaway electron mitigation coils.