B-field Scaling of Locked Mode Error Field Threshold in Alcator C-Mod*

One of the most ITER-relevant locked mode issues is the scaling of the threshold for error field locking, $\tilde B/B$, versus machine size, $R$. One way to obtain this is by comparing the locking threshold on tokamaks of different size. But the size scaling can also be obtained from just a single machine, utilizing dimensionless constraint arguments that relate it to $B$-field and density scaling. This alternative approach may provide a result with smaller uncertainty. On Alcator C-Mod this $B$-field scaling experiment has been carried out while also matching the ITER $q_{95}$ ($\sim3.2$) and $n/n_G$ (0.17, which is the ITER ohmic value and is the most relevant for locked modes). $B_T$ was varied shot-to-shot from 3 to 7 tesla while the applied 2/1 error field was ramped during the steady-state portion of each shot to find the locking threshold. The result gives a $B$-field scaling exponent of -1.13, which in turn yields an exponent for the size scaling ($R$) of 0.59. This implies a locking threshold for $\tilde B_{21}/B$ of $\sim0.8\times10^{-4}$ in ITER at its ohmic density. This $B$-field scaling experiment in C-Mod included a point at the actual ITER field (5.3 T), in addition to the ITER $q_{95}$ and $n/n_G$, which further reduces the extrapolation uncertainty.