Model for Effect of Non-Resonant Error Field on Resonant Error Field Locking in Ohmic Plasmas in DIII-D

Relatively small resonant ($m/n=2/1$) static error fields $B_{res}$ are shielded in Ohmic plasmas by the natural rotation at the electron diamagnetic drift frequency. However at low enough density and/or high enough $B_{res}$ the drag due to $B_{res}$ lowers rotation such that a bifurcation results going from shielding to an amplified state, a locked mode [1]. The empirically well-known Ohmic scaling is locking density $\sim$$B_{res}$; this breaks down at lower density in DIII-D with either optimized error field correction by the $n=1$ C-coil (no handedness) or at yet lower density with the $n=1$ I-coil (with ``dominantly" resonant field pitch). Relatively larger non-resonant error fields $B_{non-res}$ also exert drag on the plasma rotation but pull the rotation in the ion diamagnetic drift direction [2]. An analytic model that includes both resonant and non-resonant drag accounts for the limit on low density. The possibility of improved correction, i.e. less drag, by using both coil sets will be considered.\par \vskip6pt \noindent [1] J.T.\ Scoville and R.J.\ La Haye, Nucl.\ Fusion {\bf 43}, 250 (2003).\par \noindent [2] R.J.\ La Haye, S.~Guenter, D.A.\ Humphreys, J.~Lohr, T.C.\ Luce, {\em et~al.}, Phys.\ Plasmas {\bf 9}, 2051 (2002).