Neoclassical toroidal viscosity and error-field penetration in tokamaks

A model for field error penetration is developed that includes both resonant and non-resonant perturbed 3-D magnetic fields [1]. The non-resonant components give rise to a global neoclassical toroidal viscous [NTV] torque while a single resonant component produces a localized electromagnetic braking torque on its respective resonant surface. The NTV torque tries to keep the plasma flowing at a rate comparable to the ion diamagnetic flow. A phenomenological cross-field viscosity is included which resists the resonant electromagnetic torque in the vicinity of the resonant surface. Steady-state toroidal momentum balance across the resonant layer gives a solubility condition determining the ``critical'' resonant error-field strength---termed the \emph{penetration threshold}---above which rotational shielding is lost and the resonant surface locks to the lab frame. Such locking occurs in low-density start-up tokamak plasmas [2], leading to plasma disruptions or confinement degradation and is a key issue for ITER. The toroidal momentum balance equation admits a WKB-type solution which implies that NTV acts to enhance cross-field viscosity in the vicinity of the resonant surface. This enhancement makes the plasma less sensitive to error-field penetration than previously predicted [3]. In particular, if $\tau_E \propto n_e$ (neo-Alcator-like) and the perpendicular momentum confinement time has no density dependence, we find the penetration threshold scales linearly with electron density---a result giving quantitative agreement for the first time between theory and experiment [2]. \newline \newline [1] A.J.~Cole, C.C.~Hegna, and J.D.~Callen, to be published in PRL (2007). \newline [2] S.M.~Wolfe, I.R.~Hutchinson, et al., Phys.\ Plasmas \textbf{12}, 056110 (2005) and refs.~cited therein. \newline [3] A.J.~Cole and R.~Fitzpatrick, Phys.\ Plasmas \textbf{13}, 032503 (2006) and refs.~cited therein.