The error-field penetration process of the dynamic ergodic divertor (DED) on the TEXTOR tokamak has been investigated analytically in terms of a single fluid MHD model with a finite plasma resistivity and viscosity in a cylindrical geometry. The linear model produces a localization of the induced current at the resonance surface and predicts a vortex structure of the velocity field near the resonance layer. Moreover, effects of the Alfvén resonance for the error-field penetration are identified by two peaks in the radial profiles of the perturbed toroidal current and the perturbed magnetic flux when the relative rotation velocity between the DED and the rotating tokamak plasma is set to large. Fine structures of the vorticity induced by the DED in the vicinity of the rational surface disappear by introducing a finite plasma perpendicular viscosity. In addition, it is shown that the two peaks of the perturbed toroidal current overlap by an anomalous plasma perpendicular viscosity. Likewise, a bifurcation of the penetration process from the suppressed to the excited state is obtained by a quasi-linear approach taking into account modifications of the radial profiles of the equilibrium current and the plasma rotation due to the DED. A comparison with real experimental results of the DED on the TEXTOR tokamak is shown.
Nonlinear Magnetohydrodynamics