Resistive wall induced forbidden bands of mode rotation frequency on the COMPASS-D tokamak

Rapid variations in the rotation frequency of a 2/1 tearing mode have been observed in the COMPASS-D tokamak when the frequency is in the range 5 kHz-500 Hz. This range of frequencies. referred to as the 'forbidden' frequency band, is explained in terms of an analytical model for toroidal force balance. The model balances the toroidal torque due to viscous fluid coupling between the island and the naturally rotating plasma against the electromagnetic Forces on the mode due to interaction with a resistive wall and interaction with any error fields which may be resonant with the mode. Simple analytical expressions are derived for the values of the upper and lower bounds of the forbidden band. The size of the forbidden band is found to depend only on the initial mode rotation frequency and the wail time for the mode. The model is also employed to explain modes that alternate in frequency between die upper and lower limits of the forbidden band, a phenomenon referred to as mode 'skipping'. when a low level error field is applied.