the zonal fields maintain their coherence for a limited amount of time, $\tau_{zf}$. This fact is modelled by assuming a temporal variation of the modified stability parameter, so that $\delta\Delta'=\delta\Delta_{max}'\cos[(2\pi/\tau_{zf})
t]$, where $\delta\Delta_{max}'$ is a constant. A critical parameter of the problem is therefore the ratio between this time scale and that typical of the evolution of the NTM. From Eq.\[13\] we infer that this time is a fraction of the local resistive time (calculated with the neoclassical resistivity and the minor radius) $\tau_{NTM}\sim 0.1 \tau_\eta$, since the saturated island width can be usually estimated around one tenth of $r_s$. We expect that rapidly varying zonal fields, such that $\zeta\equiv\tau_{zf}/\tau_\eta\ll 1$, will not be an efficient trigger for the NTM as their effect is averaged to zero. On the other hand, if $\tau_{zf}/\tau_\eta$ is of the order or greater than one (although the latter possibility is difficult to achieve in fusion plasmas) the zonal fields can drive $w$ above its seed island limit.

The solution of Eq.\[13\] leads to three basic dynamic behaviors for a stable configuration ($\Delta_0'<0$) in the presence of a corrugation. When $\delta\Delta'_{max}<|\Delta'|$ the corrugation is not strong enough to produce any island (region $1$ in Fig.\[fig8\](a)). 