the cut-off due to the banana orbit effect [@Bergmann2002] and $C_0$ is a constant proportional to the poloidal $\beta$ [@LeHaye2006].

We remark that our purpose is to sketch with an heuristic model the mechanism that could allow NTM formation. A detailed analysis would require a self consistent treatment of Rutherford equation coupled with an equation for the rotation frequency of the magnetic island. The theoretical uncertainties on the exact form of this coupling make an attempt to employ more complicated models to study the problem at hand a futile exercise.

In absence of zonal fields and if $\Delta_0'<0$, Eq.\[13\] predicts a minimum island width, $w_{seed}$, below which the perturbation is always stabilized and the NTM does not reach macroscopic size. Conversely, when the threshold is exceeded, the dynamical evolution takes the island to its stationary saturation amplitude, $w_{sat}$. To destabilize the NTM an island of sufficient size is therefore required. This “seed” island could be produced by some other MHD activity in the plasma, such as sawteeth, fishbone instabilities or Edge Localized Modes. In the following we investigate NTM dynamics without a seed \[i.e. $w(0)=0$\] island but in presence of zonal fields.

From experimental observations [@Fujisawa2007; @Fujisawa2008], we expect that 