the presence of small scale, small amplitude current corrugations. The scaling that we have obtained is verified by numerical codes in slab geometry, and its validity is confirmed in this Section for cylindrical geometry, which is more relevant for experimental applications. In order to proceed, we perform a numerical study with the “shooting” code introduced in the previous Section.

We assume a “rounded” equilibrium current density [@Furth1973] given by: $J_{eq0}=J_0/[1+(r/r_0)^4]^{3/2}$, which implies an equilibrium magnetic flux: $\psi_{eq0}=-0.25 J_0r_0^2\sinh^{-1}[
(r/r_0)^2]$. Here $J_0$ represents the current density at the cylinder axis and $r_0$ is a measure of the width of the current channel. In the following we take $J_0=2/0.7$ and $r_0=\sqrt{1/5}$, so that the mode $m=2$, $n=1$ resonates at $r_s\cong0.73$ and $m=3$, $n=2$ at $r_s\cong0.61$. In our model, the “zonal” field that generates the current corrugation is sinusoidal and localized around a radius $R$ by a Gaussian envelope of width $\rho$ (taken as $0.2$ in all the simulations): $\delta\psi_{eq}=A\cos[K(r-R)]e^{-(r-R)^2/\rho^2}$.

We investigate the effect of the corrugation on $m=2$, $n=1$ and $m=3$, $n=2$ modes, which are stable in the “smooth” configuration since $\Delta'_{2,1}\cong-2.19$ and $\Delta'_{3,2}\cong-3.28$. We observe that the effect produced by $\delta\psi_{eq}$ on the stability parameter changes as the localization radius of 