the definition of the stability parameter, as shown in Refs.[@FKR; @Coppi1966]. We will address this subject, together with a discussion of the generation of the “zonal” pressure, in a future publication.

The paper is organized as follows. In Section II we describe the basic model behind the calculation of $\Delta'$ for a given equilibrium current density. We then describe the effect of small modifications of the current density on the stability parameter by using a perturbative approach. These results are applied to a slab configuration in Section III, where a simple analytic scaling for $\delta\Delta'$ is found. In Section IV we apply the scaling to a cylindrical problem and we verify its validity using a numerical code. Our results are used to investigate the onset of the NTMs in the presence of current corrugations in Section V. Finally, in Section VI we draw our conclusions.

Model
=====

The 2D fluid equations employed in our analysis are well suited to describe plasmas confined by a large toroidal magnetic field. We restrict our attention to configurations with small inverse aspect ratio, $\epsilon=a/R_0$, where $a$ and $R_0$ are the minor and major radius of the machine. This leads to a simplification of the 