the other variables accordingly. The operator $d\cdots/dt=\partial\cdots/\partial t +
\mathbf{V}_{\mathbf{E}\times \mathbf{B}}\cdot\nabla\cdots$ contains the $\mathbf{E}\times \mathbf{B}$ drift velocity, $\nabla_{\|}=\mathbf{B}/|\mathbf{B}|\cdot\nabla$ is the parallel gradient, and the vorticity $U=\mathbf{e}_z\cdot\nabla\times
\mathbf{V}_{\mathbf{E}\times \mathbf{B}}$. The current density is related to the magnetic flux through Ampere’s law, which in a slab gives: $J=-\nabla^2 \psi$.

The theoretical dispersion relation appropriate for this model is [@Militello2003]: $$\label{12} \gamma^{5/4}-\gamma^{1/4}b
S^{-1}=0.48(\Delta'_0+\delta\Delta') S^{-3/4}k_y^{1/2},$$ where $b=[J_{eq0}''(0)+\delta J_{eq}''(0)]/[J_{eq0}(0)+\delta
J_{eq}(0)]$ (note that for $b=0$ we recover the classic solution of Ref.[@FKR], called FKR solution in the following). Inspection of Eq.\[12\] shows that current corrugation affects the growth rate through both $\delta\Delta'$ and $b$.

The linearized version of the system \[10\]-\[11\] is solved using a finite difference eigenvalue numerical code, benchmarked with analytical cases. In all the simulations, the Lundquist number is $S=10^{3}$. In absence of corrugations, the stability parameter is uniquely defined by $k_y$ according to the relation: $\Delta'_0=2(1-k_y^2)^{1/2}\tan[(1-k_y^2)^{1/2}\pi/2]$ (see e.g. Ref.[@Grasso2001]). We start by choosing $k_y=0.94$, so that the “smooth” equilibrium is characterized by $\Delta'_0=0.41$ and it is therefore tearing mode unstable. Solving Eq.\[12\], we find that the perturbation has growth rate $\gamma=0.0033$ (note that the growth rate is normalized with respect to the Alfven frequency) and the resistive layer has a width $\lambda\cong
