geometry and, in particular, it allows the use of a cylindrical tokamak approximation. In the following, the cylindrical coordinates $(r,\theta,z)$ represent the radial, poloidal and “toroidal” direction, respectively. Furthermore, we order $\beta$ as $\epsilon$, which implies that the electromagnetic effects are relatively small, although not negligible.

We represent the magnetic field as: $$\label{1} \textbf{B}=B_z \textbf{e}_z + \nabla \psi_p \times
\textbf{e}_z.$$ where $B_z\cong const$ is the component of the magnetic field in the “toroidal” direction (i.e. along the cylinder axis) and $\psi_p$ is the poloidal magnetic flux. In order to describe a single helicity tearing mode it is convenient to introduce an helical coordinate: $\xi= \theta-\frac{n}{mR_0}z$. In the same way, we express the magnetic flux in terms of its helicoidal component, which is given by: $\psi=\psi_p+\frac{r^2nB_z}{2mR_0}$. Finally, the helicoidal magnetic flux can be decomposed in its equilibrium and perturbed part (the tearing mode) and the latter can be expressed by a Fourier series: $\psi=\psi_{eq}(r)+\displaystyle\sum_m \widetilde{\psi}_m(r)
e^{i(\gamma t - m \xi)}$. The magnetic flux and the “toroidal” current density, $J$, are related through Ampere’s law, so that $(4\pi/c)J=-\nabla_{\perp}^2 \psi_p=-\nabla_{\perp}^2
\psi+\frac{2nB_z}{mR_0}$, where $\nabla_{\perp}^2
\psi=r^{-1}\partial_r (r\partial_r \psi)+ r^{-2}\partial^2_\xi
\psi$ and $c$ is the speed of light. The mode resonant surface, where the flux reconnects, 