is such that the magnetic winding number (the safety factor), $q(r)=\frac{rB_z}{R_0B_\theta}$, is equal to $m/n$ ($B_\theta$ is the poloidal magnetic field). The safety factor then can be easily expressed as a function of the equilibrium “toroidal” current, $(4\pi/c)J_{eq}=-r^{-1}\partial_r
(r \partial_r\psi_{eq})+\frac{2nB_z}{mR_0}$: $$\label{2} q=\frac{c}{4\pi}\frac{r^2B_z}{R_0\int dr [r J_{eq}(r)]}.$$

In a high temperature plasma with low resistivity, and within our approximations, the structure of the linear tearing mode far from the resonant surface can be obtained by solving the scalar equation $\mathbf{e}_z \cdot \nabla \times (\mathbf{J} \times
\mathbf{B}) =0$ (i.e. the projection of the curl of the plasma momentum balance without inertial or viscous effects). Using Eq.\[1\] [@Strauss1976] and the definition of the helicoidal flux it is possible to cast this equation in the following form: $$\label{3} [J,\psi]=0,$$ where the operator $[A,B]=r^{-1}(\partial_r A\partial_\theta B -
\partial_\theta A\partial_r B)$. The linear version of Eq.\[3\] is: $$\label{4} \frac{1}{r}\frac{d}{d
r}\left(r\frac{d\widetilde{\psi}}{dr}\right)-\left(\frac{m^2}{r^2}-\frac{J_{eq}'}{\psi_{eq}'}\right)\widetilde{\psi}=0,$$ where the helicoidal magnetic field is given by: $-\psi_{eq}'=\frac{rB_z}{R_0}(\frac{1}{q}-\frac{n}{m})$, the prime represents derivation with respect to $r$, the subscript $m$ is dropped and the factor $4\pi/c$ is absorbed in the definition of the current. It is clear now that the ideal MHD approximation employed so far does not hold in the neighborhood of the resonant surface, as 