is the number of grid points, to be of the same order of magnitude for both normal and hyperdiffusion, i.e.$$\frac{Re_1}{N^2} \sim \frac{Re_n}{N^{2n}} \quad \longrightarrow \quad Re_n \sim Re_1\, N^{ 2(n-1) }$$ For instance a numerical grid with $N=512$ points which requires a Reynolds number $Re_1 = 800$ with ordinary diffusion, can implement $Re_4 \sim 10^{19}$, removing diffusive effects at the large scales, and allowing (if present) the resolution of an inertial range.

The numerical integration of the RMHD equations (\[eq:adim1\])-(\[eq:adim3\]) is substantially simplified by using the potentials of the velocity ($\varphi$) and magnetic field ($\psi$), $$\label{eq:potfi}
\mathbf{u}_\perp = \mathbf{\nabla} \times 
\left( \varphi\, \mathbf{e}_z \right), \qquad
\mathbf{b}_\perp = \mathbf{\nabla} \times 
\left( \psi\, \mathbf{e}_z \right),$$ linked to vorticity and current by $\omega =- \mathbf{\nabla}^2_\perp \varphi$ and $j = - \mathbf{\nabla}^2_\perp \psi$.

We solve numerically equations (\[eq:adim1\])-(\[eq:adim3\]) written in terms of the potentials (see [@rap07]) in Fourier space, i.e. we advance the Fourier components in the $x$-$y$ directions of the scalar potentials $\varphi$ and $\psi$. Along the $z$ direction no Fourier transform is performed so that we can impose non-periodic boundary conditions (specified in § \[sec:bc\]), and a central second-order finite difference scheme is used. In the $x$-$y$ plane a Fourier pseudospectral method 