so that $Re_1 = Re = Re_m$ corresponds to the kinetic and magnetic Reynolds number (considered of equal and uniform value): $$\label{r1}
Re = \frac{\rho_0\, \ell u_{ph}}{\nu}, \qquad
Re_m = \frac{4\pi \rho_0 \, \ell u_{ph} }{\eta c^2},$$ where viscosity $\nu$ and resistivity $\eta$ are taken to be constant and uniform ($c$ is the speed of light).

We have performed numerical simulations with both $n=1$ and $n=4$. Hyperdiffusion is used because with a limited resolution the diffusive timescales associated with ordinary diffusion are small enough to affect the large scale dynamics and render very difficult the resolution of an inertial range, even with a grid with 512x512 points in the x-y plane (the highest resolution grid we used for the plane). The diffusive time $\tau_n$ at the scale $\lambda$ associated with the dissipative terms used in (\[eq:adim1\])-(\[eq:adim2\]) is given by: $$\label{eq:taud}
\tau_n \sim Re_n\, \lambda^{2n}$$ While for $n=1$ the diffusive time decreases relatively slowly towards smaller scales, for $n=4$ it decreases far more rapidly. This allows to have longer diffusive timescales at large spatial scales and similar diffusive timescales at the resolution scale. Numerically we require that the diffusion time at the resolution scale $\lambda_{min} = 1 / N$, where N 