in § \[sec:disc\] we summarize and discuss our results.

PHYSICAL MODEL {#sec:model}
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A coronal loop is a closed magnetic structure threaded by a strong axial field, with the footpoints rooted in the photosphere. This makes it a strongly anisotropic system, as measured by the relative magnitude of the Alfvén velocity associated with the axial magnetic field $v_{\mathcal A} \sim 2000\ \textrm{km}\, \textrm{s}^{-1}$ compared to the typical photospheric velocity $u_{ph} \sim 1\ \textrm{km}\, \textrm{s}^{-1}$.

We study the loop dynamics in a simplified Cartesian geometry, neglecting field line curvature, i.e. the toroidality of loops. Our loop is a “straightened out” box, with an orthogonal square cross section of size $\ell$ (along which the x-y directions lie), and an axial length $L$ (along the z direction) embedded in an axial homogeneous uniform magnetic field $\mathbf{B}_0 = B_0\ \mathbf{e}_z$. This simplified geometry allows us to perform simulations with both high numerical resolution and long-time duration.

In § \[sec:ge\] we introduce the equations used to model the dynamics, while in § \[sec:bc\] we give the boundary and initial conditions used in our numerical simulations.

Governing Equations {#sec:ge}
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The dynamics of a plasma embedded in a strong axial magnetic field are well described by 