smaller than the typical wavelength in the magnetosphere ($\lambda \sim 100\,$km). In this case the energy transmission coefficient for waves perpendicular to the surface is approximately [cf. @Link2014; @Li2015] $$\mathcal{T} =\frac{4 v_{\rm me}/c}{(1+v_{\rm me}/c )^2}\approx 0.04 \left (\frac{v_{\rm me}/c}{0.01} \right), 
\label{eq:transmission}$$ for typical physical conditions in the magnetar crust. Given the low transmission coefficients of magnetospheric Alfvén waves hitting the crust as well as the differences on timescales between the crust and the magnetosphere (typically $\sim 10$ times shorter in the later) it is reasonable to consider that most of the crust remains rigid during any dynamical rearrangement of the magnetosphere.

In our magnetar model we will consider two regions: A force-free region ([*exterior*]{}, hereafter) consisting of the magnetosphere and the force-free part of the outer crust as well as the magnetar [*interior*]{} for the remainder of the NS, which we will consider to be fixed during our simulations. The limit between both regions is a spherical surface below the NS surface, where magnetic field lines are anchored, and is located below the transition density between inner and outer crust at a density $\rho<4\times 10^{11}\,$gcm$^{-3}$. For the purpose of describing the simulations we will refer to this transition point simply 