of the dynamical behavior we can neglect the secular evolution of the field.

### Dynamical timescales {#sec:dynamical}

The [*dynamical timescale*]{} is set by the travel time of waves propagating in the different regions of the magnetar. In the magnetosphere, the mass density can be neglected in view of the dominating magnetic field energy density. Also, the velocity of Alfvén and fast magnetosonic waves is degenerated to the speed of light. Hence, within $\sim 100$km the whole magnetosphere is coupled through timescales smaller than $1$ms, which sets the scale for the dynamical evolution of the magnetosphere. In this region it is possible to neglect the inertia of the fluid in the evolution equations of so-called FFE, which is used in the numerical simulations of this work.

In the outermost parts of the crust, the force-free condition still holds because of low densities. At sufficiently high densities, elastic forces of the solid crust and pressure gradients break this condition. To estimate the transition density one may consider the depth at which waves propagate at a velocity significantly different to the speed of light. Two possible waves can travel in the interior of the magnetised crust, the so-called magnetosonic (ms) waves, related to 