of light in the magnetosphere. Inside the outer crust ($\rho < 4\times 10^{11}$gcm$^{-3}$), all characteristic speeds transition from the speed of light to a significantly lower value, in a region that can still be considered force-free. This transition depends on the magnetic field strength, happening deeper inside the star for larger values of $B_{\rm pole}$. Given these characteristic speeds, any global rearrangement of the magnetosphere can modify the entire structure of the crust (of size $\sim 2 \pi R_*$) on a timescale of $\sim 1$ ms for magnetosonic waves and $\sim 10$ms for magnetoelastic waves.

One last aspect to consider is the ability of magnetospheric waves to transmit energy into the crust. The discussion should be limited to Alfvén waves, which become magnetoelastic waves once they penetrate the crust; the energy carried by fast magnetosonic waves in the magnetosphere can be neglected due to the small density, which renders the compressibility effects of fast-magnetosonic waves unimportant.

Since the characteristic time in the magnetosphere is $\sim 1$ms, the typical frequency of the waves generated during its dynamics is in the kHz range. At this frequency, the crust can be considered as a thin layer because its thickness ($\sim 1$km) is much 