system, one has to multiply the *geometrised* quantity by its conversion factor expressed in CGS.[]{data-label="tab:unit_conversions"}

![Magnetospheric energy normalised to the vacuum dipole energy (equation \[eq:edipole\]) of the initial equilibrium models, for different values of the parameter ${P_{\rm c}}$ (in units of $P$ at the equator). The solid and dashed lines correspond to a series of models with constant $s$ and $\sigma$. The colored dots correspond to the initial data models used in our simulations.[]{data-label="fig:initial_model"}](images/figure2.pdf){width="45.00000%"}

Due to the long rotational period of observed magnetars pushing the location of the light cylinder to great distances, it is possible to neglect the rotation of the neutron star when building numerical models of magnetospheres in the near zone. The equilibrium structure of a non-rotating axisymmetric force-free magnetosphere is given through the well-known GSE [@Luest1954; @Grad1958; @Shafranov1966]. This approach has been followed in several recent papers [e.g. @Spitkovsky2006; @Beskin2010; @Vigano2011; @Glampedakis2014; @Fujisawa2014; @Pili2015; @Akgun2016; @Akgun2018a; @Kojima2017; @Kojima2018; @Kojima2018b]. In most of these works, the toroidal field is confined within a magnetic surface near the equator, smoothly transitioning to vacuum at large distances. In stationary, non-rotating, axisymmetric magnetosphere models, the toroidal field cannot extend to the poles. Otherwise, the toroidal field would extend all the way 