to the current passing through the same area. Its functional dependence on $P$ can be chosen freely (consistently with any continuity and convergence requirements, particularly for the currents), which is equivalent to setting boundary conditions for $T$ at the surface of the star. Here, we invoke the same functional form for $T(P)$ as in @Akgun2016 [@Akgun2018a]. Thus, the toroidal field is confined within some [*critical*]{} magnetic surface ($P = {P_{\rm c}}$), $$\begin{aligned}
T\left(P\right)=\left\{\begin{array}{ccc}
s\times (P-{P_{\rm c}})^\sigma& : & P \geqslant {P_{\rm c}}\\ 
0 & : & \text{else}
\end{array}\right.,
\label{eq:toroidal}\end{aligned}$$ $s$ being a parameter determining the relative strength of the toroidal field with respect to the poloidal field. In order to avoid divergences in the currents we must demand that the power index satisfies $\sigma \geqslant 1$. For a pure dipolar field, the poloidal stream function in the magnetosphere is $$\begin{aligned}
P = \frac{1}{2}B_{\rm pole}\frac{R_*^3}{r}\sin^2\theta,\end{aligned}$$ while the toroidal stream function is $T=0$ everywhere. We will consider the simplest cases where the boundary value of $P$ at the surface of the magnetar coincides with that of a dipolar field, and, therefore, the initial data is symmetric with respect to the equator. For different choices of the functional relation $T(P)$ given by equation 