$E\in \Lambda^1(\mathscr M)$ and the magnetic field $\mathscr B \in \Lambda^1(\mathscr M)$ are defined as follows. The electric field $E$ is defined by the splitting $F = E \wedge \mathrm dt + B$, where the two form $B$ includes no term with $\mathrm dt$. The magnetic field is defined by the splitting $\star F = \mathscr E - \mathscr B \wedge \mathrm dt$, where $\star : \Lambda^2(\mathscr M) \to \Lambda^2(\mathscr M)$ is the Hodge star operator and $\mathscr E$ is a two-form with no $\mathrm dt$-term. Cf. [@f12] for details. Define $\beta := \partial_z A_{\varrho} - \partial_\varrho A_{z}$. Then a calculation yields that the toroidal magnetic field component $\mathscr B_\varphi$ takes the form $$\label{tor_mag}
\mathscr B_\varphi = 2c e^{-2\mu} \varrho H \beta,$$ and the poloidal magnetic field components, $\mathscr B_\varrho$ and $\mathscr B_z$, contain only the $t$- and the $\varphi$-component of $A$. In fact a calculation yields $$\begin{aligned}
\mathscr B_\varrho &=- \frac{2 e^{- 2\nu/c^2}}{c \varrho H} \left( c^2 e^{4\nu/c^2} A_{\varphi,z} - \varrho^2 H^2 \omega (A_{t,z} + \omega A_{\varphi,z}) \right), \\
\mathscr B_z &= \frac{2 e^{- 2\nu/c^2}}{c \varrho H} \left( c^2 e^{4\nu/c^2} A_{\varphi,\varrho} - \varrho^2 H^2 \omega (A_{t,\varrho} + \omega A_{\varphi,\varrho}) \right).\end{aligned}$$

Next we introduce the parameter $\gamma = \frac{1}{c^2}$ and 