All Figures

$\begin{figure} \par\includegraphics[height=5.8cm,width=8cm,clip]{3915Fig1a.eps}\... ...e*{3mm} \includegraphics[height=5.8cm,width=8cm,clip]{3915Fig1b.eps}\end{figure}$ Figure 1: Variation of the velocity vs. r/r_* for different values of $\mu$ in a) and $\nu$ in b). The other parameters are $\nu =1.185$ , $\delta = 2.113$ , $\kappa = 0.5$ , $\lambda = 1.9995$ in a), and $\mu =0.1$ , $\delta = 1.0$ , $\kappa = 0.5$ , $\lambda =1.0$ in b).
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In the text

$\begin{figure} \par\includegraphics[height=4.4cm,width=8cm,clip]{3915Fig2a.eps}\... ...e*{1mm} \includegraphics[height=4.4cm,width=8cm,clip]{3915Fig2b.eps}\end{figure}$ Figure 2: Comparison between two jet solutions with $\lambda =1.0$ ( $\epsilon =0.089$ ) and 1.2 ( $\epsilon =0.824$ ). In a) we plot the velocity along the polar axis and in b) the dimensionless electric current density along the polar axis. The other parameters are $\mu =0.1$ , $\nu = 0.65$ , $\delta = 1.4$ , $\kappa = 0.2$ and $\Pi _{\star } = 0.75$ .
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In the text

$\begin{figure} \par\includegraphics[height=7.8cm,width=7.2cm,clip]{3915Fig3a.eps... ...{8mm} \includegraphics[height=7.8cm,width=7.2cm,clip]{3915Fig3b.eps}\end{figure}$ Figure 3: Morphology in the poloidal plane of the streamlines of the two solutions of the previous figure and their light cylinders for $\lambda =1.0$ ( $\epsilon =0.089$ ) in a) and $\lambda = 1.2$ ( $\epsilon =0.824$ ) in b). As in Fig. 2, the other parameters are $\mu =0.1$ , $\nu = 0.65$ , $\delta = 1.4$ , $\kappa = 0.2$ and $\Pi _{\star } = 0.75$ . The light cylinders are represented by the two thick solid lines which surround the jets, and the different regions of validity of our solutions are shown: solid, dashed and dashed-dotted lines correspond to streamlines where the two quantities (defined in Sect. 2.2) $x_{\rm A}^2 G^2$ and $(2 + \delta \alpha )\left (1 + \delta \alpha \right )^2 - 2$ are <0.01, <0.1 and >0.1, respectively.
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In the text

$\begin{figure} \par\includegraphics[height=7.3cm,width=7.3cm,clip]{3915Fig4a.eps... ...{8mm} \includegraphics[height=7.3cm,width=7.3cm,clip]{3915Fig4b.eps}\end{figure}$ Figure 4: Morphology of the poloidal streamlines for two solutions corresponding to an Inefficient Magnetic Rotator (IMR, $\epsilon = -1.747$ ) in a), and an Efficient Magnetic Rotator (EMR, $\epsilon = 1.128$ ) in b). We chose $\mu =0.1$ in both cases, while the other parameters are $\nu =0.781$ , $\kappa =0.49$ , $\delta =2.613$ , $\lambda =0.880$ and $\Pi _\star =1.4$ in a), and $\nu =0.541$ , $\kappa =0.39$ , $\delta =3.253$ , $\lambda =1.401$ and $\Pi _\star =1.26$ in b). The various regions of validity of our solutions are shown as in Fig. 3.
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In the text

$\begin{figure} \par\includegraphics[height=4.4cm,width=8cm,clip]{3915Fig5a.eps}\... ...e*{3mm} \includegraphics[height=4.4cm,width=8cm,clip]{3915Fig5b.eps}\end{figure}$ Figure 5: Variation of the energy flux normalized to the mass energy, along the external streamline for the IMR solution in a) and the EMR solution in b) of the previous figure. The Poynting energy is $\leq$ 1% of the enthalpy at the base of the flow and is not plotted. The parameters are the same as in Fig. 4.
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In the text

$\begin{figure} \par\includegraphics[height=4.4cm,width=7.8cm,clip]{3915Fig6a.eps... ...6mm} \includegraphics[height=4.4cm,width=7.8cm,clip]{3915Fig6b.eps} \end{figure}$ Figure 6: Plot of the transverse forces for the relativistic IMR a) and EMR b). Forces are normalized by their maximum value, usually reached at the base of the flow. The parameters are the same as in Fig. 4.
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In the text

$\begin{figure} \par\includegraphics[height=7.2cm,width=7.3cm,clip]{3915Fig7a.eps... ...6mm} \includegraphics[height=7.2cm,width=7.25cm,clip]{3915Fig7b.eps}\end{figure}$ Figure 7: Morphology of the poloidal streamlines for non relativistic IMR a) and EMR b): the parameters are the same as in Fig. 4. with $\mu = 10^{-5}$ .
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In the text

$\begin{figure} \par\includegraphics[height=6cm,width=7.8cm,clip]{3915Fig8a.eps}\... ...*{4mm} \includegraphics[height=6cm,width=7.8cm,clip]{3915Fig8b.eps} \end{figure}$ Figure 8: Plot of the transverse forces for the non relativistic IMR a) and EMR b). We assumed $\mu = 10^{-5}$ while the other parameters are identical to the corresponding relativistic solutions displayed in Figs. 4.
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In the text

$\begin{figure} \par\includegraphics[height=4.3cm,width=7.7cm,clip]{3915Fig9a.eps... ... \par\includegraphics[height=4.3cm,width=7.7cm,clip]{3915Fig9b.eps} \end{figure}$ Figure 9: Plot of the asymptotic dimensionless cross section of the jet $G^2_{\infty }$ in a), and the asymptotic velocity in b) as a function of the parameter $\mu$ on a logarithmic scale. The other parameters are those given for the previous relativistic IMR and EMR solutions.
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In the text

$\begin{figure} \par\includegraphics[height=4.5cm,width=8cm,clip]{3915Fig10.eps} \end{figure}$ Figure 10: Density of the electric current normalized $\bar{I}_{z}$ , in the classical and the relativistic jets for EMR shown in the previous figures.
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In the text

$\begin{figure} \par\includegraphics[height=4.5cm,width=8cm,clip]{3915Fig11a.eps}... ...mm}\includegraphics[height=4.65cm,width=7.65cm,clip]{3915Fig11d.eps}\end{figure}$ Figure 11: Plot of the energies normalized by the parameter $\mu$ . In a) is shown the relativistic solution for an EMR, previously displayed in Fig. 5b with $\mu = 10^{-1}$ . In c) is shown the corresponding non relativistic solution with $\mu = 10^{-5}$ . In b) we plot an intermediate solution with $\mu = 10^{-2}$ . Plots b) and c) are identical which shows that for such small values of $\mu$ , the energies vary linearly with gravity, while this is not true in a). In d) we plot the ratio between the asymptotic velocity and the escape velocity at the surface of the corona as a function of $\log{(1/\mu)}$ .
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In the text

$\begin{figure} \par\includegraphics[height=5.8cm,width=8cm,clip]{3915Fig1a.eps}\... ...e*{3mm} \includegraphics[height=5.8cm,width=8cm,clip]{3915Fig1b.eps}\end{figure}$	Figure 1: Variation of the velocity vs. r/r_* for different values of $\mu$ in a) and $\nu$ in b). The other parameters are $\nu =1.185$ , $\delta = 2.113$ , $\kappa = 0.5$ , $\lambda = 1.9995$ in a), and $\mu =0.1$ , $\delta = 1.0$ , $\kappa = 0.5$ , $\lambda =1.0$ in b).
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$\begin{figure} \par\includegraphics[height=4.4cm,width=8cm,clip]{3915Fig2a.eps}\... ...e*{1mm} \includegraphics[height=4.4cm,width=8cm,clip]{3915Fig2b.eps}\end{figure}$	Figure 2: Comparison between two jet solutions with $\lambda =1.0$ ( $\epsilon =0.089$ ) and 1.2 ( $\epsilon =0.824$ ). In a) we plot the velocity along the polar axis and in b) the dimensionless electric current density along the polar axis. The other parameters are $\mu =0.1$ , $\nu = 0.65$ , $\delta = 1.4$ , $\kappa = 0.2$ and $\Pi _{\star } = 0.75$ .
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$\begin{figure} \par\includegraphics[height=4.4cm,width=8cm,clip]{3915Fig5a.eps}\... ...e*{3mm} \includegraphics[height=4.4cm,width=8cm,clip]{3915Fig5b.eps}\end{figure}$	Figure 5: Variation of the energy flux normalized to the mass energy, along the external streamline for the IMR solution in a) and the EMR solution in b) of the previous figure. The Poynting energy is $\leq$ 1% of the enthalpy at the base of the flow and is not plotted. The parameters are the same as in Fig. 4.
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$\begin{figure} \par\includegraphics[height=4.4cm,width=7.8cm,clip]{3915Fig6a.eps... ...6mm} \includegraphics[height=4.4cm,width=7.8cm,clip]{3915Fig6b.eps} \end{figure}$	Figure 6: Plot of the transverse forces for the relativistic IMR a) and EMR b). Forces are normalized by their maximum value, usually reached at the base of the flow. The parameters are the same as in Fig. 4.
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$\begin{figure} \par\includegraphics[height=7.2cm,width=7.3cm,clip]{3915Fig7a.eps... ...6mm} \includegraphics[height=7.2cm,width=7.25cm,clip]{3915Fig7b.eps}\end{figure}$	Figure 7: Morphology of the poloidal streamlines for non relativistic IMR a) and EMR b): the parameters are the same as in Fig. 4. with $\mu = 10^{-5}$ .
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$\begin{figure} \par\includegraphics[height=6cm,width=7.8cm,clip]{3915Fig8a.eps}\... ...*{4mm} \includegraphics[height=6cm,width=7.8cm,clip]{3915Fig8b.eps} \end{figure}$	Figure 8: Plot of the transverse forces for the non relativistic IMR a) and EMR b). We assumed $\mu = 10^{-5}$ while the other parameters are identical to the corresponding relativistic solutions displayed in Figs. 4.
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$\begin{figure} \par\includegraphics[height=4.3cm,width=7.7cm,clip]{3915Fig9a.eps... ... \par\includegraphics[height=4.3cm,width=7.7cm,clip]{3915Fig9b.eps} \end{figure}$	Figure 9: Plot of the asymptotic dimensionless cross section of the jet $G^2_{\infty }$ in a), and the asymptotic velocity in b) as a function of the parameter $\mu$ on a logarithmic scale. The other parameters are those given for the previous relativistic IMR and EMR solutions.
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$\begin{figure} \par\includegraphics[height=4.5cm,width=8cm,clip]{3915Fig10.eps} \end{figure}$	Figure 10: Density of the electric current normalized $\bar{I}_{z}$ , in the classical and the relativistic jets for EMR shown in the previous figures.
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