All Figures

$\begin{figure} \par\includegraphics[width=8cm,clip]{8360fg01.eps}\end{figure}$ Figure 1: Schematic diagram of our model of the PNS.
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In the text

$\begin{figure} \par\includegraphics[width=6.2cm,clip]{8360fg02.eps}\end{figure}$ Figure 2: Top panel: profiles of the normalized function $\alpha ^\prime$ at the beginning of the numerical simulation for t=0(solid line) and at the end of the numerical simulation for $t=40~\rm s$ (dashed line); bottom panel: the same as in the top panel but for $\eta ^\prime$ .
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{8360fg03.eps}\end{figure}$ Figure 3: Behaviour of the 2-norm of ${\cal B}_{\rm t}$ as a function of the number of diffusion times ( $t/\tau _{\rm D}$ ) for the Aq configuration, |q| = 2, $C_\alpha =4$ ( $250~{\rm ms} \leq P \leq 750~{\rm ms}$ ), and for different seed magnetic field strengths, $B_{\rm s}$ . The growth-rate of the magnetic field during its amplification phase, before reaching the saturation, is almost independent of the seed magnetic field.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{8360fg04.eps}\end{figure}$ Figure 4: The same as in the Fig. 3 but for ${\cal B}_{\rm p}$ .
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{8360fg05.eps}\end{figure}$ Figure 5: Behaviour of the dynamo solutions as a function of the PNS spin period P and of the differential rotation strength |q| for three different values of $\xi$ , related to the turnover time of the convective eddies in the NFI zone.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{8360fg06.eps}\end{figure}$ Figure 6: Intensity of the final toroidal field ${\cal B}_{\rm t}$ in units of $B_{\rm eq}$ , at the end of the $40~\rm s$ NFI evolution time, as a function of the differential rotation parameter |q| for different values of $C_\alpha$ . The simulation refers to the configuration A, thus without $\eta$ -quenching.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{8360fg07.eps}\end{figure}$ Figure 7: The same as in Fig. 6 but for ${\cal B}_{\rm p}$ .
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{8360fg08.eps}\end{figure}$ Figure 8: Intensity of the toroidal field ${\cal B}_{\rm t}$ in units of $B_{\rm eq}$ , at the end of the $40~\rm s$ NFI evolution time, plotted as a function of the differential rotation parameter |q| for $C_\alpha =6$ ( $167~{\rm ms}<P<500~{\rm ms}$ ), and an initial seed magnetic field of $10^{-7}~B_{\rm eq}$ . The simulation shows the comparison between a configuration with $\eta$ -quenching (Aq) and without $\eta$ -quenching (A).
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In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{8360fg09.eps}\end{figure}$ Figure 9: The same as in the Fig. 8 but for ${\cal B}_{\rm p}$ .
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{8360fg10.eps}\end{figure}$ Figure 10: Spatial distribution of the toroidal component of the magnetic field at different time steps, for configuration Aq, with $C_\alpha =10$ and |q|=0.1. For this configuration $\alpha$ is different from zero only in regions with |z|>0.3.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{8360fg11.eps}\end{figure}$ Figure 11: Behaviour of the 2-norm of ${\cal B}_{\rm p}$ as a function of the number of diffusion times ( $t/\tau$ ) for the A and Aq configurations, |q| = 2, $C_\alpha =4$ ( $250~\rm ms \leq {\it P} \leq 750~\rm ms$ ), and for seed magnetic field strengths of $B_{\rm s}=10^{-4}B_{\rm eq}$ . The growth-rate of the magnetic field during its first amplification phase is the same for both configurations, which are eventually driven to saturation by the $\alpha$ -quenching.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{8360fg01.eps}\end{figure}$	Figure 1: Schematic diagram of our model of the PNS.
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$\begin{figure} \par\includegraphics[width=6.2cm,clip]{8360fg02.eps}\end{figure}$	Figure 2: Top panel: profiles of the normalized function $\alpha ^\prime$ at the beginning of the numerical simulation for t=0(solid line) and at the end of the numerical simulation for $t=40~\rm s$ (dashed line); bottom panel: the same as in the top panel but for $\eta ^\prime$ .
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$\begin{figure} \par\includegraphics[width=8cm,clip]{8360fg04.eps}\end{figure}$	Figure 4: The same as in the Fig. 3 but for ${\cal B}_{\rm p}$ .
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$\begin{figure} \par\includegraphics[width=8cm,clip]{8360fg05.eps}\end{figure}$	Figure 5: Behaviour of the dynamo solutions as a function of the PNS spin period P and of the differential rotation strength \|q\| for three different values of $\xi$ , related to the turnover time of the convective eddies in the NFI zone.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{8360fg06.eps}\end{figure}$	Figure 6: Intensity of the final toroidal field ${\cal B}_{\rm t}$ in units of $B_{\rm eq}$ , at the end of the $40~\rm s$ NFI evolution time, as a function of the differential rotation parameter \|q\| for different values of $C_\alpha$ . The simulation refers to the configuration A, thus without $\eta$ -quenching.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{8360fg07.eps}\end{figure}$	Figure 7: The same as in Fig. 6 but for ${\cal B}_{\rm p}$ .
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$\begin{figure} \par\includegraphics[width=8.2cm,clip]{8360fg09.eps}\end{figure}$	Figure 9: The same as in the Fig. 8 but for ${\cal B}_{\rm p}$ .
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$\begin{figure} \par\includegraphics[width=8cm,clip]{8360fg10.eps}\end{figure}$	Figure 10: Spatial distribution of the toroidal component of the magnetic field at different time steps, for configuration Aq, with $C_\alpha =10$ and \|q\|=0.1. For this configuration $\alpha$ is different from zero only in regions with \|z\|>0.3.
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