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$\begin{figure} \par\includegraphics[width=5.6cm,clip]{5524f1.eps} \end{figure}$ Figure 1: A sketch of the equilibrium configuration showing a slice (in r and z) of a cylindrically symmetric uniform coronal loop, of length 2L and radius a. The plasma density in the tube interior is $\rho _{\rm i}$ and the coronal region is of density $\rho _{\rm e}$ . In the chromospheric layers (of depth L-W), the density is $\rho _{\rm che}$ in the external chromosphere and $\rho _{\rm chi}$ in the internal chromosphere. The magnetic field is everywhere uniform and directed parallel to the loop. The footpoints of the loop are fixed at the chromospheric/photospheric base ( $z = \pm L$ ).The configuration is cylindrically symmetric.
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In the text

$\begin{figure} \par\mbox{\subfigure[]{\includegraphics[width=6cm,clip]{5524f2a.e... ...{4mm} \subfigure[]{\includegraphics[width=6cm,clip]{5524f2b.ps} } } \end{figure}$ Figure 2: a) Dispersion diagram for $v_{\rm Ae}=2.5 v_{\rm Ai}$ , $v_{\rm Ache}=0.25 v_{\rm Ai}$ and W / L =0.8, showing the dimensionless frequency $\omega L / v_{\rm Ai}$ as a function of a/ L. The solid and dashed curves are kink and sausage modes respectively. Case b) shows the results of a) but scaling the frequency against the tube radius a and plotting logarithmically as a function of L/a. The cutoff curve is displayed in a) and b) by the dotted line.
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{5524f3.ps} \end{figure}$ Figure 3: Plot of the dimensionless frequency $\omega L / v_{\rm Ai}$ as a function of W/L for $v_{\rm Ae}=2.5 v_{\rm Ai}$ , $v_{\rm Ache}=0.25 v_{\rm Ai}$ and a loop radius a=0.1 L. The solid line represents the fundamental kink mode, which is the only one mode trapped for these parameters. The dotted curve shows the dimensionless cutoff frequency as a function of W/L. Only the fundamental kink mode is below the cutoff for this value of a/L, as we can check in Fig. 2a.
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{5524f4.ps} \end{figure}$ Figure 4: Superposition of plots of dimensionless frequency $\omega L / v_{\rm Ai}$ against W/L with $v_{\rm Ae}=2 v_{\rm Ai}$ and a=0.1 L, for $v_{\rm Ache}=0.125v_{\rm Ae}$ (solid), $v_{\rm Ache}=0.25v_{\rm Ae}$ (dashed) and $v_{\rm Ache}=0.5v_{\rm Ae}$ (dash-dotted). The cutoff lines for each of these cases have been overplotted as dotted lines and labelled "1'', "2'' and "3'', respectively.
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In the text

$\begin{figure} \par\mbox{\subfigure[]{\includegraphics[width=6cm,clip]{5524f5a.p... ...4mm} \subfigure[]{\includegraphics[width=6cm,clip]{5524f5b.ps} }}\end{figure}$ Figure 5: Plots of $P_{{\rm T}}/ \rho _{\rm i} v_{\rm Ai}^2$ as a function of a) the radial coordinate r/a for the loop apex z/L=0, and b) of the longitudinal coordinate z/L for r=a. Here we fix $v_{\rm Ae}=2.5 v_{\rm Ai}$ , $v_{\rm Ache}=0.25 v_{\rm Ai}$ and a=0.1 L. The following parameters were used: W/L=0.79 (solid line), W/L=0.89 (dotted line), and W/L=0.99 (dashed line).
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In the text

$\begin{figure} \par\mbox{\subfigure[]{\includegraphics[width=6cm,clip]{5524f6a.p... ...e{4mm} \subfigure[]{\includegraphics[width=6cm,clip]{5524f6b.ps} }} \end{figure}$ Figure 6: Plots showing $\omega L / v_{\rm Ai}$ as a function of W / L for structured loops surrounded by structured media. The solid curve is the fundamental kink mode and the dotted curve shows the dimensionless cutoff frequency as a function of W/Lwith $v_{\rm Ae}=2.5 v_{\rm Ai}$ and a/L =0.1. The following parameters were used: a) $v_{\rm Achi}=0.25 v_{\rm Ai}$ and $v_{\rm Ache}=0.35 v_{\rm Ai}$ , b) $v_{\rm Achi}=0.35 v_{\rm Ai}$ and $v_{\rm Ache}=0.25 v_{\rm Ai}$ .
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In the text

$\begin{figure} \par\mbox{\subfigure[]{\includegraphics[width=6cm,clip]{5524f7a.p... ...{4mm} \subfigure[]{\includegraphics[width=6cm,clip]{5524f7b.ps} }}\end{figure}$ Figure 7: Plots of a) $P_{{\rm T}}/ \rho _{\rm i} v_{\rm Ai}^2$ and b) $v_r/v_{\rm Ai}$ as a function of the longitudinal coordinate z/L along the loop boundary (r=a). The following parameters were used: W/L=0.25 (dotted line), W/L=0.5 (dashed line), W/L=0.75 (dot-dashed line), W/L=0.9 (long-dashed line), W/L=0.99 (solid line), with $v_{\rm Ae}=2.5 v_{\rm Ai}$ , $v_{\rm Achi}=0.25 v_{\rm Ai}$ , $v_{\rm Ache}=0.35 v_{\rm Ai}$ and a/L =0.1. The normalization has been chosen so that the slope of $P_{{\rm T}}$ at the footpoint z=L is the same for each W/L.
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{5524f8.ps} \end{figure}$ Figure 8: Plots of $P_{{\rm T}}/ \rho _{\rm i} v_{\rm Ai}^2$ as a function of the radial coordinate r/a, for the loop apex z/L=0. The following parameters were used: W/L=0.1 (solid line), W/L=0.5 (dotted line), and W/L=0.99(dashed line), with $v_{\rm Ae}=2.5 v_{\rm Ai}$ , $v_{\rm Achi}=0.25 v_{\rm Ai}$ , $v_{\rm Ache}=0.35 v_{\rm Ai}$ and a/L =0.1.
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In the text

$\begin{figure} \par\mbox{\subfigure[]{\includegraphics[width=6cm,clip]{5524f5a.p... ...4mm} \subfigure[]{\includegraphics[width=6cm,clip]{5524f5b.ps} }}\end{figure}$	Figure 5: Plots of $P_{{\rm T}}/ \rho _{\rm i} v_{\rm Ai}^2$ as a function of a) the radial coordinate r/a for the loop apex z/L=0, and b) of the longitudinal coordinate z/L for r=a. Here we fix $v_{\rm Ae}=2.5 v_{\rm Ai}$ , $v_{\rm Ache}=0.25 v_{\rm Ai}$ and a=0.1 L. The following parameters were used: W/L=0.79 (solid line), W/L=0.89 (dotted line), and W/L=0.99 (dashed line).
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$\begin{figure} \par\includegraphics[width=7.8cm,clip]{5524f8.ps} \end{figure}$	Figure 8: Plots of $P_{{\rm T}}/ \rho _{\rm i} v_{\rm Ai}^2$ as a function of the radial coordinate r/a, for the loop apex z/L=0. The following parameters were used: W/L=0.1 (solid line), W/L=0.5 (dotted line), and W/L=0.99(dashed line), with $v_{\rm Ae}=2.5 v_{\rm Ai}$ , $v_{\rm Achi}=0.25 v_{\rm Ai}$ , $v_{\rm Ache}=0.35 v_{\rm Ai}$ and a/L =0.1.
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