All Figures

$\begin{figure} \par\includegraphics[width=13.5cm,clip]{fig1.eps}\end{figure}$ Figure 1: Model of a plane shock wave in the shock wave rest frame in two coordinate projections: a) XY, and b) XZ. The shock has the thickness d. The angle $\theta _{\rm Bn}$ is the angle between the upstream magnetic field $\vec{B_1}$ and the shock normal $\vec{n}$ . The upstream plasma velocity is $\vec{V_1}$ , the downstream magnetic field is $\vec{B}_2$ . The induced electric field $\vec{E} = -\vec{V_1} \times \vec{B_1}$ is supposed to be constant everywhere. Trajectories of reflected and transmitted electrons are shown. The scales of coordinates in the plot are not the same, the scale of X being much smaller than the scales of Y and Z (which are identical).
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In the text

$\begin{figure} \includegraphics[width=11.5cm,clip]{fig2.eps}\end{figure}$ Figure 2: A shock wave propagates through a flux rope in Case 1. Magnetic field lines are shown by the thick lines, the gray scale displays the plasma pressure P; the large plasma pressure gradients indicate the position of the shock. The figure shows a result of 2.5-D MHD numerical simulations: there was no dependency on the z coordinate, but z components of vectors were taken into account. Initial density within the flux rope is twice that in the ambient medium; also, the central flux rope's magnetic field magnitude is four times the ambient value. The coordinates x and y are in solar radii (Rs).
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In the text

$\begin{figure} \includegraphics[width=11.2cm,clip]{fig3.eps}\end{figure}$ Figure 3: A shock wave propagates through a flux rope in Case 2. The layout is similar to Fig. 2. As in Case 1, the flux rope's initial density is twice the ambient value, but the initial central magnetic field magnitude is one-half the background value.
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In the text

$\begin{figure} \par\includegraphics[width=15.1cm,clip]{fig4.eps}\end{figure}$ Figure 4: Changes of the angle $\theta _{\rm Bn}$ along the shock surface for a) Case 1 and b) Case 2. Case 2 has more complex variations. Top plots show global views to the magnetic field lines (thin lines) and the shock shapes (thick lines) approximated by the expressions mentioned in the text for our two cases. Parts marked by boxes are zoomed in the middle plots, which display locations of a nearly perpendicular shock in the flux ropes. The shock drawn by the thick line is gray coded: the black line marks the interval of $\theta _{\rm Bn}$ between $88^\circ$ and $90^\circ$ , and decreasing gray tones mark the intervals $86^\circ$ - $88^\circ$ , $80^\circ$ - $86^\circ$ , and below $80^\circ$ . The same coding is applied in the bottom graphs. $\Delta y$ is the grid size (e.g., Fig. 2 covers 480 grid points).
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In the text

$\begin{figure} \par\includegraphics[width=13.2cm,clip]{fig5.eps}\end{figure}$ Figure 5: The profiles of the magnetic (left panel) and electric (middle and right panels) fields through the shock (the value of 1.0 at the vertical axis corresponds to 1 $\mu$ T, 0.1 Vm^-1, and 0.2 Vm^-1 for the left, middle, and right panels, respectively). $\Delta x$ is the grid size ( $\Delta x = \Delta y$ ). The shock wave is located between $X/\Delta x = -2$ and 0. The profiles in the left and middle panels are in the upstream plasma rest frame (frame of the MHD simulations), the profiles in the right panel are in the shock rest frame. Shown are components B_X, B_Y, B_Z, -E_X, E_Y, and -E_Z; B and E are field magnitudes. More explanation is in the text.
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In the text

$\begin{figure} \par\includegraphics[width=13.2cm,clip]{fig6.eps}\end{figure}$ Figure 6: The profiles of the magnetic and electric fields through the shock. The layout is the same as in Fig. 5.
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In the text

$\begin{figure} \par\includegraphics[width=12cm,clip]{fig7.eps}\end{figure}$ Figure 7: Interactions of supra-thermal electrons with a shock inside a flux rope. The capital letters denote the regions around the shock, U and D are the upstream and downstream regions, respectively, S is the shock layer; the bullets and N mark the place of the nose (the origin of the XYZ system). The curved lines are electron trajectories. The larger arrows show the directions of the axes, the smaller ones directions of electron motion. The letter i indicates the injection points of electrons, r and t label parts of trajectories where electrons are reflected or transmitted, respectively. For a purpose of a better readability, the X-scale inside the shock is much lower than the upstream X-scale and the latter is different for different plots; however, general proportions were kept, i.e., the largest upstream trajectory among the plots is also the largest in reality.
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{fig8.eps}\end{figure}$ Figure 8: Omnidirectional intensity of electrons (per unit energy) at the downstream side of the shock (in arbitrary units) as a function of energy for Case 1 (solid line) and Case 2 (dashed line) compared to the initial intensity (dash-dotted line).
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In the text

$\begin{figure} \includegraphics[width=11.2cm,clip]{fig3.eps}\end{figure}$	Figure 3: A shock wave propagates through a flux rope in Case 2. The layout is similar to Fig. 2. As in Case 1, the flux rope's initial density is twice the ambient value, but the initial central magnetic field magnitude is one-half the background value.
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$\begin{figure} \par\includegraphics[width=13.2cm,clip]{fig6.eps}\end{figure}$	Figure 6: The profiles of the magnetic and electric fields through the shock. The layout is the same as in Fig. 5.
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$\begin{figure} \par\includegraphics[width=7.8cm,clip]{fig8.eps}\end{figure}$	Figure 8: Omnidirectional intensity of electrons (per unit energy) at the downstream side of the shock (in arbitrary units) as a function of energy for Case 1 (solid line) and Case 2 (dashed line) compared to the initial intensity (dash-dotted line).
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