All Figures

$\begin{figure} \par\includegraphics[angle=270,width=8.2cm,clip]{5714fig1.ps}\end{figure}$ Figure 1: Characteristics of the hyperbolic system of Eq. (24) for the case $E_\parallel =0$ . Characteristics for forward moving particles and backward moving particles are shown by solid and dotted lines respectively.
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In the text

$\begin{figure} \par\includegraphics[angle=270,width=8.2cm,clip]{5714fig2.ps}\end{figure}$ Figure 2: Characteristics of the hyperbolic system of Eq. (24) for the case $F_\parallel =0$ . Characteristics for forward moving particles and backward moving particles are shown by solid and dotted lines respectively.
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In the text

$\begin{figure} \par\includegraphics[angle=270,width=8.15cm,clip]{5714fig3.ps}\end{figure}$ Figure 3: The analytic solution for u₁/u₂=4 and v₀=0.25u₁ for the case $F_\parallel =0$ . The downstream and upstream distributions are shown by solid and dashed lines respectively. The height of the vertical lines corresponds to the coefficients in Eqs. (34) and (35).
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In the text

$\begin{figure} \par\includegraphics[width=8.4cm,clip]{5714fig4.ps}\end{figure}$ Figure 4: The results of simulation of the parallel shock with Mach number 3.77, $T_{\rm e}/T_{\rm i}=0$ and energy independent free path $\lambda =0.2$ . The forward and backward particle distributions downstream N₊ and N_- are shown on the top panel by solid and dashed lines respectively. Plasma velocity u, pressure of ions P and electric force $F=qE_\parallel$ are shown on the bottom panel by solid, dashed and dotted lines respectively. The total compression ratio r=4.05 is obtained.
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In the text

$\begin{figure} \par\includegraphics[width=8.4cm,clip]{5714fig5.ps}\end{figure}$ Figure 5: The results of simulation of the parallel shock with Mach number 7.75, $T_{\rm e}/T_{\rm i}=0$ and energy independent free path $\lambda =0.2$ . The forward and backward particle distributions downstream N₊ and N_- are shown on the top panel by solid and dashed lines respectively. Plasma velocity u, pressure of ions P and electric force $F=qE_\parallel$ are shown on the bottom panel by solid, dashed and dotted lines respectively. The total compression ratio r=6.67 is obtained.
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In the text

$\begin{figure} \par\includegraphics[width=8.4cm,clip]{5714fig6.ps}\end{figure}$ Figure 6: Comparison of our model with the cosmic ray modified shock approach for a parallel shock with Mach number 7.75, $T_{\rm e}/T_{\rm i}=0$ and energy independent free path $\lambda =0.2$ . The downstream distributions for our model and for the cosmic ray approach are shown in the top panel by solid and dashed lines respectively. Plasma velocity u from our simulations, pressure of ions P and velocity profile for the cosmic ray approach are shown in the bottom panel by dotted, dashed and solid lines respectively.
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In the text

$\begin{figure} \par\includegraphics[width=8.4cm,clip]{5714fig7.ps}\end{figure}$ Figure 7: Simulation of the quasi-parallel shock with $\theta =15^{\circ }$ , Mach number M= 7.75, $T_{\rm e}/T_{\rm i}=0$ and energy independent free path $\lambda =0.2$ . The forward and backward particle distributions N₊ and N_- are shown in the top panel by solid and dashed lines respectively. Plasma velocity u, pressure of ions P and electric force $F=qE_\parallel$ shown in the bottom panel by solid, dashed and dotted lines respectively. The total compression ratio r=7.21 is obtained.
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In the text

$\begin{figure} \par\includegraphics[angle=270,width=8.2cm,clip]{5714fig1.ps}\end{figure}$	Figure 1: Characteristics of the hyperbolic system of Eq. (24) for the case $E_\parallel =0$ . Characteristics for forward moving particles and backward moving particles are shown by solid and dotted lines respectively.
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$\begin{figure} \par\includegraphics[angle=270,width=8.2cm,clip]{5714fig2.ps}\end{figure}$	Figure 2: Characteristics of the hyperbolic system of Eq. (24) for the case $F_\parallel =0$ . Characteristics for forward moving particles and backward moving particles are shown by solid and dotted lines respectively.
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$\begin{figure} \par\includegraphics[angle=270,width=8.15cm,clip]{5714fig3.ps}\end{figure}$	Figure 3: The analytic solution for u₁/u₂=4 and v₀=0.25u₁ for the case $F_\parallel =0$ . The downstream and upstream distributions are shown by solid and dashed lines respectively. The height of the vertical lines corresponds to the coefficients in Eqs. (34) and (35).
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