Laser-driven shock waves studied by x-ray radiography

Multimegabar laser-driven shock waves are unique tools for studying matter under extreme conditions. Accurate characterization of shocked matter is for instance necessary for measurements of equation of state data or opacities. This paper reports experiments performed at the LULI facility on the diagnosis of shock waves, using x-ray-absorption radiography. Radiographs are analyzed using standard Abel inversion. In addition, synthetic radiographs, which also take into account the finite size of the x-ray source, are generated using density maps produced by hydrodynamic simulations. Reported data refer to both plane cylindrical targets and hemispherical targets. Evolution and deformation of the shock front could be followed using hydrodynamic simulations.

Figure 1

Sketch of the experimental setup.

Figure 2

(a) Cylindrical target with a flat interaction surface and (b) hemispherical target.

Figure 3

(a) Radiography test of a hemispherical target, compared with (b) a synthetic radiograph and (c) the Abel transform of the numerical density map.

Figure 4

Transmission of the hemispherical target along the line $z=130\mu \mathrm{m}$. The experimental result (dots) is compared with the synthetic radiograph (red curve) and the Abel transform of the numerical density map (black curve).

Figure 5

Experimental radiographs: (a) cylindrical target at $t=4.7$ ns and (b) and (c) spherical target at $t=2.7$ ns and $t=4.7$ ns, respectively.

Figure 6

Shock wave in the cylindrical target: (a) experimental radiograph and (b) synthetic radiograph. The laser pulse driving the shock comes from the right-hand side.

Figure 7

Cylindrical target. Experimental transmission (dots, with error bars) and simulated transmission (black curve). The red curve is the simulated transmission curve shifted 7 $\mu \mathrm{m}$ to the left.

Figure 8

Cylindrical target. Simulated transmission for different dimensions of the x-ray source. The labels in the figure refer to the source FWHM. The black curve is the same as in Fig. 7.

Figure 9

Cylindrical target. Simulated density maps at times (a) $t=0.7$ ns, (b) $t=2.7$ ns, and (c) $t=4.7$ ns.

Figure 10

Density maps from Abel inversion of the experimental radiograph shown in Fig. 6. (a) Abel inversion of the raw data and (b) Abel inversion applied after a Gaussian smoothing 2 pixels in radius of the raw data.

Figure 11

Density profile along the line $r=40\mu \mathrm{m}$: Abel transform of the raw experimental data (green curve) vs dued simulation, shifted 7 $\mu \mathrm{m}$ to the left (red dashed curve).

Figure 12

Density profile along the line $r=40\mu \mathrm{m}$. Abel transform of the filtered experimental data (green curve) vs dued simulation, shifted 7 $\mu \mathrm{m}$ to the left (red dashed curve).

Figure 13

Experimental radiographs (top) and synthetic radiographs (bottom) for the hemispherical target. The shock wavefront appears (a) quite flat at 2.7 ns and (b) definitely curved at 4.7 ns.

Figure 14

Hemispherical target. Experimental transmission (dots) and simulated transmission (black curve) at $t=2.7$ ns. The red curve is the simulated transmission curve shifted 5 $\mu \mathrm{m}$ to the right.

Figure 15

Same as Fig. 14, at time $t=4.7$ ns.

Figure 16

dued simulation of the hemispherical target, showing simulated density maps at three selected times: (a) $t=0.7\mathrm{ns}$, (b) $t=2.7\mathrm{ns}$, and (c) $t=4.7\mathrm{ns}$.