• High Power Laser Science and Engineering
  • Vol. 9, Issue 3, 03000e47 (2021)
K. Batani1、*, A. Aliverdiev2、3, R. Benocci4, R. Dezulian5, A. Amirova6, E. Krousky7、8, M. Pfeifer7、8, J. Skala7, R. Dudzak7、8, W. Nazarov9, and D. Batani10、11
Author Affiliations
  • 1IPPLM, Warsaw, Poland
  • 2IGRRE JIHT RAS, Makhachkala, Russia
  • 3Dagestan State University, Makhachkala, Russia
  • 4Università di Milano Bicocca, Milan, Italy
  • 5Liceo Scientifico ‘Galileo Galilei’, Trento, Italy
  • 6IP DFRC RAS, Makhachkala, Russia
  • 7Institute of Physics, Czech Academy of Sciences, Prague, Czech Republic
  • 8Institute of Plasma Physics, Czech Academy of Sciences, Prague, Czech Republic
  • 9Independent Foam Target Supplier, St Andrews, UK
  • 10University Bordeaux, CEA, CNRS, Talence, France
  • 11Plasma Physics Department, National Research Nuclear University MEPhI, Moscow, Russia
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    DOI: 10.1017/hpl.2021.33 Cite this Article Set citation alerts
    K. Batani, A. Aliverdiev, R. Benocci, R. Dezulian, A. Amirova, E. Krousky, M. Pfeifer, J. Skala, R. Dudzak, W. Nazarov, D. Batani. Shock dynamics and shock collision in foam layered targets[J]. High Power Laser Science and Engineering, 2021, 9(3): 03000e47 Copy Citation Text show less
    Scheme of the experimental setup.
    Fig. 1. Scheme of the experimental setup.
    Examples of time-resolved images of target rear-side self-emission obtained with the streak camera: (a) shot 30165, E ∼ 9 J, simple Al target; (b) shot 30142, E ∼ 50 J, simple Al target; (c) shot 30141, E ∼ 115 J, simple Al target; (d) shot 30150, E ∼ 50 J, Al + foam 5 g/cm3; (e) shot 30151, E ∼ 50 J, Al + foam 50 mg/cm3 with embedded Au nanoparticles; (f) shot 30147, E ∼ 50 J, Al + foam 50 mg/cm3; (g) shot 30148, E ∼ 115 J, Al + foam 50 mg/cm3; (h) shot 30167, E ∼ 161 J, Al + foam 50 mg/cm3. For the case of (a) and (h), the separation between the two spots was 100 μm instead of the nominal 200 μm.
    Fig. 2. Examples of time-resolved images of target rear-side self-emission obtained with the streak camera: (a) shot 30165, E ∼ 9 J, simple Al target; (b) shot 30142, E ∼ 50 J, simple Al target; (c) shot 30141, E ∼ 115 J, simple Al target; (d) shot 30150, E ∼ 50 J, Al + foam 5 g/cm3; (e) shot 30151, E ∼ 50 J, Al + foam 50 mg/cm3 with embedded Au nanoparticles; (f) shot 30147, E ∼ 50 J, Al + foam 50 mg/cm3; (g) shot 30148, E ∼ 115 J, Al + foam 50 mg/cm3; (h) shot 30167, E ∼ 161 J, Al + foam 50 mg/cm3. For the case of (a) and (h), the separation between the two spots was 100 μm instead of the nominal 200 μm.
    Streak images for the shots for fiduciary calibration: shot 30138 (left) and 30139 (right).
    Fig. 3. Streak images for the shots for fiduciary calibration: shot 30138 (left) and 30139 (right).
    X-ray streak-camera images on target front side. Time goes from left to right with time window 2 ns.
    Fig. 4. X-ray streak-camera images on target front side. Time goes from left to right with time window 2 ns.
    Shock breakout time versus laser energy for simple Al 10-μm targets and for foam-layered Al targets (foam density 50 mg/cm3).
    Fig. 5. Shock breakout time versus laser energy for simple Al 10-μm targets and for foam-layered Al targets (foam density 50 mg/cm3).
    Shock breakout time versus target structure for laser energy of 50 J.
    Fig. 6. Shock breakout time versus target structure for laser energy of 50 J.
    (a) Experimental results for 10 μm Al target (from Figure (c)). (b) Temperature of the target rear side versus space and time from 2D simulations and a 10 μm Al target. (c) The same for a target of 10 μm Al + 50 μm foam. In both cases the focal spot FWHM was 70 μm, the time profile of the laser pulse was Gaussian, and the peak intensity was 1.25 × 1015 W/cm2.
    Fig. 7. (a) Experimental results for 10 μm Al target (from Figure (c)). (b) Temperature of the target rear side versus space and time from 2D simulations and a 10 μm Al target. (c) The same for a target of 10 μm Al + 50 μm foam. In both cases the focal spot FWHM was 70 μm, the time profile of the laser pulse was Gaussian, and the peak intensity was 1.25 × 1015 W/cm2.
    Temperature of target rear side versus space and time. Results of 2D simulations for Gaussian profile, peak laser intensity 1.25 × 1015 W/cm2 and spot diameter 70 μm (FWHM): (a) 10 μm Al target; (b) 10 μm Al + 50 μm foam; (c) 60 μm Al target. Note: in case (c), the shock breakout image appears much more elongated simply because of the slower shock velocity which increases the time delay between the breakout at the center of the focal spot and at the edges of the focal spot.
    Fig. 8. Temperature of target rear side versus space and time. Results of 2D simulations for Gaussian profile, peak laser intensity 1.25 × 1015 W/cm2 and spot diameter 70 μm (FWHM): (a) 10 μm Al target; (b) 10 μm Al + 50 μm foam; (c) 60 μm Al target. Note: in case (c), the shock breakout image appears much more elongated simply because of the slower shock velocity which increases the time delay between the breakout at the center of the focal spot and at the edges of the focal spot.
    Time evolution of the rear-side self-emission (arbitrary units) for right (blue solid line) and left (red solid line) spots and for the middle area (dashed black curve). Shot 30148 foam–Al, 50 mg/cm3, E = 115 J. To reduce noise, the displayed signal corresponds to space integration with a width of 25 pixels around the central positions.
    Fig. 9. Time evolution of the rear-side self-emission (arbitrary units) for right (blue solid line) and left (red solid line) spots and for the middle area (dashed black curve). Shot 30148 foam–Al, 50 mg/cm3, E = 115 J. To reduce noise, the displayed signal corresponds to space integration with a width of 25 pixels around the central positions.
    The temperature of the rear side obtained in 2D MULTI simulation for: (a) 10 μm Al; (b) 10 μm Al+ 50 mg/cm3 foam. For these simulations, we used a laser pulse with spatial flat-top profile and a Gaussian time profile, duration 300 ps (FWHM), wavelength 0.44 μm (simulations with Gaussian spatial profile yield the same results). (c) and (d) Experimental rear-side self-emission streak images from Figure 2 (shots 30142 and 30147).
    Fig. 10. The temperature of the rear side obtained in 2D MULTI simulation for: (a) 10 μm Al; (b) 10 μm Al+ 50 mg/cm3 foam. For these simulations, we used a laser pulse with spatial flat-top profile and a Gaussian time profile, duration 300 ps (FWHM), wavelength 0.44 μm (simulations with Gaussian spatial profile yield the same results). (c) and (d) Experimental rear-side self-emission streak images from Figure 2 (shots 30142 and 30147).
    The spatial pressure profiles from simulations in foam (50 mg/cm3)–Al targets. The plots are shown in Lagrangian coordinates, i.e., R and z correspond to the initial position of each cell in the simulation mesh. In the images, the blue line and the blue rectangle show the position of the target (foam) surface and the position of the 10 μm Al foil, respectively.
    Fig. 11. The spatial pressure profiles from simulations in foam (50 mg/cm3)–Al targets. The plots are shown in Lagrangian coordinates, i.e., R and z correspond to the initial position of each cell in the simulation mesh. In the images, the blue line and the blue rectangle show the position of the target (foam) surface and the position of the 10 μm Al foil, respectively.
    Time t = 0.4 ns: (left) hydro-simulations (as in Figure 11 but rotated by 90°); (right) pressure profiles at z = 18 and 47 μm (dashed lines A and B in the figure on the left). Here (I) is the forward shock travelling in Al, (II) is the reverse shock travelling back in the foam, (III) is the forward shock, still expanding radially in the foam, and (IV) is the region where the two radially expanding shocks have collided.
    Fig. 12. Time t = 0.4 ns: (left) hydro-simulations (as in Figure 11 but rotated by 90°); (right) pressure profiles at z = 18 and 47 μm (dashed lines A and B in the figure on the left). Here (I) is the forward shock travelling in Al, (II) is the reverse shock travelling back in the foam, (III) is the forward shock, still expanding radially in the foam, and (IV) is the region where the two radially expanding shocks have collided.
    Time t = 0.45 ns: (left) hydro-simulations (as in Figure 11 but rotated by 90°); (right) pressure profiles at z = 18 and 41 μm (dashed lines A and B on the left). Here (I) to (IV) are the same as in Figure 12. Note: in position A, the radial forward shocks (II) and the reverse shocks (III) have practically merged.
    Fig. 13. Time t = 0.45 ns: (left) hydro-simulations (as in Figure 11 but rotated by 90°); (right) pressure profiles at z = 18 and 41 μm (dashed lines A and B on the left). Here (I) to (IV) are the same as in Figure 12. Note: in position A, the radial forward shocks (II) and the reverse shocks (III) have practically merged.
    Time t = 0.52 ns: (left) hydro-simulations (as in Figure 11 but rotated by 90°); (right) pressure profiles at z = 18 and 45 μm (dashed lines A and B on the left). Here (I) to (IV) are the same as in Figure 12, except for (V) which here represents the relaxation wave travelling back into Al after shock breakout on rear side. Again, in position A, the radial forward shocks (II) and the reverse shocks (III) have practically merged.
    Fig. 14. Time t = 0.52 ns: (left) hydro-simulations (as in Figure 11 but rotated by 90°); (right) pressure profiles at z = 18 and 45 μm (dashed lines A and B on the left). Here (I) to (IV) are the same as in Figure 12, except for (V) which here represents the relaxation wave travelling back into Al after shock breakout on rear side. Again, in position A, the radial forward shocks (II) and the reverse shocks (III) have practically merged.
    Plasma expansion on target front side at t = 0.18 ns showing the collision of the two plasma plumes. Here the target is 10 μm Al irradiated by the laser with 50 J energy.
    Fig. 15. Plasma expansion on target front side at t = 0.18 ns showing the collision of the two plasma plumes. Here the target is 10 μm Al irradiated by the laser with 50 J energy.
    Shot #3014130147301483015030151
    TargetAl 10 μmFoam 50 mg/cmFoam 50 mg/cm3Foam 5 mg/cm3Foam 50 mg/cm3
    50 μm + Al 10 μm50 μm + Al 10 μm50 μm + Al 10 μm50 μm Au clusters
    + Al 10 μm
    E on target (J)115501155050
    Laser intensity on target (1015 W/cm2)3.01.33.01.31.3
    Total filter thickness on laser beam (cm)2.03.92.03.93.9
    Left shockΔtbreakout (ps)280465600320760
    Right shockΔtbreakout (ps)2905156203601000
    Δtcentral luminosity (ps)- ∼910870 ∼7601250
    Table 1. Summary of shot conditions and experimental results. The values of intensity are the average values calculated over the focal spot size (70 μm) and the laser pulse duration (300 ps) taking into account approximately losses due to the use of various filters and the split into two different spots. The time Δt corresponds to the difference between shock breakout at target rear side and the arrival of laser beam on target front. The shock breakout time is measured at half of rise for the left and the right spots. We also report the time at which the luminosity in the central region begins to rise. Time zero is taken 300 ps (FWHM of the laser pulse) before the arrival of the maximum of the laser on target front side, in agreement with that used in hydro-simulations.
    K. Batani, A. Aliverdiev, R. Benocci, R. Dezulian, A. Amirova, E. Krousky, M. Pfeifer, J. Skala, R. Dudzak, W. Nazarov, D. Batani. Shock dynamics and shock collision in foam layered targets[J]. High Power Laser Science and Engineering, 2021, 9(3): 03000e47
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