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SCIENCE CHINA Physics, Mechanics & Astronomy, Volume 60 , Issue 5 : 055201(2017) https://doi.org/10.1007/s11433-017-9016-x

Theoretical and simulation research of hydrodynamic instabilities in inertial-confinement fusion implosions

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  • ReceivedJan 12, 2017
  • AcceptedMar 2, 2017
  • PublishedMar 23, 2017
PACS numbers

Abstract


Acknowledgment

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11275031, 11675026, 11475032, 11475034, 11575033, and 11274026), the Foundation of President of Chinese Academy of Engineering Physics (Grant No. 2014-1-040), and the National Basic Research Program of China (Grant No. 2013CB834100). The author would like to thank XiaoJin Yu, BenLin Yang, WanHai Liu, YeSheng Tao, KaiGe Zhao, BeiBei Sun, Tao Cheng, XinHe Huo, BingSong Zheng, ZhongQiang Liu, ShaoYong Tu, Shuai Zhang, YanTao Yang, ZuoLi Xiao, JianJun Tao, YanBiao Gan, AiGuo Xu, GuangCai Zhang, JianFa Gu, ZhenSheng Dai, JiWei Li, DongGuo Kang, YongSheng Li, Meng Li, ChangLi Liu, XiuMei Qiao, FengJun Ge, HuaSen Zhang, Yi Shi, Gang Pang, YingKui Zhao, WenJun Sun, QingHong Zeng, GuangWei Meng, BiYao Ouyang, Heng Yong, YouSheng Zhang, BiaoLin Tian, LiLi Wang, WuDi Zheng, ShiYang Zou for fruitful discussions. We gratefully acknowledge technical supports from the Shenguang-II operation group for assistance, and the supports from the technical staffs for target fabrication and plasma diagnostics during the experiments.


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  • Figure 1

    Schematic of physics scenario of the ICF central hot-spot ignition implosion in the view of evolution of hydrodynamic instabilities. (a) Shock transit; (b) acceleration regime; (c) deceleration phase; (d) stagnation and burn.

  • Figure 2

    (Color online) The linear growth rate of KHI versus the combination of density and velocity transition layers for $k=1$ with $L_{\rho}/L_{u}=0.1$, 1, and 10, respectively. The initial conditions are $\rho _{1}=4.25$ g/cm$^{3}$, $\rho_{2}=0.5$ g/cm$^{3}$, $U_{1}=1$ cm/$\mu$s and $U_2=-1$ cm/$\mu$s.

  • Figure 3

    (Color online) The normalized NSAs of the fundamental mode of the RTI with corrections up to different orders for arbitrary $A$.

  • Figure 4

    (Color online) Temporal evolutions of the normalized amplitudes of the first three harmonics $\eta_{1}/\lambda$, $-\eta_{ 2}/\lambda$, and $\eta_{3}/\lambda$ for Atwood number $A=1$. The solid curves give the results of initiating interface perturbation alone and the dashed curves are the results of initiating velocity perturbation alone.

  • Figure 5

    (Color online) Typical temporal evolution of the interface of the KHI in the WN regime initiated by a single-mode small-amplitude perturbation. The ($x,\eta$) plane is plotted at time $t=0$.

  • Figure 6

    (Color online) Comparison of the temporal evolution of bubble velocity of the RTI in two-dimensional (dotted line) and three-dimensional (solid line) geometries.

  • Figure 7

    (Color online) Temporal evolution of the upper and lower interfaces initiated by only the lower interface perturbation for $kd=0.2$ (a) and $kd=1.6$ (b).

  • Figure 8

    (Color online) Temporal evolution of the interface position $r(\theta,t)$ for Atwood numbers $A=1$ (a) and $A=-1$ (b) with perturbation mode number $m=8$. In (a), the interface develops outside-to-inside asymmetry with the wave crests broadening into bubbles and the troughs thinning into spikes (e.g., the hot-spot interface during the deceleration phase in ICF implosions). On the other hand, in (b), the interface grows into outside-to-inside asymmetry with the wave crests thinning into spikes and the troughs broadening into bubbles (e.g., the ablation front during the acceleration stage in ICF implosions).

  • Figure 9

    (Color online) Interfacial profiles for perturbation modes $m=1$ (a), $m=2$ (b), $m=3$ (c), $m=4$ (d), $m=6$ (e), $m=16$ (f), with Atwood numbers $A=1$, initiated by only velocity perturbation, at $CR=$ 1, 2, 3, and 4, respectively. Note that the colors (red, blue, cyan, and purple) correspond to the values of convergence ($CR=$ 1, 2, 3, and 4). The average radius of the interface is also plotted by dashed lines.

  • Figure 10

    (Color online) The normalized nonlinear saturation amplitude ($\eta_s/\lambda$) versus the perturbation wavelength ($\lambda$) for the three different interface widths ($L_{\rm D}$).

  • Figure 11

    (Color online) Linear growth rate curves of the CRTI (black), WPARTI (red), and SPARTI (blue) from simulation (symbols) and theoretical (lines) results, respectively. The cut-off perturbation wavelength obtained from both the simulation and theoretical predictions are about 3.2 and 6.0 $\mu$m in the WPARTI and SPARTI, respectively.

  • Figure 12

    (Color online) Iso-density contours for a 20-$\mu$m-wavelength perturbation with an initial perturbation amplitude 0.00021 $\mu$m at the time of $t= 5.5$ ns (a) and $t= 7.0$ ns (b) in the WPARTI. The iso-density contours from the right to the left are, respectively, $\rho_{\rm i}=0.3$, $0.35$, $0.4$, $0.5$, $0.6$, $0.7$, $0.8$, $1.2$, $2.4$, and $4.2$ g/cm$^{3}$.

  • Figure 13

    Normalized linear saturation amplitude $\eta_s/\lambda$ at different perturbation wavelengths ($\lambda$) obtained from the strong, moderate, and weak ablation surfaces, respectively, in the WPARTI.

  • Figure 14

    The typical nonlinear evolutions of the CRTI initiated by short-, moderate-, and long-wavelength perturbations. (a) A 8-$\mu$m-wavelength and 0.00731-$\mu$m-amplitude perturbation; (b) a 24-$\mu$m-wavelength and 0.00731-$\mu$m-amplitude perturbation; (c) a 60-$\mu$m-wavelength and 0.00711-$\mu$m-amplitude perturbation.

  • Figure 15

    Typical nonlinear evolutions of the WPARTI initiated by the short-, moderate-, and long-wavelength perturbations. (a) A short-wavelength perturbation with perturbation wavelength $\lambda=3.7$ $\mu$m and initial perturbation amplitude $\eta_{ 0}=0.00079$ $\mu$m; (b) a moderate-wavelength perturbation with $\lambda=16.0$ $\mu$m and $\eta_{0}=0.00172$ $\mu$m; (c) a long-wavelength perturbation with $\lambda=60.0$ $\mu$m and $\eta_{0}=0.00650$ $\mu$m.

  • Figure 16

    Typical nonlinear evolutions of the SPARTI initiated by the short-, moderate-, and long-wavelength perturbations. (a) A short-wavelength perturbation with $\lambda=8.0$ $\mu$m and $\eta_{0}=0.00570$ $\mu$m; (b) a moderate-wavelength perturbation with $\lambda=24.0$ $\mu$m and $\eta_{0}=0.00707$ $\mu$m; (c) a long-wavelength perturbation with $\lambda=60.0$ $\mu$m and $\eta_{ 0}=0.00640$ $\mu$m.

  • Figure 17

    Profiles of the density contours for spikes and bubbles in the weak preheating RTI (with the parameters $\alpha=0.7$ and $\beta=0.4$) initiated by a 12-$\mu$m-wavelength and 0.4-$\mu$m-amplitude perturbation. The master spike pattern can be seen in panel (a). The second density spike pattern can be seen at the top and bottom of panel (b). In panel (c), the mass flux $\rho {\boldsymbol u}$ is also plotted. In panel (d), the master spike pattern ruptures.

  • Figure 18

    (Color online) Normalized accelerations ($a/g$) for the spike and bubble versus time ($t$) for a 20-$\mu$m-wavelength and 0.0069-$\mu$m-amplitude perturbation. Solid lines represent the bubble acceleration and the dashed lines represent the spike acceleration for the CRTI (black), WPARTI (red), and SPARTI (blue), respectively.

  • Figure 19

    (Color online) The comparison of linear growth rate (a) and frequency (b) between the CKHI and the AKHI.

  • Figure 20

    (Color online) The temporal evolution of the amplitudes of the fundamental mode (black), the second (red) and third (blue) harmonics in the CKHI (squares) and the AKHI (circles) with a single-mode perturbation $\lambda=25$ $\mu$m.

  • Figure 21

    The density fields of the CKHI and the AKHI with a single-mode perturbation at time of $t= 10$ (a), 12 (b), 14 (c), and 16 ns (d), respectively, with $\lambda$ = 50 $\mu$m and $\eta_{0}$ =0.0056 $\mu$m. Scales are the same for all plots. The width equals 60 $\mu$m and the height equals 50 $\mu$m.

  • Figure 22

    The density fields of the CKHI and the AKHI with a two-mode perturbation at time of $t= 10$ (a), 12 (b), 14 (c), 16 (d), and 18 ns (e), respectively. The perturbation wavelengths are $\lambda_{1}$ = 100 $\mu$m, $\lambda_{2}$ = 50 $\mu$m and initial amplitudes are $\eta_{10}=\eta_{20}=0.03199$ $\mu$m. Scales are the same for all plots. The width equals 120 $\mu$m and the height equals 100 $\mu$m.

  • Figure 23

    The density and vorticity fields for a single-mode $20$-$\mu$m-wavelength perturbation with an initial 0.007-$\mu$m-amplitude at time of $t=8.4$ (a), 9.6 (b), and 10.8 ns (c), respectively. Scales are the same for all plots. The width equals 62 $\mu$m and the height equals 20 $\mu$m.

  • Figure 24

    (Color online) Typical face-on back-lighting image from framing camera in indirect-driven experiments for a 50-$\mu$m-wavelength perturbation with an initial 3.0-$\mu$m-amplitude. The four strips (strip 1-4) are timed from bottom to top. Every strip consists of 4 image (image 1-4) which are timed from right to left. The value of time reflects the trigger time of the strip relative to the start of the back-lighting pulse. Each image in the strip is separated by $56$ ps.

  • Figure 25

    (Color online) Typical side-on back-lighting image from framing camera at the time of $2.0$ ns in direct-driven experiments for a 54-$\mu$m-wavelength perturbation with an initial 2.0-$\mu$m-amplitude (lower side) and an initial 4.8-$\mu$m-amplitude (upper side). The drive is a 0.35-$\mu$m-wavelength beam which is 2 ns in duration with an energy output about 1.2 kJ. The corresponding simulation result from LARED-S is also plotted on the left side.

  • Figure 26

    The radial profiles of density, velocity in $r$-direction, and pressure at the time of $-0.27$ (a) and $-0.17$ (b) ns in the decompression-and-recompression (DR) high-foot implosions.

  • Figure 27

    Comparison of density contours between the simple high-foot implosions (a) and the DR high-foot implosions (b) at the stagnation time for the perturbation of mode number $\ell=16$ initially seeded on the inner DT-ice surface with perturbation amplitude $A_{0}=1.0$ $\mu$m. Scales are the same for the two plots. The width equals the length being 120 $\mu$m. The white line marks the ion temperature contour of 4.3 keV.

  • Figure 28

    (Color online) Typical profiles of density and pressure during the acceleration regime in the hybrid-drive ICF implosions. The radiation ablation front ($r\approx505$ $\mu$m) and the electron ablation front ($r\approx540$ $\mu$m) are marked with dash-dotted lines

  • Figure 29

    (Color online) Comparison of the ablation front growth-factor spectrum versus the mode number at peak implosion velocity, with perturbations initially seeded on the ablator outer surface, for the low-foot indirect-drive (ID) ICF hot-spot ignition implosion, the high-foot indirect-drive ICF hot-spot ignition implosion, and the hybrid-drive ICF hot-spot non-isobaric-ignition implosion.

  • Figure 30

    (Color online) Comparison of the hot-spot growth-factor spectrum versus the mode number at stagnation time, with perturbations initially seeded on the ablator outer surface, for the low-foot indirect-drive (ID) ICF hot-spot ignition implosion, the high-foot indirect-drive ICF hot-spot ignition implosion, and the hybrid-drive ICF hot-spot non-isobaric-ignition implosion.

  • Figure 31

    Comparison of density contours at stagnation time, for the low-foot indirect-drive ICF hot-spot ignition implosion, the high-foot indirect-drive ICF hot-spot ignition implosion, and the hybrid-drive ICF hot-spot non-isobaric-ignition implosion, initiated by a perturbation of mode number $\ell=8$ seeded on the inner DT-ice surface with initial amplitude $A_{0}=4.0$ $\mu$m. Scales are the same for the three plots. The width equals the length being 120 $\mu$m.

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