Vol.35 (Dec) 2025 | Article no.31 2025
Indirect-drive double-shell implosions have been performed at 100 kJ laser facility in China. The system of differential equations for the unablated mass, the average implosion velocity, and the ablation front radius of an outer shell within an indirect-drive double-shell capsule during acceleraction and deceleraction phases has been proposed from conservation principles of hydrodynamics. In addition, corrected rocket model for the inner shell has been built; the radius and velocity of the outer surface of the inner shell, as well as the radius and velocity of the inner shell mass center, are solved and give simple expressions. These relations provide the maximum implosion velocity and remaining unablated mass in terms of the initial capsule and the radiation temperature. These results are compared with numerical simulations, and good agreements have been observed.
Kinds of approach are used with lasers to generate the energy flux and pressure required to drive inertial confinement fusion (ICF), such as indirect, direct, and hybrid drive (ID, DD, and HD) [1,2,3,4,5]. In the ID approach, the laser energy is absorbed and converted to x-rays by a high-Z hohlraum that surrounds the target [6, 7]. In the DD approach, a spherical target is illuminated directly with a number of individual laser beams [8]. The HD approach is a coupling of ID and DD, in which the ID lasers first drive the shock to perform a spherical symmetry implosion and produce a large-scale corona plasma, and then the DD lasers drive a supersonic electron thermal wave piling up the corona plasma into high density and forming a HD pressurized plateau with a large width [9]. In the above approaches, the energy flux is absorbed by the plasma ablating from the imploding capsule and then is transferred into the central low-density region (hot spot). The D-T fuel in the target is heated by shocks and shell-compression to thermonuclear conditions, where the local heating by \(\alpha\)-particles exceeds all other losses, including the conduction loss, the mechanism loss, and the radiative loss [10].
Within the central-spot ICF ignition, the acceleraction phase is the first phase of an implosion. In this phase, a small fraction of the driver energy is transferred to the capsule as kinetic energy. The inner part of the shell is accelerated by the ablation of its outer part. This phase starts at time that the rarefraction wave comes back to the ablation srurface and ends at time of the maximum shell velocity while the pressure in the central gas equals the shell pressure [10,11,12,13]. Assuming adiabatic compression of the central gas, \(P\sim R^{-5}\), where P and R are the pressure and radius of the central gas. Multiple shock reflections off the incoming inner shell and an increase in gas pressure lead to the shell deceleraction. During the deceleraction phase, the compressing material enclosed by the inner shell develops into a low-density and high-temperature region called the hot spot [14].
Different from the above mentioned central spot ignition, alternative laser fusion schemes seek to separate the hot spot formation from the shell acceleraction [15], such as the shock ignition [16, 17], the fast ignition [18], the double-shell ignition [19, 20], and the triple-shell resolver ignition [21, 22]. The separation of the hot-spot formation from the shell acceleraction relaxes the stringent requirements for the conventional central-spot ignition, although other challenges occur, such as the target fabrication and diagnosis. Taking a double-shell implosion as an example, the typical capsule occupies two middle or high Z layers, to obtain enough hydrodynamic efficiency. For such double-shell capsule design, the Au inner layer has a maximum velocity of \(\sim\)220 km/s, and the DT inner layer requires an implosion velocity of \(\sim\)370 km/s owing to the different specific internal energy for Au and DT [19]. This replies lower Rayleigh–Taylor (RT) instability on the inner shell for the double-shell design comparied to the conventional single-shell design during both the acceleraction and deceleraction phases. Additionally, the Fermi-degeneracy of electrons determines the pressure of the high compressed shell at the end of the deceleraction phase, scaling as \(P \sim (
In recent years, there has been a considerable effort to investigate the hydrodynamic and perturbated characteristics of the double-shell implosions. The physics of single- and double-shell implosions were compared and simple models were built to investigate the potential ignition scheme at the National Ignition Facility (NIF) [19]. DD double-shell implosion was proposed to be a platform for burning-plasma physics studies for the reason that DD ICF can couple more energy to the imploding shells [15]. Simulation results suggested that double-shell targets are more susceptible to the fill tube than typical single-shell ignition capsule designs, due to the higher density gradient between the shell and the fill tube hole, and mitigation strategy was discussed [20, 23]. Simulated and experimetal results on momentum transfer to different layers were presented. With a 1 MJ laser drive, the experimental data indicated that \(22 \% \pm 3 \%\) of the ablator kinetic energy couples into inner shell kinetic energy [24]. Within the 100 kJ laser facility in China, ID double-shell implosions were performed, the neutron yield was close to \(10^{10}\), and the YOC\(_{1D}\) was about \(27\%\) [25]. DD implosion experiments of a cone inserted double-shell target were carried out at the SG-II Upgrade laser facility. Time-resolved radiographic images of the targets were obtained with hard x-rays, and areal density of the target was evaluated [26].
In this manuscript, the hydrodynamic characteristics of the double-shell capsule implosion at 100 kJ laser facility are investigated. The shock and rarefraction wave properties are analyzed. There are distinct differences between the double-shell scheme and the conventional single-shell design, especially for the acceleraction of the inner shell due to no ablation source (x-ray flux or laser pulse) in the double-shell scheme. Analytical models are presented to study the outer and inner shell energetics, including the trajectory and velocity at the ablation surface, as well as those at the mass center. One-dimensional (1D) hydrocode MULTI [27, 28] is used to simulate the double-shell implosions, and the numerical simulations are compared with the analytical results.
The 100 kJ laser facility in China is a new ICF facility, with 48 laser beams in a wavelength of 351 nm and the maximum output energy of 180 kJ in 3 ns [29]. The double-shell implosions can be performed at 100 kJ laser facility. Within the typical double-shell target design, the capsule is driven by hohlraum radiation. The vacuum cylindrical hohlraums are made of gold, with a length of 4250 μm and a diameter of 2500 μm. There are two laser-entrance holes (LEH) of diameter 1400 μm at the two ends. Forty-eight laser beams irradiates the hohlraum with square laser pulse of \(\sim\)3.2 ns. Total laser energy is 101 kJ with single beam energy of 2100 J. As shown in Fig. 1a, the radiation temperature (Tr) has a peak value of \(\sim\)228 eV. The structure and size of the capsule is shown in Fig. 1b. CH material is adopted to be ablator with the thickness of 90 μm. The CH ablator covers a 18-μm Al layer and a 20-μm CH layer. The 20-μm CH layer benefits the target fabrication because the technology of magnetron sputtering is adopted and Al particles can be spyttered uniformed on the CH layer. In addition, the three-layer outer shell can help to mitigate the classical RT problem during the outer-shell evolution and collision. It not only reduces the Atwood number but also increases the density scale length at the collisional surface. As a result, a 128-μm outer shell can be thought as multiple “tamper” layers to obtain enough drive efficiency and acceptable instability growth. A CH-foam cushion layer is originally placed between the two shells. The spherical collision between the outer and inner shells could vary from completely inelastic to elastic depends on the CH-foam thickness and density [15, 19]. In our design, the thickness of the CH-foam is 325 μm and the density is 15 mg/cm\(^{3}\). Eight micrometer Al and 4 μm SiO2 layers are used to be the inner shell. D2 fuel gas is filled at a pressure of 100 atm inside the inner shell.
a The designed radiation temperature pulse; b the structure and size of the capsule (color online)
The trajectories of shocks and rarefraction waves for the typical double-shell capsule at 100 kJ laser facility are presented in Fig. 2. A contour plot (shock plot) of the logarithmic derivative of material density, \(\dfrac{1}{\rho } \dfrac{d \rho }{dr}\), versus Lagrangian index and time is shown. Shock and ablation front features are indicated, which displays many of the radiation-hydrodynamics aspects of the typical double-shell implosion at 100 kJ laser facility as follows:
(1) Radiation incident on the ablator is absorbed by the outer shell during the laser pulse. The shell material is ablated and a ablation surface is formed according to the mass ablation rate \(\dot{m}_{a}\). The ablation surface helps the complex behavior of the flow in the capsule, owing to the complicated interactions between the ablation surface and the outlet shocks and rarefraction waves.
The evolution of shocks and rerefraction waves in the double-shell implosion (color online)
(2) A ablative shock is driven inward in the CH ablator, we call it the first shock. When it reaches the interface of CH and Al, a shock comes back to the ablation surface and reflects into a rarefraction wave. The ablative shock transmits into Al layer and becomes a much stronger shock because of the greater density and sound speed of Al compared to those of the CH ablator. Afterwards, the first shock originates from the radiation ablation of the outer shell breaks out the other five interfaces respectively, and finally collides with shocks from other directions in the capsule center.
(3) Rarefraction waves are excited in the capsule implosion progresses, when shocks enter the light materials (low density and sound speed), such as CH foam and D2 gas. It should be pointed out that there is another strong shock driving the implosion of the inner shell, and we call it the second shock. It is originated at an time from a rarefraction wave reaching the ablative front and generating a steeping compression wave. The second shcok catches up the first shock after the the first shock passages the D2 gas interface. The two shocks imerges into a strong shock in D2 gas, compressing and heating the central gas.
During the passage of the ablative shock through the outer shell, the outside part of the shell material is ablated, and the shocked mass between the shock front and the ablation front starts to move. After the breaking out of the first shock through the inner surface of the outer shell, the whole unablated mass of the outer shell starts to move. The acceleraction is distinguished as two phases according to the outlet of the first shock in the inner gas comes back to the ablation front [12]. In the first phase, the velocity can be considered as uniform with the velocity \(u_{a}\) at the ablation surface only in the region between the ablation radius and the first shock, but not in all the shell. The average implosion velocity u remains smaller than \(u_{a}\). This remains available after the rarefraction originated from the inner surface of the outer shell comes back to the ablation surface. In the second phase, the velocity is approximately uniform in all the outer shell. The velocity \(u_{a}\) is now close to the average implosion velocity u. The CH-foam cushion is shocked by the first shock and then compressed quasi-adiabatically by the outer shell, generating a larger, pressure reservoir exterior to the outer and inner shell. When the pressure in the CH-foam exceeds the drive pressure, the shell has a acceleraction \(\sim\)0 and begins to decelerate. The outer shell does PdV work on the CH-foam, compressing and heating it, and the CH-foam plasma does PdV work on the outer shell, compressing it. The outer shell stagnation occurs when the CH-foam pressure and outer shell pressure are equal.
Schematic representation of an outer shell rocket model for a double-shell capsule (color online)
The outer shell is driven by the radiation with a ablative pressure \(P_{a}\) and compressed by the CH-foam cushion with a pressure \(P_{D}\). A sketch of the concept is shown in Fig. 3 illustrating \(P_{a}\) and \(P_{D}\). The integral conservation equations of mass and momentum for the unablated outer shell are:
where M and R are the unablated outer shell mass and ablation front radius in units of g and cm. We have \(\dot{m}_{a} = 1.092Tr^{2.78}\) with Tr are in unit of eV [12]. It should be noted that here CH-foam pressure \(P_{D}\) is introduced in the momentum equation, which is different from the conventional single-shell rocket model [12], for the reason that the CH-foam pressure cannot be neglected in the double-shell implosion. The velocity at the ablation front can be written as \(\dfrac{dR}{dt}=u_{a}\). Since \(u_{a}\) is approximated to u in the first phase of the acceleraction, and \(u_{a} = u\) in the second phase of the acceleraction, we can simplify the movement of the ablation surface as:
Equations (1), (2) and (3) constitute a complete system of differential equations, which describes the time evolution of M, u, and R during the acceleraction of the outer shell in terms of \(\dot{m}_{a}\), \(P_{a}\), and \(P_{D}\). It seems better to simplify \(P_{a}\) by assuming that it depends only on the radiation temperature, a fit of \(P_{a}\) gives [12]:
where \(P_{a}\) and Tr are in units of Mbar and eV.
The pressure in the CH-foam cushion is not easy to theoretically described, because of the complicated details of the shocks and rarefraction waves, as well as the compressions of both the outer and inner shells. A more simple behavior can be observed from hydro-simulations, if some relevant approximations are considered. Figure 4 demonstrates a fitting curve of the CH-foam pressure which is taken from numerical simulations in the typical double-shell capsules, and the dashed lines represent the CH-foam pressure from simulations with different CH-foam thickness. The time depended fitting of the CH-foam pressure at 100 kJ laser facility is as follows:
where \(P_{D}\) and t are in units of Mbar and ns.
The time dependent pressure in the CH-foam cushion in the typical double-shell capsule at 100 kJ laser facility. The dashed lines represent CH-foam pressures from simulations with different CH-foam thickness (color online)
The rocket model of the acceleraction of the double-shell target is solved, and the corresponding numerical simulations are performed with the 1D hydrocode MULTI [27, 28]. In the multi-group radiation-hydrodynamics code, the hydrodynamic equations are solved in a Lagrangian formulation with coupled thermal transport, and radiation energy deposition mechanism [28]. Figure 5 gives the results of the numerical integration of the system for the ablation front R, the unablated outer shell mass M, and the outer shell velocity u. They are compared to R, M, and u issued from numerical simulations, with a good agreement during the whole outer shell evolution.
It seems that the above rocket model, Eqs. (1), (2) and (3) together with the ablation pressure Eq. (4) and CH-foam pressure Eq. (5), could capture the main characteristics of the outer shell movements not only in the acceleraction phase but also in the deceleraction phase. However, we note that there are two approximations in the rocket model. Firstly, the ablation velocity \(u_{a}\) is replaced by the shell velocity u in the first phase of the acceleraction, although \(u_{a}\) is a little greater than u in this phase. Secondly, the CH-foam pressure is supposed to be given in the outer shell mass center, although the CH-foam plasma compresses the inner surface of the outer shell.
The inner shell is driven by CH-foam cushion with a pressure \(P_{D}\). A sketch of the concept is shown in Fig. 6. When the first shock breaks out from the inner shell into the gas, the inner shell starts to move, gains kinetic energy, and initially compresses the D2 gas. The inner shell reaches maximum kinetic energy when the D2 gas pressure exceeds the drive pressure in the foam. This roughly coincides with the arrival of the reflected outgoing shock at the inner shell/gas interface. The inner shell begins to decelerate. Be different from the acceleraction phase of the outer shell, there is no ablation surface in the inner shell, and the CH-foam pressure acts on the outer surface of the inner shell. Similarly to the ablation surface movement formula, the outer surface evolution of the inner shell could be obtained. Since there is no ablation of the inner shell, the shell mass keeps constant, the outer surface radius and momentum equations for the inner shell are:
Schematic representation of an inner shell rocket model during the acceleraction phase for a double-shell capsule (color online)
However, the outer surface velocity u must not be confused with the implosion velocity U defined from kinetic energy, which could be observed as \(U^{2} = \dfrac{1}{M} \int v^{2} \rho 4 \pi r^{2} dr\). In order to get U, the inner shell is treated as a thin shell with a constant mass M, and we ignore the pressure of any interior gas during the acceleraction phase. Then the acceleraction at a radius r is simply given as: \(a(r) = -4 \pi \dfrac{P_{D}}{M} r^{2}\). Knowing that \(\int a(r) dr = \dfrac{1}{2} U^{2}\), we can obtain \(U^{2} = \dfrac{8 \pi }{M} \int P_{D} r^{2} dr\). As a result, the differential equations which describe the evolution of the inner shell r and U during the acceleraction in terms of \(P_{D}\) can be written here:
The comparison of radius and velocities at the outer surface as well as at the mass center of the inner shell during the acceleraction phase (color online)
Figure 7 gives the results from the analytical models (6)–(7) and (8)–(9), which presents the trajectory evolution of the outer surface and the mass center of the inner shell correspondingly. As can be seen from Fig. 7a, the mass center trajectory leads the outer surface trajectory. Roughly the time depended thickness of the inner shell could be estimated from Fig. 7a. Both the two models indicate that the inner shell starts to move at \(\sim\)4.5 ns, and the mass center velocity U is much greater than the out surface velocity u. Although thin shell assumption is adopted, the inner shell is pushed forward with increasing shell thickness, which is demonstrated in Fig. 7a. Since the inner shell mass is constant, the shell density keeps increasing in the acceleraction.
Figure 8 presents the rocket model data and the numerical results. The numerical results is rightly reproduced by the rocket model data, which means the above rocket models could be used to describe the inner shell evolution of the double-shell capsule at 100 kJ laser facility during the acceleraction phase. However, when the D2 gas pressure and inner shell pressure are equal, the deceleraction of the inner shell begins. The gas internal energy increases due to shock and compression heating (in the absence of \(\alpha\)-heating). The inner shell hydrodynamic evolution and the energetic propertics of the central gas during the deceleraction phase is not discussed in this work.
The acceleraction and deceleraction phases of the outer and inner shells of the double-shell capsule are different from those of the single-shell target. The CH-foam cushion plays important roles on the hydrodynamic behaviors of different layers of the target, and the most dependent factor about the CH-foam cushion is the varying pressure, which prevents the acceleraction of the outer shell and drives the acceleraction of the inner shell. Within the scope of the typical double-shell capsule at 100 kJ laser facility, the time dependent pressure of the CH-foam cushion is taken from the numerical simulations with the 1D hydrocode MULTI. Accompanied by the CH-foam pressure, the corrected rocket models are built to describe the hydrodynamic evolution during the acceleraction and deceleraction phases of the outer shell, as well as that during the acceleraction phase of the inner shell. Comparisons are performed between the analytical solutions and the numerical simulations, and excellent agreements have been achieved.
With the help of the proposed rocket models, one can give simple expressions of the trajectory and velocity of the outer and inner shells, as well as the residual unablated mass, which has great effect on the target implosion robustness. The models are useful for understanding the underlying physics of the double-shell capsules at 100 kJ laser facity, and optimizing the target design to observe high neutron yield and to minimize the laser energy required.
Not applicable.
J. Lindl, P. Amendt, R. Berger, S. Glendinning, S. Glenzer, S. Haan, R. Kauffman, O. Landen, L. Suter. The physics basis for ignition using indirect-drive targets on the National Ignition Facility. Phys. Plasmas 11, 339 (2004)
R. Betti, O.A. Hurricane, Inertial-confinement fusion with lasers. Nat. Phys. 12, 435 (2016)
J. Yan, J. Li, X. He, L. Wang, Y. Chen, F. Wang, X. Han, K. Pan, J. Liang, Y. Li, Z. Guan, X. Liu, X. Che, Z. Chen, X. Zhang, Y. Xu, B. Li, M. He, H. Cai, L. Hao, Z. Liu, C. Zheng, Z. Dai, Z. Fan, B. Qiao, F. Li, S. Jiang, M.Y. Yu, S. Zhu, Experimental confirmation of driving pressure boosting and smoothing for hybrid-drive inertial fusion at the 100-kJ laser facility. Nat. Commun. 14, 5782 (2023)
Y.D. Yoon, The canonical vorticity framework and its applications in collisionless, magnetized plasma physics. AAPPS Bull. 35, 6 (2025)
S. Sangaroon, K. Ogawa, M. Isobe, Neutron emission spectrometer in magnetic confinement fusion. AAPPS Bull. 34, 34 (2024)
O.A. Hurricane, P.K. Patel, R. Betti, D.H. Froula, S.P. Regan, S.A. Slutz, M.R. Gomez, M.A. Sweeney, Physics principles of inertial confinement fusion and U.S. program overview. Rev. Mod. Phys. 95, 025005 (2023)
J. Yan, H. Shen, Z. Chen, H. Cao, C. Sun, Z. Dai, J. Li, W. Jiang, Z. Song, X. Peng, X. Zhang, B. Yu, Y. Pu, T. Huang, Y. Dong, L. Wang, S. Jiang, X. He, The influence of driven asymmetry on yield degradation in shaped-pulse indirect-drive implosion experiments at the 100 kJ laser facility. Nucl. Fusion 61, 016011 (2021)
R.S. Craxton, K.S. Anderson, T.R. Boehly, V.N. Goncharov, D.R. Harding, J.P. Knauer, R.L. McCrory, P.W. McKenty, D.D. Meyerhofer, J.F. Myatt, A.J. Schmitt, J.D. Sethian, R.W. Short, S. Skupsky, W. Theobald, W.L. Kruer, K. Tanaka, R. Betti, T.J.B. Collins, J.A. Delettrez, S.X. Hu, J.A. Marozas, A.V. Maximov, D.T. Michel, P.B. Radha, S.P. Regan, T.C. Sangster, W. Seka, A.A. Solodov, J.M. Soures, C. Stoeckl, J.D. Zuegel, Direct-drive inertial confinement fusion: A review. Phys. Plasmas 22, 110501 (2015)
X.T. He, J.W. Li, Z.F. Fan, L.F. Wang, J. Liu, K. Lan, J.F. Wu, W.H. Ye, A hybrid-drive nonisobaric-ignition scheme for inertial confinement fusion. Phys. Plasmas 23, 082706 (2016)
S. Atzeni, J. Meyer-ter-Vehn, The Physics of Inertial Fusion (Clarendon, Oxford, 2004)
J. Lindl, Development of the indirect-drive approach to inertial confinement fusion and the target physics basis for ignition and gain. Phys. Plasmas 2, 3933 (1995)
Y. Saillard, Acceleration phase and improved rocket model for indirectly driven capsules. Laser Part. Beams 22, 451 (2004)
R. Betti, K. Anderson, V.N. Goncharov, R.L. McCrory, D.D. Meyerhofer, S. Skupsky, R.P.J. Town, Deceleration phase of inertial confinement fusion implosions. Phys. Plasmas 9, 2277 (2002)
W.L. Shang, C. Stoeckl, R. Betti, S.P. Regan, T.C. Sangster, S.X. Hu, A. Christopherson, V. Gopalaswamy, D. Cao, W. Seka, D.T. Michel, A.K. Davis, P.B. Radha, F.J. Marshall, R. Epstein, A.A. Solodov, Properties of hot-spot emission in a warm plastic-shell implosion on the OMEGA laser system. Phys. Rev. E 98, 033210 (2018)
S.X. Hu, R. Epstein, W. Theobald, H. Xu, H. Huang, V.N. Goncharov, S.P. Regan, P.W. McKenty, R. Betti, E.M. Campbell, D.S. Montgomery, Direct-drive double-shell implosion: A platform for burning-plasma physics studies. Phys. Rev. E 100, 063204 (2019)
R. Betti, C.D. Zhou, K.S. Anderson, L.J. Perkins, W. Theobald, A.A. Solodov, Shock Fast Ignition of Thermonuclear Fuel with High Areal Density. Phys. Rev. Lett. 98, 155001 (2009)
W.L. Shang, R. Betti, S.X. Hu, K. Woo, L. Hao, C. Ren, A.R. Christopherson, A. Bose, W. Theobald, Electron Shock Ignition of Inertial Fusion Targets. Phys. Rev. Lett. 119, 195001 (2017)
H. Nagatomo, T. Johzaki, M. Hata, Y. Sentoku, S. Fujioka, K. Mima, H. Sakagami, Improvement of ignition and burning target design for fast ignition scheme. Nucl. Fusion 61, 126032 (2021)
D.S. Montgomery, W.S. Daughton, B.J. Albright, A.N. Simakov, D.C. Wilson, E.S. Dodd, R.C. Kirkpatrick, R.G. Watt, M.A. Gunderson, E.N. Loomis, E.C. Merritt, T. Cardenas, P. Amendt, J.L. Milovich, H.F. Robey, R.E. Tipton, M.D. Rosen, Design considerations for indirectly driven double shell capsules. Phys. Plasmas 25, 092706 (2018)
B.M. Haines, J.P. Sauppe, P.A. Keiter, E.N. Loomis, T. Morrow, D.S. Montgomery, L. Kuettner, B.M. Patterson, T.E. Quintana, J. Field, M. Millot, P. Celliers, D.C. Wilson, H.F. Robey, R.F. Sacks, D.J. Stark, C. Krauland, M. Rubery, Constraining computational modeling of indirect drive double shell capsule implosions using experiments. Phys. Plasmas 28, 032709 (2021)
K. Molvig, M.J. Schmitt, B.J. Albright, E.S. Dodd, N.M. Hoffman, G.H. McCall, S.D. Ramsey, Low Fuel Convergence Path to Direct-Drive Fusion Ignition. Phys. Rev. Lett. 116, 255003 (2016)
B.D. Keenan, W.T. Taitano, K. Molvig, Physics of the implosion up until the time of ignition in a revolver (triple-shell) capsule. Phys. Plasmas 27, 042704 (2020)
B.M. Haines, W.S. Daughton, E.N. Loomis, E.C. Merritt, D.S. Montgomery, J.P. Sauppe, J.L. Kline, Computational study of instability and fill tube mitigation strategies for double shell implosions. Phys. Plasmas 26, 102705 (2019)
E.C. Merritt, J.P. Sauppe, E.N. Loomis, T. Cardenas, D.S. Montgomery, W.S. Daughton, D.C. Wilson, J.L. Kline, S.F. Khan, M. Schoff, M. Hoppe, F. Fierro, R.B. Randolph, B. Patterson, L. Kuettner, R.F. Sacks, E.S. Dodd, W.C. Wan, S. Palaniyappan, S.H. Batha, P.A. Keiter, J.R. Rygg, V. Smalyuk, Y. Ping, P. Amendt, Experimental study of energy transfer in double shell implosions. Phys. Plasmas 26, 052702 (2019)
J. Yan, X. Zhang, J. Li, Z. Dai, B. Chen, L. Jing, Z. Chen, T. Huang, W. Jiang, B. Yu, Y. Pu, Z. Song, K. Deng, Z. Cao, F. Wang, S. Jiang, S. Liu, J. Yang, Preliminary experiments on hohlraum-driven double-shell implosion at the ShenGuang-III laser facility. Nucl. Fusion 58, 076020 (2018)
C. Tian, M. Yu, L. Shan, Y. Wu, T. Zhang, B. Bi, F. Zhang, Q. Zhang, D. Liu, W. Wang, Z. Yuan, S. Yang, L. Yang, W. Zhou, Y. Gu, B. Zhang, Radiography of direct drive double shell targets with hard x-rays generated by a short pulse laser. Nucl. Fusion 59, 046012 (2019)
R. Ramis, R. Schmalz, J. Meyer-ter-Vehn, MULTI — A computer code for one-dimensional multigroup radiation hydrodynamics. Comput. Phys. Commun. 49, 475 (1988)
W.L. Shang, J.M. Yang, Y.S. Dong, Enhancement of laser to x-ray conversion with a low density gold target. Appl. Phys. Lett. 102, 094105 (2013)
W. Zheng, X. Wei, Q. Zhu, F. Jing, D. Hu, X. Yuan, W. Dai, W. Zhou, F. Wang, D. Xu, X. Xie, B. Feng, Z. Peng, L. Guo, Y. Chen, X. Zhang, L. Liu, D. Lin, Z. Dang, Y. Xiang, R. Zhang, F. Wang, H. Jia, X. Deng, Laser performance upgrade for precise ICF experiment in SG-Ⅲ laser facility. Matter radiat. Extremes 2, 243 (2017)
Thanks to all the authors.
The authors would like to thank the National Natural Science Fund of China (Grant NO. 11775203).
W. L. Shang and W. Jiang contributed equally to this work. The authors are grateful to the other authors for many useful discussions.
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