Theoretical and numerical research of wire array Z-pinch and dynamic hohlraum at IAPCM

Ding Ning; Zhang Yang; Xiao Delong; Wu Jiming; Dai Zihuan; Yin Li; Gao Zhiming; Sun Shunkai; Xue Chuang; Ning Cheng; Shu Xiaojian; Wang Jianguo

doi:10.1016/j.mre.2016.06.001

Volume 1 Issue 3

May 2016

Turn off MathJax

Article Contents

Article Navigation > Matter and Radiation at Extremes > 2016 > 1(3):

Ding Ning, Zhang Yang, Xiao Delong, Wu Jiming, Dai Zihuan, Yin Li, Gao Zhiming, Sun Shunkai, Xue Chuang, Ning Cheng, Shu Xiaojian, Wang Jianguo. Theoretical and numerical research of wire array Z-pinch and dynamic hohlraum at IAPCM[J]. Matter and Radiation at Extremes, 2016, 1(3). doi: 10.1016/j.mre.2016.06.001

Citation:

Ding Ning, Zhang Yang, Xiao Delong, Wu Jiming, Dai Zihuan, Yin Li, Gao Zhiming, Sun Shunkai, Xue Chuang, Ning Cheng, Shu Xiaojian, Wang Jianguo. Theoretical and numerical research of wire array Z-pinch and dynamic hohlraum at IAPCM[J]. Matter and Radiation at Extremes, 2016, 1(3). doi: 10.1016/j.mre.2016.06.001

Citation:

Ding Ning, Zhang Yang, Xiao Delong, Wu Jiming, Dai Zihuan, Yin Li, Gao Zhiming, Sun Shunkai, Xue Chuang, Ning Cheng, Shu Xiaojian, Wang Jianguo. Theoretical and numerical research of wire array Z-pinch and dynamic hohlraum at IAPCM[J]. Matter and Radiation at Extremes, 2016, 1(3). doi: 10.1016/j.mre.2016.06.001

PDF( 4334 KB)

Theoretical and numerical research of wire array Z-pinch and dynamic hohlraum at IAPCM

doi: 10.1016/j.mre.2016.06.001

Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, PR China

More Information

Corresponding author: *Corresponding author. E-mail address: ding_ning@iapcm.ac.cn (N. Ding).
Received Date: 2016-04-04
Accepted Date: 2016-05-10
Publish Date: 2016-05-15

Abstract

Abstract

Dense Z-pinch plasmas are powerful and energy-efficient laboratory sources of X-rays, and show the possibility to drive inertial confinement fusion (ICF). Recent advances in wire-array Z-pinch and Z-pinch dynamic hohlraum (ZPDH) researches at the Institute of Applied Physics and Computational Mathematics are presented in this paper. Models are setup to study different physical processes. A full circuit model (FCM) was used to study the coupling between Z-pinch implosion and generator discharge. A mass injection model with azimuthal modulation was setup to simulate the wire-array plasma initiation, and the two-dimensional MHD code MARED was developed to investigate the Z-pinch implosion, MRT instability, stagnation and radiation. Implosions of nested and quasi-spherical wire arrays were also investigated theoretically and numerically. Key processes of ZPDH, such as the array–foam interaction, formation of the hohlraum radiation, as well as the following capsule ablation and implosion, were analyzed with different radiation magneto-hydrodynamics (RMHD) codes. An integrated 2D RMHD simulation of dynamic hohlraum driven capsule implosion provides us the physical insights of wire-array plasma acceleration, shock generation and propagation, hohlraum formation, radiation ablation, and fuel compression.
- Wire-array,
- Z-pinch,
- Dynamic holhraum,
- Inertial confinement fusion (ICF)

FullText(HTML)

References(99)

References

[1]	N.R. Pereira, J. Davis, N. Rostoker, X-rays from Z-pinches on relativistic electron-beam generators, J. Appl. Phys. 64 (1988) R1–R27.10.1063/1.341808
[2]	R.B. Spielman, C. Deeney, G.A. Chandler, M.R. Douglas, D.L. Fehl, et al., Tungsten wire-array Z-pinch experiments at 200 TW and 2 MJ, Phys. Plasmas 5 (1998) 2105–2111.10.1063/1.872881
[3]	C. Deeney, M.R. Douglas, R.B. Spielman, T.J. Nash, D.L. Peterson, et al., Enhancement of X-ray power from a Z pinch using nested-wire arrays, Phys. Rev. Lett. 81 (1998) 4883–4886.10.1103/physrevlett.81.4883
[4]	T.J. Nash, M.S. Derzon, G.A. Chandler, R. Leeper, D. Fehl, et al., High-temperature dynamic hohlraums on the pulsed power driver Z, Phys. Plasmas 6 (1999) 2023–2029.10.1063/1.873457
[5]	S.A. Slutz, M.R. Douglas, J.S. Lash, R.A. Vesey, G.A. Chandler, et al., Scaling and optimization of the radiation temperature in dynamic hohlraums, Phys. Plasmas 8 (2001) 1673–1691.10.1063/1.1360213
[6]	J. Bailey, G. Chandler, S. Slutz, G.R. Bennett, G. Cooper, et al., X-ray imaging measurements of capsule implosions driven by a Z-pinch dynamic hohlraum, Phys. Rev. Lett. 89 (2002) 095004.10.1103/physrevlett.89.095004
[7]	S.A. Slutz, J.E. Bailey, G.A. Chandler, G.R. Bennett, G. Cooper, et al., Dynamic hohlraum driven inertial fusion capsules, Phys. Plasmas 10 (2003) 1875–1882.10.1063/1.1565117
[8]	C.L. Ruiz, G.W. Cooper, S.A. Slutz, J.E. Bailey, G.A. Chandler, et al., Production of thermonuclear neutrons from deuterium-filled capsule implosions driven by Z-pinch dynamic hohlraums, Phys. Rev. Lett. 93 (2004) 015001.10.1103/physrevlett.93.015001
[9]	G.A. Rochau, J.E. Bailey, G.A. Chandler, G. Cooper, G.S. Dunham, et al., High performance capsule implosions driven by the Z-pinch dynamic hohlraum, Plasma Phys. Control. Fusion 49 (2007) B591.10.1088/0741-3335/49/12b/s55
[10]	S.A. Slutz, M.C. Herrmann, R.A. Vesey, A.B. Sefkow, D.B. Sinars, et al., Pulsed-power-driven cylindrical liner implosions of laser preheated fuel magnetized with an axial field, Phys. Plasmas 17 (2010) 056303.10.1063/1.3333505
[11]	C. Xue, N. Ding, S. Sun, D. Xiao, Y. Zhang, et al., Full circuit model for coupling pulsed power driver with Z-pinch load, Acta Phys. Sin. 63 (2014) 125207.
[12]	L. Wang, J. Wu, N. Guo, J. Han, M. Li, et al., Investigation of the resistance and inductance of planar wire array at Qiangguang accelerator, Plasma Sci. Technol. 14 (2012) 842–846.10.1088/1009-0630/14/9/13
[13]	L.B. Yang, H.D. Liao, C.W. Sun, K. Ouyang, J. Li, et al., RT instability in cylindrical implosion of jelly ring, Chin. Phys. 13 (2004) 1747.10.1088/1009-1963/13/10/031
[14]	S. Zhao, C. Xue, X. Zhu, R. Zhang, H. Luo, et al., Determining the resistance of X-pinch plasma, Chin. Phys. B 22 (2013) 045205.10.1088/1674-1056/22/4/045205
[15]	J. Deng, W. Xie, S. Feng, M. Wang, H. Li, et al., Initial performance of the primary test stand, IEEE Trans. Plasma Sci. 41 (2013) 2580–2583.
[16]	W. Zou, F. Guo, L. Chen, S. Song, M. Wang, et al., Full circuit calculation for electromagnetic pulse transmission in a high current facility, Phys. Rev. ST Accel. Beams 17 (2014) 110401.10.1103/physrevstab.17.110401
[17]	C. Xue, N. Ding, Y. Zhang, D. Xiao, S. Sun, et al., Full circuit simulation for electromagnetic pulse forming and transforming in the PTS facility, High Power Laser Part. Beams 28 (2016) 014014.
[18]	N. Ding, Y. Zhang, Q. Liu, D. Xiao, X. Shu, et al., Effects of various inductances on the dynamic models of the Z-pinch implosion of nested wire arrays, Acta Phys. Sin. 58 (2009) 1083–1090.
[19]	J. Huang, N. Ding, C. Xue, S. Sun, Two-dimensional magnetohydrodynamic studies of implosion modes of nested wire array Z-pinches, Phys. Plasmas 21 (2014) 072707.10.1063/1.4890474
[20]	L. Yin, J. Wu, Y. Yao, A cell functional minimization scheme for parabolic problem, J. Comput. Phys. 229 (2010) 8935–8951.10.1016/j.jcp.2010.08.018
[21]	L. Yin, J. Wu, Y. Yao, A cell functional minimization scheme for domain decomposition method on non-orthogonal and non-matching meshes, Numer. Math. 128 (2014) 773–804.10.1007/s00211-014-0623-3
[22]	J. Wu, Z. Gao, Z. Dai, A stabilized linearity-preserving scheme for the heterogeneous and anisotropic diffusion problems on polygonal meshes, J. Comput. Phys. 231 (2012) 7152–7169.10.1016/j.jcp.2012.06.042
[23]	Z. Gao, J. Wu, A small stencil and extremum-preserving scheme for anisotropic diffusion problems on arbitrary 2D and 3D meshes, J. Comput. Phys. 250 (2013) 308–331.10.1016/j.jcp.2013.05.013
[24]	J. Wu, Z. Gao, Interpolation-based second-order monotone finite volume schemes for anisotropic diffusion equations on general grids, J. Comput. Phys. 275 (2014) 569–588.10.1016/j.jcp.2014.07.011
[25]	L. Yin, J. Wu, Z. Gao, The cell functional minimization scheme for the anisotropic diffusion problems on arbitrary polygonal grids, ESAIM M2AN 49 (1) (2015) 193–220.10.1051/m2an/2014030
[26]	Z. Gao, J. Wu, A second-order positivity-preserving finite volume scheme for diffusion equations on general meshes, SIAM J. Sci. Comput. 37 (1) (2015) A420–A438.
[27]	T.W.L. Sanford, G.O. Allshouse, B.M. Marder, T.J. Nash, R.C. Mock, et al., Improved symmetry greatly increases X-ray power from wire-array Z-pinches, Phys. Rev. Lett. 77 (1996) 5063–5066.10.1103/physrevlett.77.5063
[28]	T.W.L. Sanford, R.C. Mock, R.B. Spielman, D.L. Peterson, D. Mosher, et al., Increased X-ray power generated from low-mass large-number aluminum-wire-array Z-pinch implosions, Phys. Plasmas 10 (1998) 3737–3754.10.1063/1.872984
[29]	V.V. Aleksandrov, E.V. Grabovski, A.N. Gribov, G.M. Oleinik, A.A. Samokhin, et al., Transportation of an electromagnetic pulse to the load in the angara-5-1 facility, Plasma Phys. Rep. 34 (2008) 911–919.10.1134/s1063780x08110044
[30]	S.V. Lebedev, F.N. Beg, S.N. Bland, J.P. Chittenden, A.E. Dangor, et al., Snowplow-like behavior in the implosion phase of wire array Z-pinches, Phys. Plamsas 9 (2002) 2293–2301.10.1063/1.1466466
[31]	C.A. Jennings, J.P. Chittenden, M.E. Cuneo, W.A. Stygar, D.J. Ampleford, et al., Circuit model for driving three-dimensional resistive MHD wire array Z-pinch calculations, IEEE Trans. Plasma Sci. 36 (2010) 529–539.
[32]	M.E. Cuneo, E.M. Waisman, S.V. Lebedev, J.P. Chittenden, W.A. Stygar, et al., Characteristics and scaling of tungsten-wire-array Z-pinch implosion dynamics at 20 MA, Plasma Phys. Rep. 71 (2005) 046406.10.1103/PhysRevE.71.046406
[33]	E.V. Grabovski, G.G. Zukakishvili, K.N. Mitrofanov, G.M. Oleinik, I.N. Frolov, et al., Study of the magnetic fields and soft X-ray emission generated in the implosion of double wire arrays, Plasma Phys. Rep. 32 (2010) 32–46.
[34]	S.V. Lebedev, F.N. Beg, S.N. Bland, J.P. Chittenden, A.E. Dangor, et al., Effect of discrete wires on the implosion dynamics of wire array Z-pinches, Phys. Plasmas 8 (2001) 3734–3747.10.1063/1.1385373
[35]	J.B. Greenly, J.D. Douglass, D.A. Hammer, B.R. Kusse, S.C. Glidden, et al., A 1 MA, variable risetime pulse generator for high energy density plasma research, Rev. Sci. Instrum. 79 (2008) 073501.10.1063/1.2949819
[36]	V.V. Alexsandrov, A.V. Branitskii, G.S. Volkov, E.V. Grabovskii, M.V. Zurin, et al., Dynamics of heterogeneous liners with prolonged plasma creation, Plasma Phys. Rep. 27 (2001) 89–109.10.1134/1.1348487
[37]	P.V. Sasorov, B.V. Oliver, E.P. Yu, T.A. Mehlhorn, One-dimensional ablation in multiwire arrays, Phys. Plasmas 15 (2008) 022702.10.1063/1.2832715
[38]	E.P. Yu, B.V. Oliver, D.B. Sinars, T.A.M.M.E. Cuneo, et al., Steady-state radiation ablation in the wire-array Z-pinch, Phys. Plasmas 14 (2007) 022705.10.1063/1.2435332
[39]	E.P. Yu, M.E. Cuneo, M.P. Desjarlais, R.W. Lemke, D.B. Sinars, et al., Three-dimensional effects in trailing mass in the wire-array Z pinch, Phys. Plasmas 15 (2008) 056301.10.1063/1.2837050
[40]	S.C. Bott, S.V. Lebedev, D.J. Ampleford, S.N. Bland, J.P. Chittenden, et al., Dynamics of cylindrically converging precursor plasma flow in wire-array Z-pinch experiments, Phys. Rev. E 74 (2006) 046403.10.1103/physreve.74.046403
[41]	F.N. Beg, S.V. Lebedev, S.N. Bland, J.P. Chittenden, A.E. Dangor, et al., The dynamics of single and nested nickel wire array Z-pinch implosions, IEEE Trans. Plasma Sci. 30 (2002) 552–558.10.1109/tps.2002.1024289
[42]	J. Huang, S. Sun, N. Ding, C. Ning, D. Xiao, et al., Numerical studies of ablated-plasma dynamics and precursor current of wire-array Z-pinches, Phys. Plasmas 18 (2011) 042704.10.1063/1.3574349
[43]	J. Huang, S. Sun, D. Xiao, N. Ding, C. Ning, et al., Two-dimensional numerical studies of ablated-plasma dynamics of wire-array Z-pinches, Acta Phys. Sin. 59 (2010) 6351–6361.
[44]	S. Lebedev, D. Ampleford, S. Bland, S. Bott, J. Chittenden, et al., Implosion dynamics of wire array Z-pinches: experiments at Imperial College, Nucl. Fusion 44 (12) (2004) S215.10.1088/0029-5515/44/12/s12
[45]	C. Ning, S.K. Sun, D.L. Xiao, Y. Zhang, N. Ding, et al., Numerical studies of the effects of precursor plasma on the performance of wire-array Z-pinches, Phys. Plamsas 17 (2010) 062703.10.1063/1.3430633
[46]	M.G. Haines, A heuristic model of the wire array Z-pinch, IEEE Trans. Plasma Sci. 26 (1998) 1275–1281.10.1109/27.725160
[47]	D.L. Peterson, R.L. Bowers, J.H. Brownell, A.E. Greene, K.D. McLenithan, et al., Two-dimensional modeling of magnetically driven Rayleigh Taylor instabilities in cylindrical Z-pinches, Phys. Plasmas 3 (1996) 368–381.10.1063/1.871862
[48]	D.L. Peterson, R.L. Bowers, K.D. McLenithan, C. Deeney, G.A. Chandler, et al., Characterization of energy flow and instability development in two-dimensional simulations of hollow Z-pinches, Phys. Plasmas 5 (1996) 3302–3310.
[49]	T.W. Hussey, N.F. Roderick, U. Shumlak, R.B. Spielman, C. Deeney, et al., A heuristic model for the nonlinear Rayleigh-Taylor instability in fast Z-pinches, Phys. Plasmas 2 (1995) 2055–2062.10.1063/1.871292
[50]	R. Latham, J.A. Nation, F.L. Curzon, A. Folkierski, Growth of surface instabilities in a linear pinched discharge, Nature 186 (1960) 624–625.10.1038/186624a0
[51]	R.L. Bowers, G. Nakafuji, A.E. Greene, K.D. McLenithan, D.L. Peterson, et al., Two-dimensional modeling of X-ray output from switched foil implosions on Procyon, Phys. Plasmas 3 (1996) 3448–3468.10.1063/1.871594
[52]	T.W.L. Sanford, R.C. Mock, B.M. Marder, T.J. Nash, R.B. Spielman, et al., Variation of high-power aluminum-wire array Z-pinch dynamics with wire number, load mass, and array radius, AIP Conf. Proc. 409 (1997) 561–573.10.1063/1.53920
[53]	D.L. Peterson, R.L. Bowers, J.H. Brownell, C. Lund, W. Matuska, et al., Application of 2-D simulations to hollow Z-pinch implosions, AIP Conf. Proc. 409 (1997) 201–210.10.1063/1.53929
[54]	J.H. Hammer, J.L. Eddleman, P.T. Springer, M. Tabak, A. Toor, et al., Two-dimensional radiation-magnetohydrodynamic simulations of SATURN imploding Z-pinches, Phys. Plasmas 3 (1996) 2063–2069.10.1063/1.872003
[55]	M.R. Douglas, C. Deeney, N.F. Roderick, Effect of sheath curvature on Rayleigh-Taylor mitigation in high-velocity uniform-fill, Z-pinch implosions, Phys. Rev. Lett. 78 (1997) 4577–4580.10.1103/physrevlett.78.4577
[56]	X.M. Qiu, L. Huang, G.D. Jian, Finite Larmor radius magnetohydrodynamic analysis of the Rayleigh-Taylor instability in Z-pinches with sheared axial flow, Phys. Plasmas 14 (2007) 032111.10.1063/1.2717583
[57]	X.M. Qiu, L. Huang, G.D. Jian, Mitigation effect of finite Larmor radius on Rayleigh-Taylor instability in Z-pinch implosions, Chin. Phys. Lett. 19 (2002) 217–219.10.1088/0256-307x/19/2/324
[58]	X.M. Qiu, L. Huang, G.D. Jian, Stabilization of viscosity on Rayleigh-Taylor instability in Z-pinches, Chin. Phys. Lett. 21 (2004) 689–692.10.1088/0256-307x/21/4/028
[59]	Y. Zhang, N. Ding, The mitigation effect of sheared axial flow on the Rayleigh-Taylor instability in Z-pinch plasma, Nucl. Fusion & Plasma Phys. 25 (2005) 15–21.
[60]	Y. Zhang, N. Ding, Effects of compressibility on the magneto-Rayleigh-Taylor instability in Z-pinch implosions with sheared axial flows, Phys. Plasmas 13 (2006) 022701.10.1063/1.2167912
[61]	Y. Zhang, N. Ding, The effect of axial flow on the stability in the Z-pinch, Acta Phys. Sin. 55 (2006) 2333–2339.
[62]	Y. Zhang, N. Ding, Stability analysis of viscous Z-pinch plasma with a sheared axial flow, Chin. Phys. B 17 (2008) 2994–3002.10.1088/1674-1056/17/8/039
[63]	N. Ding, Y. Zhang, Q. Liu, Simplified analysis of the MHD instability in Z-pinch plamas, Nucl. Fusion Plasma Phys. 28 (2008) 101–104.
[64]	N. Ding, J. Wu, Z. Yang, S. Fu, C. Ning, et al., Simulation of Z-pinch implosion using MARED code, High Power Laser Part. Beams 20 (2008) 212–218.
[65]	Y. Zhang, J. Wu, Z. Dai, N. Ding, C. Ning, et al., Computational investigation of the magneto-Rayleigh-Taylor instability in Z-pinch implosions, Phys. Plasmas 17 (2010) 042702.10.1063/1.3381072
[66]	T.W.L. Sanford, T.J. Nash, R.C. Mock, R.B. Spielman, K.W. Struve, et al., Dynamics of a high-power aluminum-wire array Z-pinch implosion, Phys. Plasmas 4 (2010) 2188–2203.10.1063/1.872382
[67]	N. Ding, C. Ning, Z. Wang, Z. Li, R. Xu, et al., X-ray radiation power optimization in 1 MA to 4 MA wire-array implosions, Acta Phys. Sin. 60 (2011) 025209.
[68]	N. Ding, R. Xu, Z. Li, J. Yang, S. Jiang, et al., New results of sino-russian joint Z-pinch experiments, Acta Phys. Sin. 60 (2011) 045208.
[69]	N. Ding, J. Wu, Z.H. Yang, S.W. Fu, C. Ning, et al., Simulation of Z-pinch implosion using MARED code, High Power Laser Part. Beams 20 (2008) 212.
[70]	K. Lan, Y. Zhang, W. Zheng, Theoretical study on discharge-pumped soft X-ray laser in Ne-like Ar, Phys. Plasmas 6 (4343) (1999).10.1063/1.873698
[71]	K. Lan, Y. Zhang, Theoretical studies of aluminum wire array Z-pinch implosions with varying masses and radii, Eur. Phys. J. AP 19 (2002) 103.10.1051/epjap:2002055
[72]	D. Xiao, C. Ning, K. Lan, N. Ding, Preliminary studies of the mechanism of producing radiation in aluminum wire array Z-pinch implosion, Acta Phys. Sin. 59 (2010) 430.
[73]	D. Xiao, N. Ding, C. Ning, K. Lan, Non-equilibrium radiation of aluminum wire array Z-pinch, High Power Laser Part. Beams 22 (2010) 341.
[74]	D. Xiao, N. Ding, C. Ning, S. Sun, Y. Zhang, et al., Numerical investigation on the X-ray production of aluminum-wire-array z-pinch implosion, IEEE Trans. Plasma Sci. 39 (2011) 686.10.1109/tps.2010.2091723
[75]	C. Deeney, P.D. Lepell, B.H. Failor, S.L. Wong, J.P. Apruzese, et al., Increased kilo-electron-volt X-ray yields from Z-pinch plasmas by mixing elements of similar atomic numbers, Phys. Rev. E 51 (1995) 4823–4832.10.1103/physreve.51.4823
[76]	D. Xiao, N. Ding, C. Xue, J. Huang, Y. Zhang, et al., Increasing the k-shell yield of line radiation in Z-pinch implosions using alloyed al/mg wire-arrays, Phys. Plasmas 20 (2013) 013304.10.1063/1.4789458
[77]	N.A.G.J. Davis, A.L. Velikovich, Fast commutation of high current in double wire array Z-pinch loads, Appl. Phys. Lett. 70 (1997) 170–172.10.1063/1.118339
[78]	S.V. Lebedev, R. Aliaga-Rossel, S.N. Bland, J.P. Chittenden, A.E. Dangor, et al., Two different modes of nested wire array Z-pinch implosions, Phys. Rev. Lett. 84 (2000) 1708–1711.10.1103/physrevlett.84.1708
[79]	A.A. Esaulov, A.L. Velikovich, V.L. Kantsyrev, T.A. Mehlhorn, M.E. Cuneo, Wire dynamics model of the implosion of nested and planar wire arrays, Phys. Plasmas 13 (2006) 120701.10.1063/1.2402147
[80]	J.P. Chittenden, S.V. Lebedev, S.N. Bland, A. Ciardi, M.G. Haines, The different dynamical modes of nested wire array Z-pinches, Phys. Plasmas 8 (2001) 675–678.10.1063/1.1351552
[81]	A.A. Esaulov, V.L. Kantsyrev, A.S. Safronova, A. L. Velikovich, I.K. Shrestha, et al., Wire ablation dynamics model and its application to imploding wire arrays of different geometries, Phys. Rev. E 86 (2012) 046404.10.1103/PhysRevE.86.046404
[82]	J. Huang, N. Ding, C. Ning, S. Sun, Y. Zhang, et al., Numerical investigation on the implosion dynamics of wire-array Z-pinches in (r, θ) geometry, Phys. Plasmas 19 (2012) 062701.10.1063/1.4725423
[83]	M. Matzen, Z pinches as intense X-ray sources for high-energy density physics applications, Phys. Plasmas 4 (1997) 1519–1527.10.1063/1.872323
[84]	R. Leeper, T. Alberts, J. Asay, P.M. Baca, K.L. Baker, et al., Z-pinch driven inertial confinement fusion target physics research at Sandia National Laboratories, Nucl. Fusion 39 (1999) 1283–1294.10.1088/0029-5515/39/9y/306
[85]	J. Hammer, M. Tabak, S.C. Wilks, J.D. Lindl, D.S. Bailey, et al., High yield inertial confinement fusion target design for a Z-pinch-driven hohlraum, Phys. Plasmas 6 (1999) 2129–2136.10.1063/1.873464
[86]	M. Cuneo, D. Sinars, E. Waisman, D.E. Bliss, W.A. Stygar, et al., Compact single and nested tungsten-wire-array dynamics at 14c19 MA and applications to inertial confinement fusion, Phys. Plasmas 13 (2006) 056318.10.1063/1.2177140
[87]	V. Smirnov, S. Zakharov, E. Grabovskii, Increase in radiation intensity in a quasi-spherical double liner/dynamic hohlraum system, JETP Lett. 81 (2005) 442–447.10.1134/1.1984026
[88]	T. Nash, D. McDaniel, R. Leeper, C.D. Deeney, T.W.L. Sanford, et al., Design, simulation, and application of quasi-spherical 100 ns Z-pinch implosions driven by tens of mega-amperes, Phys. Plasmas 12 (2005) 052705.10.1063/1.1890945
[89]	T. Nash, P. VanDevender, D. McDaniel, L. Abbot, Quasi-spherical Direct Drive Fusion, Sandia National Laboratory Report No.SAND2007–0235.
[90]	P. VanDevender, D. McDaniel, N. Roderick, T. Nash, Quasi-spherical Direct Drive Fusion Simulations for the Z Machine and Future Accelerators, Sandia National Laboratory Report No. SAND2007–7178.
[91]	J. Degnan, F. Lehr, J. Beason, G.P. Baca, D.E. Bell, et al., Electromagnetic implosion of spherical liner, Phys. Rev. Lett. 74 (1995) 98–101.10.1103/physrevlett.74.98
[92]	J. Degnan, M. Alme, B. Austin, J.D. Beason, S.K. Coffey, et al., Compression of plasma to megabar range using imploding liner, Phys. Rev. Lett. 82 (1999) 2681–2684.10.1103/physrevlett.82.2681
[93]	Y. Zhang, N. Ding, Z. Li, S. Sun, C. Xue, et al., Dynamics of quasi-spherical Z-pinch implosions with mass redistribution and displacement modification, Phys. Plasmas 19 (2012) 122704.10.1063/1.4771575
[94]	Y. Zhang, N. Ding, Z. Li, R. Xu, S. Sun, et al., Numerical study of quasi-spherical wire-array implosions on the Qiangguang-i facility, IEEE Trans. Plasma Sci. 40 (2012) 3360–3366.10.1109/tps.2012.2219075
[95]	Y. Zhang, N. Ding, Z. Li, R. Xu, D. Chen, et al., Realization of quasi-spherical implosion using pre-shaped prolate wire arrays with a compression foam target inside, Phys. Plasmas 22 (2015) 020703.10.1063/1.4905229
[96]	J.H. Brownell, R.L. Bowers, K.D. McLenithan, D.L. Peterson, Radiation environments produced by plasma z -pinch stagnation on central targets, Phys. Plasmas 5 (1998) 2071.10.1063/1.872879
[97]	D. Xiao, S. Sun, C. Xue, Y. Zhang, N. Ding, et al., Numerical studies on the formation process of Z-pinch dynamic hohlruams and key issues of optimizing dynamic hohlraum radiation, Acta Phys. Sin. 64 (2015) 235203.
[98]	D. Xiao, N. Ding, F. Ye, J. Ning, Q. Hu, et al., Numerical and experimental investigations on the interaction of light wire-array z-pinches with embedded heavy foam converters, Phys. Plasmas 21 (2014) 042704.10.1063/1.4871394
[99]	D. Xiao, S. Sun, Y. Zhao, N. Ding, J. Wu, et al., Numerical investigation on target implosions driven by radiation ablation and shock compression in dynamic hohlraums, Phys. Plasmas 22 (2015) 052709.10.1063/1.4921332