Basic dynamic and scale study of quasi-spherical Z-pinch implosion

Zhang Yang; Sun Shun-Kai; Ding Ning; Li Zheng-Hong; Shu Xiao-Jian

doi:10.7498/aps.66.105203

Abstract

Unlike cylindrical Z pinch, a quasi-spherical implosion enables load plasma to implode inward spherically and concentrate its kinetic energy toward the center. This helps to improve the energy-transport efficiency and increase the shock-induced radiation intensity of the foam convertor, when the quasi-spherical implosion is used to drive a dynamic hohlraum (DH). In previous work, it has been proved that a spherical metal shell with an exact mass-distribution can implode spherically by the nonuniform magnetic field, whose magnitude increases with the load latitude, Bφ~cos-1θ. However, this ‘mass-redistribution’ method is hard to realize on the fast pulse power generator widely used in today's Z-pinch study. The rise time of the facility is only ~100 ns, and the load is wire arrays with typical weight about 1 mg/cm. We develop a method of gaining quasi-spherical implosion with wire arrays by adjusting their initial shape, and it proves feasible on the 1.5 MA Qiangguang-I facility. Recently, we try to realize the quasi-spherical dynamic hohlraum (QSDH) implosion on generator with higher current, such as the 4.5 MA Angara5-I or the 8 MA PTS facility, and to make a direct compare with its cylindrical equivalence. But first of all, a basic but relatively comprehensive study on the quasi-spherical implosion dynamics is necessary and useful for the future QSDH load design and optimization.#br#Comparing with the device for classical cylindrical Z-pinch implosions, the load and electrodes structures of quasi-spherical implosions are complex, which leads to distinct implosion dynamics and scale rules. In this paper, we develop a thin shell model for the quasi-spherical implosion, from which the movement equation, as well as the energy scale relation is derived analytically. It is found that under the same drive condition, the implosion velocity and total kinetic energy of cylindrical load are higher than those of quasi-spherical one. However, as we expected, the quasi-spherical implosion has larger kinetic energy density, which is important for the applications such as driving a dynamic holhraum. Besides the peak current, the kinetic energy of quasi-spherical implosion also depends on the initial size of the load. By increasing the initial radius and maximum latitude angle moderately, one can obtain higher kinetic energy and energy density of the implosion, which is crucial for the load design. The theoretical study is supported by simulation results. It is found that under a drive condition close to that of the ZR facility, a quasi-spherical load with an initial radius of 5 cm will reach a peak kinetic energy density of 3.2 MJ/cm, which is about 3 times those from the cylindrical ones.

Keywords:

Authors and contacts

1.
Institute of Applied Physics and Computational Mathematics, Beijing 100088, China;
2.
Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, Mianyang 621900, China

Corresponding author: Ding Ning, ding_ning@iapcm.ac.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11405012, 91330107, 11275030, 11675025), the Defense Industrial Technology Development Program, China (Grant No. B1520133015), and the Foundation of President of China Academy of Engineering Physics (Grant No. 2014-1-042).

References

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[14]	Cuneo M E, Sinars D B, Waisman E M Bliss D E, Stygar W A, Vesey R A, Lemke R W, Smith I C, Rambo P K, Porter J L, Chandler G A, Nash T J, Mazarakis M G, Adams R G, Yu E P, Struve K W, Mehlhorn T A, Lebedev S V, Chittenden J P, Jennings C A 2006 Phys. Plasmas 13 056318
[15]	Sanford T W L, Lemke R W, Mock R C Chandler G A, Leeper R J, Ruiz C L, Peterson D L, Chrien R E, Idzorek G C, Watt R G, Chittenden J P 2002 Phys. Plasmas 9 3573
[16]	Rochau G A, Bailey J E, Chandler G A, Cooper G, Dunham G S, Lake P W, Leeper R J, Lemke R W, Mehlhorn T A, Nikroo A, Peterson K J, Ruiz C L, Schroen D G, Slutz S A, Steinman D, Stygar W A, Varnum W 2007 Plasma Phys. Control. Fusion 49 B591
[17]	Olson C, Rochau G, Slutz S, Morrow C, Olson R, Cuneo M, Hanson D, Bennett G, Sanford T, Bailey J, Stygar W, Vesey R, Mehlhorn T, Struve K, Mazarakis M, Savage M, Pointon T, Kiefer M, Rosenthal S, Cochrane K, Schneider L, Glover S, Reed K, Schroen D, Farnum C, Modesto M, Oscar D, Chhabildas L, Boyes J, Vigil V, Keith R, Turgeon M, Cipiti B, Lindgren E, Dandini V, Tran H, Smith D, McDaniel D, Quintenz J, Matzen M K, van Devender J P, Gauster W, Shephard L, Walck M, Renk T, Tanaka T, Ulrickson M, Meier W, Latkowski J, Moir R, Schmitt R, Reyes S, Abbott R, Peterson R, Pollock G, Ottinger P, Schumer J, Peterson P, Kammer D, Kulcinski G, El-Guebaly L, Moses G, Sviatoslavsky I, Sawan M, Anderson M, Bonazza R, Oakley J, Meekunasombat P, de Groot J, Jensen N, Abdou M, Ying A, Calderoni P, Morley N, Abdel-Khalik S, Dillon C, Lascar C, Sadowski D, Curry R, McDonald K, Barkey M, Szaroletta W, Gallix R, Alexander N, Rickman W, Charman C, Shatoff H, Welch D, Rose D, Panchuk P, Louie D, Dean S, Kim A, Nedoseev S, Grabovsky E, Kingsep A, Smirnov V 2005 Fusion Sci. Tech. 47 633
[18]	Peterson K J, Sinars D B, Yu E P, Herrmann M C, Cuneo M E, Slutz S A, Smith I C, Atherton B W, Knudson M D, Nakhleh C 2012 Phys. Plasmas 19 092701
[19]	Slutz S, Vesey R 2012 Phys. Rev. Lett. 108 025003
[20]	Smirnov V P, Zakharov S V, Grabovskii E V 2005 JETP Letters 81 442
[21]	Smirnov V P, Grabovskii E V, Zakharov S V 2012 Nukleonika 57 215
[22]	Nash T J, McDaniel D H, Leeper R J, Deeney C D, Sanford T W L, Struve K, DeGroot J S 2005 Phys. Plasmas 12 052705
[23]	Grabovski E V 2012 CAEP Annual Conference on Science and Technology Mianyang, China, August 17-24, 2012
[24]	Lebedev S V, Ampleford D J, Bland S N, Bott S C, Hall G N 2006 Proceeding of 6th International Conference on Dense Z-pinches 69 Cp808
[25]	Zhang Y, Ding N, Li Z, Xu R, Sun S, Chen D, Xue C 2012 IEEE Trans. Plasma Sci. 40 3360
[26]	Zhang Y, Ding N, Li Z, Xu R, Chen D, Ye F, Zhou X, Chen F, Chen J, Li L, Xiao D, Sun S, Xue C, Shu X, Wang J 2015 Phys. Plasmas 22 020703
[27]	Degnan J H, Alme M L, Austin B S, Beason J D, Coffey S K, Gale D G, Graham J D, Havranek J J, Hussey T W, Kiuttu G F, Kreh B B, Lehr F M, Lewis R A, Lileikis D E, Morgan D, Outten C A, Peterkin Jr R E, Platts D, Roderick N F, Ruden E L, Shumlak U, Smith G A, Sommars W, Turchi P J 1999 Phys. Rev. Lett. 82 2681
[28]	Ryutov D D, Derzon M S, Matzen M K 2000 Rev. Mod. Phys. 72 167
[29]	Stone J M, Norman M L 1992 Astrophys. J. Suppl. Series 80 753
[30]	More R M 1981 Atomic Physics in Inertial Confinement Fusion, LLNL Report No UCRL-84991
[31]	Kemp A J, Meyer-ter-Vehn J 1999 MPQeos A New Equation of State Code for Hot, Dense Matter, Short Documentation (version 20)

Cited By

[1]	Spielman R B, Deeney C, Chandler G A, Douglas M R, Fehl D L, Matzen M K, McDaniel D H, Nash T J, Porter J L, Sanford T W L, Seamen J F, Stygar W A, Struve K W, Breeze S P, McGurn J S, Torres J A, Zagar D M, Gilliland T L, Jobe D O, McKenney J L, Mock R C, Vargas M, Wagoner T, Peterson D L 1998 Phys. Plasmas 5 2105
[2]	Deeney C, Douglas M R, Spielman R B, Nash T J, Peterson D L, L'Eplattenier P, Chandler G A, Seamen J F, Struve K W 1998 Phys. Rev. Lett. 81 4883
[3]	Sanford T W L, Allshouse G O, Marder B M, Nash T J, Mock R C, Spielman R B, Seamen J F, McGurn J S, Jobe D, Gilliland T L, Vargas M, Struve K W, Stygar W A, Douglas M R, Matzen M K, Hammer J H, de Groot J S, Eddleman J L, Peterson D L, Mosher D, Whitney K G, Thornhill J W, Pulsifer P E, Apruzese J P, Maron Y 1996 Phys. Rev. Lett. 77 5063
[4]	Ding N, Zhang Y, Ning C, Shu X J, Xiao D L 2008 Acta Phys. Sin. 57 3027 (in Chinese) [丁宁, 张扬, 宁成, 束小建, 肖德龙 2008 57 3027]
[5]	Xu R K, Li Z H, Guo C, Yang J L, Li L B, Song F J, Ning J M, Xia G X, Xu Z P 2003 Acta Phys. Sin. 52 1203 (in Chinese) [徐荣昆, 李正宏, 郭存, 杨建伦, 李林波, 宋凤军, 宁佳敏, 夏广新, 许泽平 2003 52 1203]
[6]	Matzen M K, Sweene, M A, Adams R G, Asay J R, Bailey J E, Bennett G R, Bliss D E, Bloomquist D D, Brunner T A, Campbell R B, Chandler G A, Coverdale C A, Cuneo M E, Davis J P, Deeney C, Desjarlais M P, Donovan G L, Garasi C J, Haill T A, Hall C A, Hanson D L, Hurst M J, Jones B, Knudson M D, Leeper R J, Lemke R W, Mazarakis M G, McDaniel D H, Mehlhorn T A, Nash T J, Olson C L, Porter J L, Rambo P K, Rosenthal S E, Rochau G A, Ruggles L E, Ruiz C L, Sanford T W L, Seamen J F, Sinars D B, Slutz S A, Smith I C, Struve K W, Stygar W A, Vesey R A, Weinbrecht E A, Wenger D F, Yu E P 2005 Phys. Plasmas 12 55503
[7]	Nash T J, Derzon M S, Chandler G A, Leeper R, Fehl D, Lash J, Ruiz C, Cooper G, Seaman J F, McGurn J, Lazier S, Torres J, Jobe D, Gilliland T, Hurst M, Mock R, Ryan P, Nielsen D, Armijo J, McKenney J, Hawn R, Hebron D, MacFarlane J J, Petersen D, Bowers R, Matuska W, Ryutov D D 1999 Phys. Plasmas 6 2023
[8]	Peterson D L, Bowers R L, Matuska W, McLenithan K D, Chandler G A, Deeney C, Derzon M S, Douglas M, Matzen M K, Nash T J, Spielman R B, Struve K W, Stygar W A, Roderick N F 1999 Phys. Plasmas 6 2178
[9]	Sanford T W L, Lemke R W, Mock R C, Peterson D L 2003 Phys. Plasmas 10 3252
[10]	Bailey J E, Chandler G A, Mancini R C Slutz S A, Rochau G A, Bump M, Buris-Mog T J, Cooper G, Dunham G, Golovkin I, Kilkenny J D, Lake P W, Leeper R J, Lemke R, MacFarlane J J, Mehlhorn T A, Moore T C, Nash T J, Nikroo A, Nielsen D S, Peterson K L, Ruiz C L, Schroen D G, Steinman D, Varnum W 2006 Phys. Plasmas 13 056301
[11]	Matzen M K 1997 Phys. Plasmas 4 1519
[12]	Lindl J 1995 Phys. Plasmas 2 3933
[13]	Hammer J H, Tabak M, Wilks S C, Lindl J D, Bailey D S, Rambo P W, Toor A, Zimmerman G B, Porter Jr J L 1999 Phys. Plasmas 6 2129
[14]	Cuneo M E, Sinars D B, Waisman E M Bliss D E, Stygar W A, Vesey R A, Lemke R W, Smith I C, Rambo P K, Porter J L, Chandler G A, Nash T J, Mazarakis M G, Adams R G, Yu E P, Struve K W, Mehlhorn T A, Lebedev S V, Chittenden J P, Jennings C A 2006 Phys. Plasmas 13 056318
[15]	Sanford T W L, Lemke R W, Mock R C Chandler G A, Leeper R J, Ruiz C L, Peterson D L, Chrien R E, Idzorek G C, Watt R G, Chittenden J P 2002 Phys. Plasmas 9 3573
[16]	Rochau G A, Bailey J E, Chandler G A, Cooper G, Dunham G S, Lake P W, Leeper R J, Lemke R W, Mehlhorn T A, Nikroo A, Peterson K J, Ruiz C L, Schroen D G, Slutz S A, Steinman D, Stygar W A, Varnum W 2007 Plasma Phys. Control. Fusion 49 B591
[17]	Olson C, Rochau G, Slutz S, Morrow C, Olson R, Cuneo M, Hanson D, Bennett G, Sanford T, Bailey J, Stygar W, Vesey R, Mehlhorn T, Struve K, Mazarakis M, Savage M, Pointon T, Kiefer M, Rosenthal S, Cochrane K, Schneider L, Glover S, Reed K, Schroen D, Farnum C, Modesto M, Oscar D, Chhabildas L, Boyes J, Vigil V, Keith R, Turgeon M, Cipiti B, Lindgren E, Dandini V, Tran H, Smith D, McDaniel D, Quintenz J, Matzen M K, van Devender J P, Gauster W, Shephard L, Walck M, Renk T, Tanaka T, Ulrickson M, Meier W, Latkowski J, Moir R, Schmitt R, Reyes S, Abbott R, Peterson R, Pollock G, Ottinger P, Schumer J, Peterson P, Kammer D, Kulcinski G, El-Guebaly L, Moses G, Sviatoslavsky I, Sawan M, Anderson M, Bonazza R, Oakley J, Meekunasombat P, de Groot J, Jensen N, Abdou M, Ying A, Calderoni P, Morley N, Abdel-Khalik S, Dillon C, Lascar C, Sadowski D, Curry R, McDonald K, Barkey M, Szaroletta W, Gallix R, Alexander N, Rickman W, Charman C, Shatoff H, Welch D, Rose D, Panchuk P, Louie D, Dean S, Kim A, Nedoseev S, Grabovsky E, Kingsep A, Smirnov V 2005 Fusion Sci. Tech. 47 633
[18]	Peterson K J, Sinars D B, Yu E P, Herrmann M C, Cuneo M E, Slutz S A, Smith I C, Atherton B W, Knudson M D, Nakhleh C 2012 Phys. Plasmas 19 092701
[19]	Slutz S, Vesey R 2012 Phys. Rev. Lett. 108 025003
[20]	Smirnov V P, Zakharov S V, Grabovskii E V 2005 JETP Letters 81 442
[21]	Smirnov V P, Grabovskii E V, Zakharov S V 2012 Nukleonika 57 215
[22]	Nash T J, McDaniel D H, Leeper R J, Deeney C D, Sanford T W L, Struve K, DeGroot J S 2005 Phys. Plasmas 12 052705
[23]	Grabovski E V 2012 CAEP Annual Conference on Science and Technology Mianyang, China, August 17-24, 2012
[24]	Lebedev S V, Ampleford D J, Bland S N, Bott S C, Hall G N 2006 Proceeding of 6th International Conference on Dense Z-pinches 69 Cp808
[25]	Zhang Y, Ding N, Li Z, Xu R, Sun S, Chen D, Xue C 2012 IEEE Trans. Plasma Sci. 40 3360
[26]	Zhang Y, Ding N, Li Z, Xu R, Chen D, Ye F, Zhou X, Chen F, Chen J, Li L, Xiao D, Sun S, Xue C, Shu X, Wang J 2015 Phys. Plasmas 22 020703
[27]	Degnan J H, Alme M L, Austin B S, Beason J D, Coffey S K, Gale D G, Graham J D, Havranek J J, Hussey T W, Kiuttu G F, Kreh B B, Lehr F M, Lewis R A, Lileikis D E, Morgan D, Outten C A, Peterkin Jr R E, Platts D, Roderick N F, Ruden E L, Shumlak U, Smith G A, Sommars W, Turchi P J 1999 Phys. Rev. Lett. 82 2681
[28]	Ryutov D D, Derzon M S, Matzen M K 2000 Rev. Mod. Phys. 72 167
[29]	Stone J M, Norman M L 1992 Astrophys. J. Suppl. Series 80 753
[30]	More R M 1981 Atomic Physics in Inertial Confinement Fusion, LLNL Report No UCRL-84991
[31]	Kemp A J, Meyer-ter-Vehn J 1999 MPQeos A New Equation of State Code for Hot, Dense Matter, Short Documentation (version 20)

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