Hybrid fluid–particle modeling of shock-driven hydrodynamic instabilities in a plasma

Cai Hong-bo; Yan Xin-xin; Yao Pei-lin; Zhu Shao-ping

doi:10.1063/5.0042973

Volume 6 Issue 3

May 2021

Turn off MathJax

Article Contents

Article Navigation > Matter and Radiation at Extremes > 2021 > 6(3): 035901

Cai Hong-bo, Yan Xin-xin, Yao Pei-lin, Zhu Shao-ping. Hybrid fluid–particle modeling of shock-driven hydrodynamic instabilities in a plasma[J]. Matter and Radiation at Extremes, 2021, 6(3): 035901. doi: 10.1063/5.0042973

Citation:

Cai Hong-bo, Yan Xin-xin, Yao Pei-lin, Zhu Shao-ping. Hybrid fluid–particle modeling of shock-driven hydrodynamic instabilities in a plasma[J]. Matter and Radiation at Extremes, 2021, 6(3): 035901. doi: 10.1063/5.0042973

Citation:

PDF( 2997 KB)

Hybrid fluid–particle modeling of shock-driven hydrodynamic instabilities in a plasma

doi: 10.1063/5.0042973

Cai Hong-bo^{1, 2
,
,
,},
Yan Xin-xin³,
Yao Pei-lin^4
,,
Zhu Shao-ping^{1, 5, 6
,}

1.
Institute of Applied Physics and Computational Mathematics, Beijing 100094, China
2.
Center for Applied Physics and Technology, HEDPS, and College of Engineering, Peking University, Beijing 100871, China
3.
Center for Applied Physics and Technology, HEDPS, School of Physics, and College of Engineering, Peking University, Beijing 100871, China
4.
Department of Engineering Physics, Tsinghua University, Beijing 100084, China
5.
Graduate School, China Academy of Engineering Physics, P.O. Box 2101, Beijing 100088, China
6.
Science and Technology on Plasma Physics Laboratory, Laser Fusion Research Center, CAEP, 621900 Mianyang, China

More Information

Corresponding author: a)Author to whom correspondence should be addressed: cai_hongbo@iapcm.ac.cn
Received Date: 2021-01-05
Accepted Date: 2021-03-01

Available Online: 2021-05-01

Publish Date: 2021-05-15

Abstract

Abstract

Shock-driven hydrodynamic instabilities in a plasma usually lead to interfacial mixing and the generation of electromagnetic fields, which are nonequilibrium processes coupling kinetics with meso- and macroscopic dynamics. The understanding and modeling of these physical processes are very challenging tasks for single-fluid hydrodynamic codes. This work presents a new framework that incorporates both kinetics and hydrodynamics to simulate shock waves and hydrodynamic instabilities in high-density plasmas. In this hybrid code, ions are modeled using the standard particle-in-cell method together with a Monte Carlo description of collisions while electrons are modeled as a massless fluid, with the electron heat flux and fluid–particle energy exchange being considered in the electron pressure equation. In high-density plasmas, Maxwell’s equations are solved using Ohm’s law instead of Ampère’s law. This hybrid algorithm retains ion kinetic effects and their consequences for plasma interpenetration, shock wave propagation, and hydrodynamic instability. Furthermore, we investigate the shock-induced (or gravity-induced) turbulent mixing between a light and a heavy plasma, where hydrodynamic instabilities are initiated by a shock wave (or gravity). This study reveals that self-generated electromagnetic fields play a role in the formation of baroclinic vorticity along the interface and in late-time mixing of the plasmas. Our results confirm the ability of the proposed method to describe shock-driven hydrodynamic instabilities in a plasma, in particular, nonequilibrium processes that involve mixing and electromagnetic fields at the interface.

FullText(HTML)

References(43)

References

[1]	O. A. Hurricane, D. A. Callahan, D. T. Casey, P. M. Celliers, C. Cerjan, E. L. Dewald, T. R. Dittrich, T. Döppner, D. E. Hinkel, L. F. Berzak Hopkins et al., “Fuel gain exceeding unity in an inertially confined fusion implosion,” Nature 506, 343 (2014).10.1038/nature13008
[2]	V. A. Smalyuk, D. T. Casey, D. S. Clark, M. J. Edwards, S. W. Haan, A. Hamza, D. E. Hoover, W. W. Hsing, O. Hurricane, J. D. Kilkenny et al., “First measurements of hydrodynamic instability growth in indirectly driven implosions at ignition-relevant conditions on the National Ignition Facility,” Phys. Rev. Lett. 112, 185003 (2014).10.1103/physrevlett.112.185003
[3]	J. P. Sauppe, S. Palaniyappan, E. N. Loomis, J. L. Kline, K. A. Flippo, and B. Srinivasan, “Using cylindrical implosions to investigate hydrodynamic instabilities in convergent geometry,” Matter Radiat. Extremes 4, 065403 (2019).10.1063/1.5090999
[4]	T. Ma, P. K. Patel, N. Izumi, P. T. Springer, M. H. Key, L. J. Atherton, L. R. Benedetti, D. K. Bradley, D. A. Callahan, P. M. Celliers et al., “Onset of hydrodynamic mix in high-velocity, highly compressed inertial confinement fusion implosions,” Phys. Rev. Lett. 111, 085004 (2013).10.1103/physrevlett.111.085004
[5]	V. A. Smalyuk, R. E. Tipton, J. E. Pino, D. T. Casey, G. P. Grim, B. A. Remington, D. P. Rowley, S. V. Weber, M. Barrios, L. R. Benedetti et al., “Measurements of an ablator-gas atomic mix in indirectly driven implosions at the National Ignition Facility,” Phys. Rev. Lett. 112, 025002 (2014).10.1103/physrevlett.112.025002
[6]	M. J. Rosenberg, H. G. Rinderknecht, N. M. Hoffman, P. A. Amendt, S. Atzeni, A. B. Zylstra, C. K. Li, F. H. Séguin, H. Sio, M. Gatu Johnson et al., “Exploration of the transition from the hydrodynamiclike to the strongly kinetic regime in shock-driven implosions,” Phys. Rev. Lett. 112, 185001 (2014).10.1103/physrevlett.112.185001
[7]	J. R. Rygg, J. A. Frenje, C. K. Li, F. H. Séguin, R. D. Petrasso, F. J. Marshall, J. A. Delettrez, J. P. Knauer, D. D. Meyerhofer, and C. Stoeckl, “Observations of the collapse of asymmetrically driven convergent shocks,” Phys. Plasmas 15, 034505 (2008).10.1063/1.2892025
[8]	T. Gong, L. Hao, Z. C. Li, D. Yang, S. W. Li, X. Li et al., “Recent research progress of laser plasma interactions in Shenguang laser facilities,” Matter Radiat. Extremes 4, 055202 (2019).10.1063/1.5092446
[9]	H. G. Rinderknecht, P. A. Amendt, S. C. Wilks, and G. Collins, “Species separation in inertial confinement fusion fuels,” Plasma Phys. Control. Fusion 60, 064001 (2018).10.1088/1361-6587/aab79f
[10]	L. Q. Shan, H. B. Cai, W. S. Zhang, Q. Tang, F. Zhang, Z. F. Song, B. Bi, F. J. Ge, J. B. Chen, D. X. Liu et al., “Experimental evidence of kinetic effects in indirect-drive inertial confinement fusion hohlraum,” Phys. Rev. Lett. 120, 195001 (2018).10.1103/physrevlett.120.195001
[11]	P.L. Yao, H.B. Cai, X.X. Yan, W.S. Zhang, B. Du, J.M. Tian et al., “Kinetic study of transverse electron-scale interface instability in relativistic shear flows,” Matter Radiat. Extremes 5, 054403 (2020).
[12]	V. A. Thomas and D. Winske, “Kinetic simulations of the Kelvin–Helmholtz instability at the magnetopause,” J. Geophys. Res. 98, 11425 (1993).10.1029/93ja00604
[13]	J. A. Stamper, K. Papadopoulos, R. N. Sudan, S. O. Dean, E. A. McLean, and J. M. Dawson, “Spontaneous magnetic fields in laser-produced plasmas,” Phys. Rev. Lett. 26, 1012 (1971).10.1103/physrevlett.26.1012
[14]	R. Chodura, “A hybrid fluid-particle model of ion heating in high-Mach-number shock waves,” Nucl. Fusion 15, 55 (1975).10.1088/0029-5515/15/1/008
[15]	C. Thoma, D. R. Welch, R. E. Clark, D. V. Rose, and I. E. Golovkin, “Hybrid-PIC modeling of laser-plasma interactions and hot electron generation in gold hohlraum walls,” Phys. Plasmas 24, 062707 (2017).10.1063/1.4985314
[16]	A. G. Sgro and C. Nielson, “Hybrid model studies of ion dynamics and magnetic field diffusion during pinch implosions,” Phys. Fluids 19, 126 (1976).10.1063/1.861309
[17]	D. P. Higginson, P. Amendt, N. Meezan, W. Riedel, H. G. Rinderknecht, S. C. Wilks, and G. Zimmerman, “Hybrid particle-in-cell simulations of laser-driven plasma interpenetration, heating, and entrainment,” Phys. Plasmas 26, 112107 (2019).10.1063/1.5110512
[18]	C. Bellei, H. Rinderknecht, A. Zylstra, M. Rosenberg, H. Sio, C. K. Li, R. Petrasso, S. C. Wilks, and P. A. Amendt, “Species separation and kinetic effects in collisional plasma shocks,” Phys. Plasmas 21, 056310 (2014).10.1063/1.4876614
[19]	R. J. Mason, “Implicit moment PIC-hybrid simulation of collisional plasmas,” J. Comput. Phys. 51, 484 (1983).10.1016/0021-9991(83)90165-1
[20]	J. R. Davies, A. R. Bell, and M. Tatarakis, “Magnetic focusing and trapping of high-intensity laser-generated fast electrons at the rear of solid targets,” Phys. Rev. E 59, 6032 (1999).10.1103/physreve.59.6032
[21]	D. R. Welch, D. V. Rose, M. E. Cuneo, R. B. Campbell, and T. A. Mehlhorn, “Integrated simulation of the generation and transport of proton beams from laser-target interaction,” Phys. Plasmas 13, 063105 (2006).10.1063/1.2207587
[22]	H. Xu, X. H. Yang, J. Liu, and M. Borghesi, “Control of fast electron propagation in foam target by high-Z doping,” Plasma Phys. Control. Fusion 61, 025010 (2019).10.1088/1361-6587/aaefce
[23]	D. Wu, W. Yu, Y. T. Zhao, D. H. H. Hoffmann, S. Fritzsche, and X. T. He, “Particle-in-cell simulation of transport and energy deposition of intense proton beams in solid-state materials,” Phys. Rev. E 100, 013208 (2019).10.1103/physreve.100.013208
[24]	J. J. Honrubia and J. Meyer-ter-Vehn, “Fast ignition of fusion targets by laser-driven electrons,” Plasma Phys. Control Fusion 51, 014008 (2009).10.1088/0741-3335/51/1/014008
[25]	B. I. Cohen, A. J. Kemp, and L. Divol, “Simulation of laser–plasma interactions and fast-electron transport in inhomogeneous plasma,” J. Comput. Phys. 229, 4591 (2010).10.1016/j.jcp.2010.03.001
[26]	F. Zhang, H. B. Cai, W. M. Zhou, Z. S. Dai, L. Q. Shan, H. Xu, J. B. Chen, F. J. Ge, Q. Tang, W. S. Zhang et al., “Enhanced energy coupling for indirect-drive fast-ignition fusion targets,” Nat. Phys. 16, 810–815 (2020).10.1038/s41567-020-0878-9
[27]	B. Lembege and F. Simonet, “Hybrid and particle simulations of an interface expansion and of collisionless shock: A comparative and quantitative study,” Phys. Plasmas 8, 3967 (2001).10.1063/1.1389862
[28]	H. B. Cai, S. Z. Wu, J. F. Wu, M. Chen, H. Zhang, M. Q. He, L. H. Cao, C. T. Zhou, S. P. Zhu, and X. T. He, “Review of the current status of fast ignition research at the IAPCM,” High Power Laser Sci. Eng. 2, 1 (2014).10.1017/hpl.2014.8
[29]	F. F. Chen, Introduction to Plasma Physics and Controlled Fusion (Springer, 1974), p. 166.
[30]	S. I. Braginskii, “Transport processes in a plasma,” in Review of Plasma Physics I (Consultants Bureau, New York, 1965).
[31]	E. M. Epperlein and M. G. Haines, “Plasma transport coefficients in a magnetic field by direct numerical solution of the Fokker–Planck equation,” Phys. Fluids 29, 1029 (1986).10.1063/1.865901
[32]	Y. T. Lee and R. M. More, “An electron conductivity model for dense plasma,” Phys. Fluids 27, 1273 (1984).10.1063/1.864744
[33]	L. Spitzer and R. Härm, “Transport phenomena in a completely ionized gas,” Phys. Rev. 89, 977 (1953); 10.1103/physrev.89.977
[34]	D. Bond, V. Wheatley, R. Samtaney, and D. I. Pullin, “Richtmyer–Meshkov instability of a thermal interface in a two-fluid plasma,” J. Fluid Mech. 833, 332 (2017).10.1017/jfm.2017.693
[35]	J. D. Huba, “NRL: Plasma formulary,” Technical Report No. 16-1231-1005, Naval Research LABPhysics Branch, Washington DC, Beam, 2004.
[36]	T. Takizuka and H. Abe, “A binary collision model for plasma simulation with a particle code,” J. Comput. Phys. 25, 205 (1997).10.1016/0021-9991(77)90099-7
[37]	M. E. Jones, D. S. Lemons, R. J. Mason, V. A. Thomas, and D. Winske, “A grid-based Coulomb collision model for PIC codes,” J. Comput. Phys. 123, 169–181 (1996).10.1006/jcph.1996.0014
[38]	R. D. Richtmyer, “Taylor instability in shock acceleration of compressible fluids,” Commun. Pure Appl. Math. 13, 297 (1960).10.1002/cpa.3160130207
[39]	E. E. Meshkov, “Instability of the interface of two gases accelerated by a shock wave,” Fluid Dyn. 4, 101 (1969).10.1007/bf01015969
[40]	B. Guan, Z. G. Zhai, T. Si, X. Y. Lu, and X. S. Luo, “Manipulation of three-dimensional Richtmyer–Meshkov instability by initial interfacial principal curvatures,” Phys. Fluids 29, 032106 (2017).10.1063/1.4978391
[41]	G. Taylor, “The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I,” Proc. R. Soc. London, Ser. A 201, 192 (1950); 10.1098/rspa.1950.0052
[42]	B. A. Remington, H.-S. Park, D. T. Casey, R. M. Cavallo, D. S. Clark, C. M. Huntington, C. C. Kuranz, A. R. Miles, S. R. Nagel et al., “Rayleigh–Taylor instabilities in high-energy density settings on the National Ignition Facility,” Proc. Natl. Acad. Sci. U. S. A. 116, 18233 (2018).10.1073/pnas.1717236115
[43]	B. Srinivasan, G. Dimonte, and X. Z. Tang, “Magnetic field generation in Rayleigh–Taylor unstable inertial confinement fusion plasmas,” Phys. Rev. Lett. 108, 165002 (2012).10.1103/physrevlett.108.165002