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Richtmyer–Meshkov instability of a thermal interface in a two-fluid plasma

Published online by Cambridge University Press:  03 November 2017

D. Bond Open the ORCID record for D. Bond [Opens in a new window] ,
V. Wheatley ,
R. Samtaney  and
D. I. Pullin
D. Bond
Affiliation:
Centre for Hypersonics, School of Mechanical and Mining Engineering, The University of Queensland, St Lucia Qld 4072, Australia
V. Wheatley
Affiliation:
Centre for Hypersonics, School of Mechanical and Mining Engineering, The University of Queensland, St Lucia Qld 4072, Australia
R. Samtaney
Affiliation:
Mechanical Engineering, Physical Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia
D. I. Pullin
Affiliation:
Graduate Aerospace laboratories, California Institute of Technology, Pasadena, CA 91125, USA
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Abstract

We computationally investigate the Richtmyer–Meshkov instability of a density interface with a single-mode perturbation in a two-fluid, ion–electron plasma with no initial magnetic field. Self-generated magnetic fields arise subsequently. We study the case where the density jump across the initial interface is due to a thermal discontinuity, and select plasma parameters for which two-fluid plasma effects are expected to be significant in order to elucidate how they alter the instability. The instability is driven via a Riemann problem generated precursor electron shock that impacts the density interface ahead of the ion shock. The resultant charge separation and motion generates electromagnetic fields that cause the electron shock to degenerate and periodically accelerate the electron and ion interfaces, driving Rayleigh–Taylor instability. This generates small-scale structures and substantially increases interfacial growth over the hydrodynamic case.

JFM classification

Instability: Instability MHD and Electrohydrodynamics: MHD and Electrohydrodynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 833 , 25 December 2017 , pp. 332 - 363
Copyright
© 2017 Cambridge University Press 

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References

Abgrall, R. & Kumar, H. 2014 Robust finite volume schemes for two-fluid plasma equations. J. Sci. Comput. 60 (3), 584–611.CrossRefGoogle Scholar
Adams, M., Colella, P., Graves, D. T., Johnson, J. N., Keen, N. D., Ligocki, T. J., Martin, D. F., McCorquodale, P. W., Modiano, D., Schwartz, P. O. et al. 2015 Chombo software package for amr applications – design document. Tech. Rep. LBNL-6616E. Lawrence Berkeley National Laboratory.Google Scholar
Arnett, D. 2000 The role of mixing in astrophysics. Astrophys. J. Suppl. 127, 213–217.Google Scholar
Bellan, P. M. 2006 Fundamentals of Plasma Physics. Cambridge University Press.Google Scholar
Brouillette, M. 2002 The Richtmyer–Meshkov instability. Annu. Rev. Fluid Mech. 34, 445–468.CrossRefGoogle Scholar
Brouillette, M. & Bonazza, R. 1999 Experiments on the Richtmyer–Meshkov instability: wall effects and wave phenomena. Phys. Fluids 11, 1127–1142.Google Scholar
Cao, J. T., Wu, Z. W., Ren, H. J. & Li, D. 2008 Effects of shear flow and transverse magnetic field on Richtmyer–Meshkov instability. Phys. Plasmas 15, 042102.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.Google Scholar
Einfeldt, B. 1988 On Godunov-type methods for gas dynamics. SIAM J. Numer. Anal. 25 (2), 294–318.Google Scholar
Evans, R. G. 1986 The influence of self-generated magnetic fields on the Rayleigh–Taylor instability. Plasma Phys. Control. Fusion 28 (7), 1021.Google Scholar
Glenzer, S. H., MacGowan, B. J., Michel, P., Meezan, N. B., Suter, L. J., Dixit, S. N., Kline, J. L., Kyrala, G. A., Bradley, D. K., Callahan, D. A. et al. 2010 Symmetric inertial confinement fusion implosions at ultra-high laser energies. Science 327, 1228.Google Scholar
Gottlieb, S., Shu, C.-W. & Tadmor, E. 2001 Strong stability-preserving high-order time discretization methods. SIAM Rev. 43 (1), 89–112.CrossRefGoogle Scholar
Hohenberger, M., Chang, P.-Y., Fiskel, G., Knauer, J. P., Betti, R., Marshall, F. J., Meyerhofer, D. D., Séguin, F. H. & Petrasso, R. D. 2012 Inertial confinement fusion implosions with imposed magnetic field compression using the OMEGA Laser. Phys. Plasmas 19, 056306.Google Scholar
Hosseini, S. H. R. & Takayama, K. 2005 Experimental study of Richtmyer–Meshkov instability induced by cylindrical shock waves. Phys. Fluids 17, 084101.Google Scholar
Igumenshchev, I. V., Zylstra, A. B., Li, C. K., Nilson, P. M., Goncharov, V. N. & Petrasso, R. D. 2014 Self-generated magnetic fields in direct-drive implosion experiments. Phys. Plasmas 21 (6), 062707.CrossRefGoogle Scholar
Khokhlov, A. M., Oran, E. S. & Thomas, G. O. 1999 Numerical simulation of deflagration to- detonation transition: the role of shock-flame interactions in turbulent flames. Combust. Flame 117, 323–339.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1987 Fluid Mechanics. Butterworth-Heinemann.Google Scholar
Lanier, N. E., Barnes, C. W., Batha, S. H., Day, R. D., Magelssen, G. R., Scott, J. M., Dunne, A. M., Parker, K. W. & Rothman, S. D. 2003 Multimode seeded Richtmyer–Meshkov mixing in a convergent, compressible, miscible plasma system. Phys. Plasmas 10, 1816.CrossRefGoogle Scholar
Lindl, J. D., Landen, O., Edwards, J., Moses, E., Adams, J., Amendt, P. A., Antipa, N., Arnold, P. A., Atherton, L. J., Azevedo, S. et al. 2014 Review of the national ignition campaign 2009–2012. Phys. Plasmas 21, 020501.Google Scholar
Lindl, J. D., McCrory, R. L. & Campbell, E. M. 1992 Progress toward ignition and burn propagation in inertial confinement fusion. Phys. Today 45, 32–40.Google Scholar
Lombardini, M., Pullin, D. I. & Meiron, D. I. 2014a Turbulent mixing driven by spherical implosions. Part 1. Flow description and mixing-layer growth. J. Fluid Mech. 748, 85–112.Google Scholar
Lombardini, M., Pullin, D. I. & Meiron, D. I. 2014b Turbulent mixing driven by spherical implosions. Part 2. Turbulence statistics. J. Fluid Mech. 748, 113–142.Google Scholar
López Ortega, A., Lombardini, M., Barton, P. T., Pullin, D. I. & Meiron, D. I. 2015 Richtmyer–Meshkov instability for elastic-plastic solids in converging geometries. J. Mech. Phys. Solids 76, 291–324.Google Scholar
López Ortega, A., Lombardini, M., Pullin, D. I. & Meiron, D. I. 2014 Numerical simulations of the Richtmyer–Meshkov instability in solid-vacuum interfaces using calibrated plasticity laws. Phys. Rev. E 89 (3), 033018.Google Scholar
Loverich, J.2003 A finite volume algorithm for the two-fluid plasma system in one dimension. Master’s thesis, University of Washington.Google Scholar
Manuel, M. J.-E., Li, C. K., Séguin, F. H., Frenje, J., Casey, D. T., Petrasso, R. D., Hu, S. X., Betti, R., Hager, J. D., Meyerhofer, D. D. et al. 2012a First measurements of Rayleigh–Taylor-induced magnetic fields in laser-produced plasmas. Phys. Rev. Lett. 108, 255006.Google Scholar
Manuel, M. J.-E., Li, C. K., Séguin, F. H., Frenje, J. A., Casey, D. T., Petrasso, R. D., Hu, S. X., Betti, R., Hager, J., Meyerhofer, D. D. et al. 2012b Rayleigh–Taylor-induced magnetic fields in laser-irradiated plastic foils. Phys. Plasmas 19 (8), 082710.Google Scholar
Markstein, G. H. 1957 Flow disturbances induced near a slightly wavy contact surface, or flame front, traversed by a shock wave. J. Aero. Sci. 24, 238–239.Google Scholar
Meshkov, E. E. 1969 Instability of the interface of two gases accelerated by a shock wave. Sov. Fluid Dyn. 4, 101–108.Google Scholar
Mikaelian, K. O. 2005 Rayleigh–Taylor and Richtmyer–Meshkov instabilities and mixing in stratified cylindrical shells. Phys. Fluids 17, 094105.Google Scholar
Mishin, V. V. & Morozov, A. G. 1983 On the effect of oblique disturbances on Kelvin–Helmholtz instability at magnetospheric boundary layers and in solar wind. Planet. Space Sci. 31 (8), 821–828.CrossRefGoogle Scholar
Mostert, W. M., Pullin, D. I., Wheatley, V. & Samtaney, R. 2017 Magnetohydrodynamic implosion symmetry and suppression of Richtmyer–Meshkov instability in an octahedrally symmetric field. Phys. Rev. Fluids 2 (1), 013701.CrossRefGoogle Scholar
Mostert, W. M., Wheatley, V., Samtaney, R. & Pullin, D. I. 2015 Effects of magnetic fields on magnetohydrodynamic cylindrical and spherical Richtmyer–Meshkov instability. Phys. Fluids 27 (10), 104102.CrossRefGoogle Scholar
Munz, C.-D., Ommes, P. & Schneider, R. 2000 A three-dimensional finite-volume solver for the Maxwell equations with divergence cleaning on unstructured meshes. Comput. Phys. Commun. 130 (1–2), 83–117.CrossRefGoogle Scholar
Perkins, L. J., Logan, B. G., Zimmerman, G. B. & Werner, C. J. 2013 Two-dimensional simulations of thermonuclear burn in ignition-scale inertial confinement fusion targets under compressed axial magnetic fields. Phys. Plasmas 20 (7), 072708.Google Scholar
Richtmyer, R. D. 1960 Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Maths 13, 297–319.Google Scholar
Samtaney, R. 2003 Suppression of the Richtmyer–Meshkov instability in the presence of a magnetic field. Phys. Fluids 15 (8), L53–L56.Google Scholar
Samtaney, R. & Pullin, D. I. 1996 On initial-value and self-similar solutions of the compressible Euler equations. Phys. Fluids 8 (10), 2650–2655.Google Scholar
Schluter, A. & Biermann, L. 1950 Interstellar magnetic fields. Zeit. Nat. Teil. A 5, 237.Google Scholar
Séguin, F. H., Li, C. K., Manuel, M. J.-E., Rinderknecht, H. G., Sinenian, N., Frenje, J. A., Rygg, J. R., Hicks, D. G., Petrasso, R. D., Delettrez, J. et al. 2012 Time evolution of filamentation and self-generated fields in the coronae of directly driven inertial-confinement fusion capsules. Phys. Plasmas 19 (1), 012701.Google Scholar
Srinivasan, B., Dimonte, G. & Tang, X.-Z. 2012 Magnetic field generation in Rayleigh–Taylor unstable inertial confinement fusion plasmas. Phys. Rev. Lett. 108, 165002.Google Scholar
Srinivasan, B. & Tang, X.-Z. 2012 Mechanism for magnetic field generation and growth in Rayleigh–Taylor unstable inertial confinement fusion plasmas. Phys. Plasmas 19, 082703.Google Scholar
Stalker, R. J. & Crane, K. C. A. 1978 Driver gas contamination in a high-enthalpy reflected shock-tunnel. AIAA J. 16, 277–279.Google Scholar
Toro, E. F., Spruce, M. & Speares, W. 1994 Restoration of the contact surface in the HLL-Riemann solver. Shock Waves 4 (1), 25–34.Google Scholar
Wheatley, V., Kumar, H. & Huguenot, P. 2010 On the role of Riemann solvers in discontinuous galerkin methods for magnetohydrodynamics. J. Comput. Phys. 229 (3), 660–680.Google Scholar
Wheatley, V., Samtaney, R. & Pullin, D. I. 2005 Stability of an impulsively accelerated perturbed density interface in incompressible MHD. Phys. Rev. Lett. 95, 125002.Google Scholar
Wheatley, V., Samtaney, R. & Pullin, D. I. 2009 The Richtmyer–Meshkov instability in magnetohydrodynamics. Phys. Fluids 21, 082102.Google Scholar
Wheatley, V., Samtaney, R., Pullin, D. I. & Gehre, R. M. 2014 The transverse field Richtmyer–Meshkov instability in magnetohydrodynamics. Phys. Fluids 26, 016102.Google Scholar
Yang, J., Kubota, T. & Zukoski, E. E. 1993 Applications of shock induced mixing to supersonic combustion. AIAA J. 31, 854–862.Google Scholar