zbMATH — the first resource for mathematics

Richtmyer-Meshkov instability of a thermal interface in a two-fluid plasma. (English) Zbl 1419.76722
Summary: 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.

76X05 Ionized gas flow in electromagnetic fields; plasmic flow
76L05 Shock waves and blast waves in fluid mechanics
76W05 Magnetohydrodynamics and electrohydrodynamics
Full Text: DOI
[1] Abgrall, R.; Kumar, H., Robust finite volume schemes for two-fluid plasma equations, J. Sci. Comput., 60, 3, 584-611, (2014) · Zbl 1299.76157
[2] 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.
[3] Arnett, D., The role of mixing in astrophysics, Astrophys. J. Suppl., 127, 213-217, (2000)
[4] Bellan, P. M., Fundamentals of Plasma Physics, (2006), Cambridge University Press
[5] Brouillette, M., The Richtmyer-Meshkov instability, Annu. Rev. Fluid Mech., 34, 445-468, (2002) · Zbl 1047.76025
[6] Brouillette, M.; Bonazza, R., Experiments on the Richtmyer-Meshkov instability: wall effects and wave phenomena, Phys. Fluids, 11, 1127-1142, (1999) · Zbl 1147.76340
[7] Cao, J. T.; Wu, Z. W.; Ren, H. J.; Li, D., Effects of shear flow and transverse magnetic field on Richtmyer-Meshkov instability, Phys. Plasmas, 15, (2008)
[8] Chandrasekhar, S., Hydrodynamic and Hydromagnetic Stability, (1961), Oxford University Press
[9] Einfeldt, B., On Godunov-type methods for gas dynamics, SIAM J. Numer. Anal., 25, 2, 294-318, (1988) · Zbl 0642.76088
[10] Evans, R. G., The influence of self-generated magnetic fields on the Rayleigh-Taylor instability, Plasma Phys. Control. Fusion, 28, 7, 1021, (1986)
[11] 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., Symmetric inertial confinement fusion implosions at ultra-high laser energies, Science, 327, 1228, (2010)
[12] Gottlieb, S.; Shu, C.-W.; Tadmor, E., Strong stability-preserving high-order time discretization methods, SIAM Rev., 43, 1, 89-112, (2001) · Zbl 0967.65098
[13] Hohenberger, M.; Chang, P.-Y.; Fiskel, G.; Knauer, J. P.; Betti, R.; Marshall, F. J.; Meyerhofer, D. D.; Séguin, F. H.; Petrasso, R. D., Inertial confinement fusion implosions with imposed magnetic field compression using the OMEGA Laser, Phys. Plasmas, 19, (2012)
[14] Hosseini, S. H. R.; Takayama, K., Experimental study of Richtmyer-Meshkov instability induced by cylindrical shock waves, Phys. Fluids, 17, (2005) · Zbl 1187.76218
[15] Igumenshchev, I. V.; Zylstra, A. B.; Li, C. K.; Nilson, P. M.; Goncharov, V. N.; Petrasso, R. D., Self-generated magnetic fields in direct-drive implosion experiments, Phys. Plasmas, 21, 6, (2014)
[16] Khokhlov, A. M.; Oran, E. S.; Thomas, G. O., Numerical simulation of deflagration to- detonation transition: the role of shock-flame interactions in turbulent flames, Combust. Flame, 117, 323-339, (1999)
[17] Landau, L. D.; Lifshitz, E. M., Fluid Mechanics, (1987), Butterworth-Heinemann
[18] 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., Multimode seeded Richtmyer-Meshkov mixing in a convergent, compressible, miscible plasma system, Phys. Plasmas, 10, 1816, (2003)
[19] Lindl, J. D.; Landen, O.; Edwards, J.; Moses, E.; Adams, J.; Amendt, P. A.; Antipa, N.; Arnold, P. A.; Atherton, L. J.; Azevedo, S., Review of the national ignition campaign 2009-2012, Phys. Plasmas, 21, (2014)
[20] Lindl, J. D.; Mccrory, R. L.; Campbell, E. M., Progress toward ignition and burn propagation in inertial confinement fusion, Phys. Today, 45, 32-40, (1992)
[21] Lombardini, M.; Pullin, D. I.; Meiron, D. I., Turbulent mixing driven by spherical implosions. Part 1. Flow description and mixing-layer growth, J. Fluid Mech., 748, 85-112, (2014)
[22] Lombardini, M.; Pullin, D. I.; Meiron, D. I., Turbulent mixing driven by spherical implosions. Part 2. Turbulence statistics, J. Fluid Mech., 748, 113-142, (2014)
[23] López Ortega, A.; Lombardini, M.; Barton, P. T.; Pullin, D. I.; Meiron, D. I., Richtmyer-Meshkov instability for elastic-plastic solids in converging geometries, J. Mech. Phys. Solids, 76, 291-324, (2015)
[24] López Ortega, A.; Lombardini, M.; Pullin, D. I.; Meiron, D. I., Numerical simulations of the Richtmyer-Meshkov instability in solid-vacuum interfaces using calibrated plasticity laws, Phys. Rev. E, 89, 3, 033018, (2014)
[25] Loverich, J.2003 A finite volume algorithm for the two-fluid plasma system in one dimension. Master’s thesis, University of Washington. · Zbl 1061.76526
[26] 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., First measurements of Rayleigh-Taylor-induced magnetic fields in laser-produced plasmas, Phys. Rev. Lett., 108, (2012)
[27] 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., Rayleigh-Taylor-induced magnetic fields in laser-irradiated plastic foils, Phys. Plasmas, 19, 8, (2012)
[28] Markstein, G. H., Flow disturbances induced near a slightly wavy contact surface, or flame front, traversed by a shock wave, J. Aero. Sci., 24, 238-239, (1957) · Zbl 0077.19201
[29] Meshkov, E. E., Instability of the interface of two gases accelerated by a shock wave, Sov. Fluid Dyn., 4, 101-108, (1969)
[30] Mikaelian, K. O., Rayleigh-Taylor and Richtmyer-Meshkov instabilities and mixing in stratified cylindrical shells, Phys. Fluids, 17, (2005) · Zbl 1187.76353
[31] Mishin, V. V.; Morozov, A. G., 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, (1983)
[32] Mostert, W. M.; Pullin, D. I.; Wheatley, V.; Samtaney, R., Magnetohydrodynamic implosion symmetry and suppression of Richtmyer-Meshkov instability in an octahedrally symmetric field, Phys. Rev. Fluids, 2, 1, (2017)
[33] Mostert, W. M.; Wheatley, V.; Samtaney, R.; Pullin, D. I., Effects of magnetic fields on magnetohydrodynamic cylindrical and spherical Richtmyer-Meshkov instability, Phys. Fluids, 27, 10, (2015)
[34] Munz, C.-D.; Ommes, P.; Schneider, R., A three-dimensional finite-volume solver for the Maxwell equations with divergence cleaning on unstructured meshes, Comput. Phys. Commun., 130, 1-2, 83-117, (2000) · Zbl 0960.78019
[35] Perkins, L. J.; Logan, B. G.; Zimmerman, G. B.; Werner, C. J., Two-dimensional simulations of thermonuclear burn in ignition-scale inertial confinement fusion targets under compressed axial magnetic fields, Phys. Plasmas, 20, 7, 072708, (2013)
[36] Richtmyer, R. D., Taylor instability in shock acceleration of compressible fluids, Commun. Pure Appl. Maths, 13, 297-319, (1960)
[37] Samtaney, R., Suppression of the Richtmyer-Meshkov instability in the presence of a magnetic field, Phys. Fluids, 15, 8, L53-L56, (2003) · Zbl 1186.76459
[38] Samtaney, R.; Pullin, D. I., On initial-value and self-similar solutions of the compressible Euler equations, Phys. Fluids, 8, 10, 2650-2655, (1996) · Zbl 1027.76642
[39] Schluter, A.; Biermann, L., Interstellar magnetic fields, Zeit. Nat. Teil. A, 5, 237, (1950)
[40] 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., Time evolution of filamentation and self-generated fields in the coronae of directly driven inertial-confinement fusion capsules, Phys. Plasmas, 19, 1, (2012)
[41] Srinivasan, B.; Dimonte, G.; Tang, X.-Z., Magnetic field generation in Rayleigh-Taylor unstable inertial confinement fusion plasmas, Phys. Rev. Lett., 108, (2012)
[42] Srinivasan, B.; Tang, X.-Z., Mechanism for magnetic field generation and growth in Rayleigh-Taylor unstable inertial confinement fusion plasmas, Phys. Plasmas, 19, (2012)
[43] Stalker, R. J.; Crane, K. C. A., Driver gas contamination in a high-enthalpy reflected shock-tunnel, AIAA J., 16, 277-279, (1978)
[44] Toro, E. F.; Spruce, M.; Speares, W., Restoration of the contact surface in the HLL-Riemann solver, Shock Waves, 4, 1, 25-34, (1994) · Zbl 0811.76053
[45] Wheatley, V.; Kumar, H.; Huguenot, P., On the role of Riemann solvers in discontinuous galerkin methods for magnetohydrodynamics, J. Comput. Phys., 229, 3, 660-680, (2010) · Zbl 1253.76133
[46] Wheatley, V.; Samtaney, R.; Pullin, D. I., Stability of an impulsively accelerated perturbed density interface in incompressible MHD, Phys. Rev. Lett., 95, (2005) · Zbl 1065.76207
[47] Wheatley, V.; Samtaney, R.; Pullin, D. I., The Richtmyer-Meshkov instability in magnetohydrodynamics, Phys. Fluids, 21, (2009) · Zbl 1183.76568
[48] Wheatley, V.; Samtaney, R.; Pullin, D. I.; Gehre, R. M., The transverse field Richtmyer-Meshkov instability in magnetohydrodynamics, Phys. Fluids, 26, (2014) · Zbl 1183.76568
[49] Yang, J.; Kubota, T.; Zukoski, E. E., Applications of shock induced mixing to supersonic combustion, AIAA J., 31, 854-862, (1993)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.