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The magnetised Richtmyer-Meshkov instability in two-fluid plasmas. (English) Zbl 07261276
Summary: We investigate the effects of magnetisation on the two-fluid plasma Richtmyer-Meshkov instability of a single-mode thermal interface using a computational approach. The initial magnetic field is normal to the mean interface location. Results are presented for a magnetic interaction parameter of 0.1 and plasma skin depths ranging from 0.1 to 10 perturbation wavelengths. These are compared to initially unmagnetised and neutral fluid cases. The electron flow is found to be constrained to lie along the magnetic field lines resulting in significant longitudinal flow features that interact strongly with the ion fluid. The presence of an initial magnetic field is shown to suppress the growth of the initial interface perturbation with effectiveness determined by plasma length scale. Suppression of the instability is attributed to the magnetic field’s contribution to the Lorentz force. This acts to rotate the vorticity vector in each fluid about the local magnetic-field vector leading to cyclic inversion and transport of the out-of-plane vorticity that drives perturbation growth. The transport of vorticity along field lines increases with decreasing plasma length scales and the wave packets responsible for vorticity transport begin to coalesce. In general, the two-fluid plasma Richtmyer-Meshkov instability is found to be suppressed through the action of the imposed magnetic field with increasing effectiveness as plasma length scale is decreased. For the conditions investigated, a critical skin depth for instability suppression is estimated.
MSC:
76 Fluid mechanics
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[1] Abgrall, R. & Kumar, H.2014Robust finite volume schemes for two-fluid plasma equations. J. Sci. Comput.60 (3), 584-611. · Zbl 1299.76157
[2] Arnett, D.2000The role of mixing in astrophysics. Astrophys. J. Suppl.127, 213-217.
[3] Bellan, P. M.2006Fundamentals of Plasma Physics. Cambridge University Press.
[4] Bond, D., Wheatley, V., Samtaney, R. & Pullin, D. I.2017Richtmyer-Meshkov instability of a thermal interface in a two-fluid plasma. J. Fluid Mech.833, 332-363. · Zbl 1419.76722
[5] Cao, J. T., Wu, Z. W., Ren, H. J. & Li, D.2008Effects of shear flow and transverse magnetic field on Richtmyer-Meshkov instability. Phys. Plasmas15, 042102.
[6] Einfeldt, B.1988On godunov-type methods for gas dynamics. SIAM J. Numer. Anal.25 (2), 294-318. · Zbl 0642.76088
[7] Gottlieb, S., Shu, C.-W. & Tadmor, E.2001Strong stability-preserving high-order time discretization methods. SIAM Rev.43 (1), 89-112. · Zbl 0967.65098
[8] Hohenberger, M., Chang, P.-Y., Fiskel, G., Knauer, J. P., Betti, R., Marshall, F. J., Meyerhofer, D. D., Séguin, F. H. & Petrasso, R. D.2012Inertial confinement fusion implosions with imposed magnetic field compression using the OMEGA Laser. Phys. Plasmas19, 056306.
[9] Li, Z. & Livescu, D.2019High-order two-fluid plasma solver for direct numerical simulations of plasma flows with full transport phenomena. Phys. Plasmas26 (1), 012109.
[10] Li, Y., Samtaney, R. & Wheatley, V.2018The Richtmyer-Meshkov instability of a double-layer interface in convergent geometry with magnetohydrodynamics. Matter Radiat. Extrem.3 (4), 207-218.
[11] Lindl, J. D., Landen, O., Edwards, J., Moses, E. & 2014Review of the national ignition campaign 2009-2012. Phys. Plasmas21, 020501.
[12] Lombardini, M., Pullin, D. I. & Meiron, D. I.2014Turbulent mixing driven by spherical implosions. Part 1. Flow description and mixing-layer growth. J. Fluid Mech.748, 85-112.
[13] Loverich, J., Hakim, A. & Shumlak, U.2011A discontinuous Galerkin method for ideal two-fluid plasma equations. Commun. Comput. Phys.9 (2), 240-268. · Zbl 1364.35278
[14] Meshkov, E. E.1969Instability of the interface of two gases accelerated by a shock wave. Sov. Fluid Dyn.4, 101-108.
[15] Mostert, W. M., Pullin, D. I., Wheatley, V. & Samtaney, R.2017Magnetohydrodynamic implosion symmetry and suppression of Richtmyer-Meshkov instability in an octahedrally symmetric field. Phys. Rev. Fluids2 (1), 013701.
[16] Mostert, W. M., Wheatley, V., Samtaney, R. & Pullin, D. I.2015Effects of magnetic fields on magnetohydrodynamic cylindrical and spherical Richtmyer-Meshkov instability. Phys. Fluids27 (10), 104102.
[17] Munz, C.-D., Ommes, P. & Schneider, R.2000aA three-dimensional finite-volume solver for the Maxwell equations with divergence cleaning on unstructured meshes. Comput. Phys. Commun.130 (1-2), 83-117. · Zbl 0960.78019
[18] Munz, C. D., Schneider, R. & Voss, U.2000bA finite-volume method for the Maxwell equations in the time domain. SIAM J. Sci. Comput.22 (2), 449-475. · Zbl 1039.78012
[19] Richtmyer, R. D.1960Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Maths13, 297-319.
[20] Samtaney, R.2003Suppression of the Richtmyer-Meshkov instability in the presence of a magnetic field. Phys. Fluids15 (8), L53-L56. · Zbl 1186.76459
[21] Samtaney, R. & Zabusky, N. J.1994Circulation deposition on shock-accelerated planar and curved density-stratified interfaces: models and scaling laws. J. Fluid Mech.269, 45-78.
[22] Sano, T., Inoue, T. & Nishihara, K.2013Critical magnetic field strength for suppression of the Richtmyer-Meshkov instability in plasmas. Phys. Rev. Lett.111 (20), 205001.
[23] Shen, N., Li, Y., Pullin, D. I., Samtaney, R. & Wheatley, V.2018On the magnetohydrodynamic limits of the ideal two-fluid plasma equations. Phys. Plasmas25 (12), 122113.
[24] Shen, N., Pullin, D. I., Wheatley, V. & Samtaney, R.2019Impulse-driven Richtmyer-Meshkov instability in hall-magnetohydrodynamics. Phys. Rev. Fluids4, 103902. · Zbl 1183.76568
[25] Smalyuk, V. A., Weber, C. R., Landen, O. L., Ali, S., Bachmann, B., Celliers, P. M., Dewald, E. L., Fernandez, A., Hammel, B. A., Hall, G., et al.2019Review of hydrodynamic instability experiments in inertially confined fusion implosions on national ignition facility. Plasma Phys. Control. Fusion62 (1), 014007.
[26] Srinivasan, B. & Tang, X.-Z.2012Mechanism for magnetic field generation and growth in Rayleigh-Taylor unstable inertial confinement fusion plasmas. Phys. Plasmas19, 082703.
[27] Vandenboomgaerde, M., Mügler, C. & Gauthier, S.1998Impulsive model for the Richtmyer-Meshkov instability. Phys. Rev. E58, 1874-1882.
[28] Wheatley, V., Kumar, H. & Huguenot, P.2010On the role of Riemann solvers in discontinuous Galerkin methods for magnetohydrodynamics. J. Comput. Phys.229 (3), 660-680. · Zbl 1253.76133
[29] Wheatley, V., Samtaney, R. & Pullin, D. I.2005Stability of an impulsively accelerated perturbed density interface in incompressible MHD. Phys. Rev. Lett.95, 125002. · Zbl 1065.76207
[30] Wheatley, V., Samtaney, R., Pullin, D. I. & Gehre, R. M.2014The transverse field Richtmyer-Meshkov instability in magnetohydrodynamics. Phys. Fluids26, 016102.
[31] Zhang, W., Almgren, A., Beckner, V., Bell, J., Blaschke, J., Chan, C., Day, M., Friesen, B., Gott, K., Graves, D., et al.2019AMReX: a framework for block-structured adaptive mesh refinement. J. Open Source Softw.4 (37), 1370.
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