Hostname: page-component-76fb5796d-r6qrq Total loading time: 0 Render date: 2024-04-26T05:58:49.200Z Has data issue: false hasContentIssue false

Observation of subcritical shocks in a collisional laboratory plasma: scale dependence near the resistive length

Published online by Cambridge University Press:  10 August 2023

D.R. Russell*
Affiliation:
Blackett Laboratory, Imperial College London, London SW7 2AZ, UK
G.C. Burdiak
Affiliation:
First Light Fusion Ltd, Yarnton, Kidlington OX5 1QU, UK
J.J. Carroll-Nellenback
Affiliation:
Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA
J.W.D. Halliday
Affiliation:
Blackett Laboratory, Imperial College London, London SW7 2AZ, UK
J.D. Hare
Affiliation:
Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge MA 02139, USA
S. Merlini
Affiliation:
Blackett Laboratory, Imperial College London, London SW7 2AZ, UK
L.G. Suttle
Affiliation:
Blackett Laboratory, Imperial College London, London SW7 2AZ, UK
V. Valenzuela-Villaseca
Affiliation:
Blackett Laboratory, Imperial College London, London SW7 2AZ, UK
S.J. Eardley
Affiliation:
Blackett Laboratory, Imperial College London, London SW7 2AZ, UK
J.A. Fullalove
Affiliation:
Blackett Laboratory, Imperial College London, London SW7 2AZ, UK
G.C. Rowland
Affiliation:
Blackett Laboratory, Imperial College London, London SW7 2AZ, UK
R.A. Smith
Affiliation:
Blackett Laboratory, Imperial College London, London SW7 2AZ, UK
A. Frank
Affiliation:
Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA
P. Hartigan
Affiliation:
Department of Physics and Astronomy, Rice University, Houston, TX 77005-1892, USA
A.L. Velikovich
Affiliation:
Plasma Physics Division, U. S. Naval Research Laboratory, Washington, DC 20375, USA
J.P. Chittenden
Affiliation:
Blackett Laboratory, Imperial College London, London SW7 2AZ, UK
S.V. Lebedev
Affiliation:
Blackett Laboratory, Imperial College London, London SW7 2AZ, UK
*
Email address for correspondence: daniel.russell@frm2.tum.de

Abstract

We present a study of subcritical shocks in a highly collisional laboratory plasma with a dynamically significant magnetic field. Shocks were produced by placing cylindrical obstacles into the supermagnetosonic ($M_{{\rm MS}} \sim 1.9$) outflow from an inverse wire array z-pinch at the MAGPIE pulsed power facility ($n_{e} \sim 8.5 \times 10^{17}\,{\rm cm}^{-3}$, $v \sim 45\,{\rm km}\,{\rm s}^{-1}$). We demonstrate the existence of subcritical shocks in this regime and find that secondary stagnation shocks form in the downstream which we infer from interferometry and optical Thomson scattering measurements are hydrodynamic in nature. The subcritical shock width is found to be approximately equal to the resistive diffusion length and we demonstrate the absence of a jump in hydrodynamic parameters. Temperature measurements by collective optical Thomson scattering showed little temperature change across the subcritical shock (${<}10\,\%$ of the ion kinetic energy) which is consistent with a balance between adiabatic and Ohmic heating and radiative cooling. We demonstrate the absence of subcritical shocks when the obstacle diameter is less than the resistive diffusion length due to decoupling of the magnetic field from the plasma. These findings are supported by magnetohydrodynamic simulations using the Gorgon and AstroBEAR codes and discrepancies between the simulations and experiment are discussed.

Type
Research Article
Copyright
Copyright © The Author(s), 2023. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Anderson, J.E. 1963 Magnetohydrodynamic Shock Waves. MIT Press.CrossRefGoogle Scholar
Braginskii, S.I. 1965 Transport processes in a plasma. Rev. Plasma Phys. 1, 205.Google Scholar
Burdiak, G.C., Lebedev, S.V., Bland, S.N., Clayson, T., Hare, J., Suttle, L., Suzuki-Vidal, F., Garcia, D.C., Chittenden, J.P., Bott-Suzuki, S., et al. 2017 The structure of bow shocks formed by the interaction of pulsed-power driven magnetised plasma flows with conducting obstacles. Phys. Plasmas 24, 072713.CrossRefGoogle Scholar
Burgess, D. & Scholer, M. 2015 Collisionless Shocks in Space Plasmas: Structure and Accelerated Particles. Cambridge University Press.CrossRefGoogle Scholar
Carroll-Nellenback, J.J., Shroyer, B., Frank, A. & Ding, C. 2013 Efficient parallelization for AMR MHD multiphysics calculations; implementation in astrobear. J. Comput. Phys. 236, 461476.CrossRefGoogle Scholar
Chittenden, J.P., Lebedev, S.V., Jennings, C.A., Bland, S.N. & Ciardi, A. 2004 a X-ray generation mechanisms in three-dimensional simulations of wire array z-pinches. Plasma Phys. Control. Fusion 46, B457.CrossRefGoogle Scholar
Chittenden, J.P., Lebedev, S.V., Oliver, B.V., Yu, E.P. & Cuneo, M.E. 2004 b Equilibrium flow structures and scaling of implosion trajectories in wire array z pinches. Phys. Plasmas 11, 11181127.CrossRefGoogle Scholar
Ciardi, A., Lebedev, S.V., Frank, A., Blackman, E.G., Chittenden, J.P., Jennings, C.J., Ampleford, D.J., Bland, S.N., Bott, S.C., Rapley, J., et al. 2007 The evolution of magnetic tower jets in the laboratory. Phys. Plasmas 14, 056501.CrossRefGoogle Scholar
Coroniti, F.V. 1970 Dissipation discontinuities in hydromagnetic shock waves. J. Plasma Phys. 4, 265282.CrossRefGoogle Scholar
Crilly, A.J., Niasse, N.P.L., Fraser, A.R., Chapman, D.A., McLean, K.M., Rose, S.J. & Chittenden, J.P. 2023 SpK: A fast atomic and microphysics code for the high-energy-density regime. High Energy Density Phys 48, 101053.CrossRefGoogle Scholar
Cunningham, A.J., Frank, A., Varnière, P., Mitran, S. & Jones, T.W. 2009 Simulating magnetohydrodynamical flow with constrained transport and adaptive mesh refinement: algorithms and tests of the astrobear code. Astrophys. J. Suppl. Ser. 182, 519542.CrossRefGoogle Scholar
Datta, R., Russell, D.R., Tang, I., Clayson, T., Suttle, L.G., Chittenden, J.P., Lebedev, S.V. & Hare, J.D. 2022 a The structure of 3-d collisional magnetized bow shocks in pulsed-power-driven plasma flows. J. Plasma Phys. 88, 905880604.CrossRefGoogle Scholar
Datta, R., Russell, D.R., Tang, I., Clayson, T., Suttle, L.G., Chittenden, J.P., Lebedev, S.V. & Hare, J.D. 2022 b Time-resolved velocity and ion sound speed measurements from simultaneous bow shock imaging and inductive probe measurements. Rev. Sci. Instrum. 93, 103530.CrossRefGoogle ScholarPubMed
Davidovits, S. & Fisch, N.J. 2016 Sudden viscous dissipation of compressing turbulence. Phys. Rev. Lett. 116, 105004.CrossRefGoogle ScholarPubMed
Davidovits, S. & Fisch, N.J. 2017 Modeling turbulent energy behavior and sudden viscous dissipation in compressing plasma turbulence. Phys. Plasmas 24, 122311.CrossRefGoogle Scholar
Davidovits, S. & Fisch, N.J. 2019 Viscous dissipation in two-dimensional compression of turbulence. Phys. Plasmas 26, 082702.CrossRefGoogle Scholar
Davies, J.R., Wen, H., Ji, J.Y. & Held, E.D. 2021 Transport coefficients for magnetic-field evolution in inviscid magnetohydrodynamics. Phys. Plasmas 28, 012305.CrossRefGoogle Scholar
Draine, B.T. 1980 Interstellar shock waves with magnetic precursors. Astrophys. J. 241, 1021.CrossRefGoogle Scholar
Drake, R.P. 2018 High-Energy-Density Physics: Foundation of Inertial Fusion and Experimental Astrophysics, 2nd edn. Springer.CrossRefGoogle Scholar
Edmiston, J.P. & Kennel, C.F. 1984 A parametric survey of the first critical mach number for a fast MHD shock. J. Plasma Phys. 32, 429441.CrossRefGoogle Scholar
Epperlein, E.M. & Haines, M.G. 1986 Plasma transport coefficients in a magnetic field by direct numerical solution of the Fokker–Planck equation. Phys. Fluids 29, 1029.CrossRefGoogle Scholar
Espinosa, G., Gil, J.M., Rodriguez, R., Rubiano, J.G., Mendoza, M.A., Martel, P., Minguez, E., Suzuki-Vidal, F., Lebedev, S.V., Swadling, G.F., et al. 2015 Collisional-radiative simulations of a supersonic and radiatively cooled aluminum plasma jet. High Energy Density Phys. 17, 7484.CrossRefGoogle Scholar
Fazzini, A., Yao, W., Burdonov, K., Béard, J., Chen, S.N., Ciardi, A., D'Humières, E., Diab, R., Filippov, E.D., Kisyov, S., et al. 2022 Particle energization in colliding subcritical collisionless shocks investigated in the laboratory. Astron. Astrophys. 665, A87.CrossRefGoogle Scholar
Fiuza, F., Swadling, G.F., Grassi, A., Rinderknecht, H.G., Higginson, D.P., Ryutov, D.D., Bruulsema, C., Drake, R.P., Funk, S., Glenzer, S., et al. 2020 Electron acceleration in laboratory-produced turbulent collisionless shocks. Nat. Phys. 16, 916920.CrossRefGoogle Scholar
Germain, P. 1960 Shock waves and shock-wave structure in magneto-fluid dynamics. Rev. Mod. Phys. 32, 951.CrossRefGoogle Scholar
Gomez, M.R., Slutz, S.A., Jennings, C.A., Ampleford, D.J., Weis, M.R., Myers, C.E., Yager-Elorriaga, D.A., Hahn, K.D., Hansen, S.B., Harding, E.C., et al. 2020 Performance scaling in magnetized liner inertial fusion experiments. Phys. Rev. Lett. 125, 155002.CrossRefGoogle ScholarPubMed
Hamilton, J. & Seyler, C.E. 2021 Formulation of 8-moment plasma transport with application to the nernst effect. Phys. Plasmas 28, 022306.CrossRefGoogle Scholar
Hansen, E.C., Frank, A., Hartigan, P. & Lebedev, S.V. 2017 The shock dynamics of heterogeneous YSO jets: 3D simulations meet multi-epoch observations. Astrophys. J. 837, 143.CrossRefGoogle Scholar
Hansen, E.C., Frank, A., Hartigan, P. & Yirak, K. 2015 Numerical simulations of mach stem formation via intersecting bow shocks. High Energy Density Phys. 17, 135139.CrossRefGoogle Scholar
Hare, J.D. 2017 High energy density magnetic reconnection experiments in colliding carbon plasma flows. PhD thesis, Imperial College London.Google Scholar
Hare, J.D., MacDonald, J., Bland, S.N., Dranczewski, J., Halliday, J.W.D., Lebedev, S.V., Suttle, L.G., Tubman, E.R. & Rozmus, W. 2019 Two-colour interferometry and thomson scattering measurements of a plasma gun. Plasma Phys. Control. Fusion 61, 085012.CrossRefGoogle Scholar
Hartigan, P. 2003 Shock waves in outflows from young stars. Astrophys. Space Sci. 287, 111122.CrossRefGoogle Scholar
Hartigan, P., Foster, J., Frank, A., Hansen, E., Yirak, K., Liao, A.S., Graham, P., Wilde, B., Blue, B., Martinez, D., et al. 2016 When shock waves collide. Astrophys. J. 823, 148.CrossRefGoogle Scholar
Hartigan, P. & Wright, A. 2015 A new diagnostic of magnetic field strengths in radiatively cooled shocks. Astrophys. J. 811, 12.CrossRefGoogle Scholar
Harvey-Thompson, A.J., Lebedev, S.V., Bland, S.N., Chittenden, J.P., Hall, G.N., Marocchino, A., Suzuki-Vidal, F., Bott, S.C., Palmer, J.B.A. & Ning, C. 2009 Quantitative analysis of plasma ablation using inverse wire array z pinches. Phys. Plasmas 16, 111.CrossRefGoogle Scholar
Hoffmann, F.D. & Teller, E. 1950 Magneto-hydrodynamic shocks. Phys. Rev. 80, 692.CrossRefGoogle Scholar
Kennel, C.F., Edmiston, J.P. & Hada, T. 1985 A quarter century of collisionless shock research. In Collisionless Shocks in the Heliosphere: A Tutorial Review (ed. R.G. Stone & B.T. Tsurutani), vol. 34, pp. 1–36. American Geophysical Union.CrossRefGoogle Scholar
Lebedev, S.V., Beg, F.N., Bland, S.N., Chittenden, J.P., Dangor, A.E., Haines, M.G., Kwek, K.H., Pikuz, S.A. & Shelkovenko, T.A. 2001 Effect of discrete wires on the implosion dynamics of wire array z pinches. Phys. Plasmas 8, 37343747.CrossRefGoogle Scholar
Lebedev, S.V., Suttle, L., Swadling, G.F., Bennett, M., Bland, S.N., Burdiak, G.C., Burgess, D., Chittenden, J.P., Ciardi, A., Clemens, A., et al. 2014 The formation of reverse shocks in magnetized high energy density supersonic plasma flows. Phys. Plasmas 21, 056305.CrossRefGoogle Scholar
Liberman, M.A. & Velikovich, A.L. 1986 Physics of Shock Waves in Gases and Plasmas. Springer.CrossRefGoogle Scholar
Maron, Y. 2020 Experimental determination of the thermal, turbulent, and rotational ion motion and magnetic field profiles in imploding plasmas. Phys. Plasmas 27, 060901.CrossRefGoogle Scholar
Maron, Y., Starobinets, A., Fisher, V.I., Kroupp, E., Osin, D., Fisher, A., Deeney, C., Coverdale, C.A., Lepell, P.D., Yu, E.P., et al. 2013 Pressure and energy balance of stagnating plasmas in z-pinch experiments: implications to current flow at stagnation. Phys. Rev. Lett. 111, 035001.CrossRefGoogle ScholarPubMed
Marshall, W. 1955 The structure of magneto-hydrodynamic shock waves. Proc. R. Soc. Lond. A 233, 367376.Google Scholar
Mitchell, I.H., Bayley, J.M., Chittenden, J.P., Worley, J.F., Dangor, A.E., Haines, M.G. & Choi, P. 1996 A high impedance mega-ampere generator for fiber z-pinch experiments. Rev. Sci. Instrum. 67, 15331541.CrossRefGoogle Scholar
Moody, J.D., Pollock, B.B., Sio, H., Strozzi, D.J., Ho, D.D.M., Walsh, C., Kemp, G.E., Kucheyev, S.O., Kozioziemski, B., Carroll, E.G., et al. 2022 a The magnetized indirect drive project on the national ignition facility. J. Fusion Energy 41, 113.CrossRefGoogle Scholar
Moody, J.D., Pollock, B.B., Sio, H., Strozzi, D.J., Ho, D.D.-M., Walsh, C.A., Kemp, G.E., Lahmann, B., Kucheyev, S.O., Kozioziemski, B., et al. 2022 b Increased ion temperature and neutron yield observed in magnetized indirectly driven d 2 -filled capsule implosions on the national ignition facility. Phys. Rev. Lett. 129, 195002.CrossRefGoogle ScholarPubMed
Mostafavi, P. & Zank, G.P. 2018 The structure of shocks in the very local interstellar medium. Astrophys. J. 854, L15.CrossRefGoogle Scholar
Niasse, N.-P.L. 2011 Development of a pseudo non-lte model for z-pinch simulations. PhD thesis, Imperial College London.Google Scholar
Oberkampf, W.L. & Roy, C.J. 2011 Verification and Validation in Scientific Computing. Cambridge University Press.Google Scholar
Perkins, L.J., Ho, D.D.-M, Logan, B.G., Zimmerman, G.B., Rhodes, M.A., Strozzi, D.J., Blackfield, D.T. & Hawkins, S.A. 2017 The potential of imposed magnetic fields for enhancing ignition probability and fusion energy yield in indirect-drive inertial confinement fusion. Phys. Plasmas 24, 062708.CrossRefGoogle Scholar
Polovin, R.V. 1961 Shock waves in magnetohydrodynamics. Sov. Phys. Usp. 3, 677.CrossRefGoogle Scholar
Russell, D.R. 2021 Bow shock interaction experiments in a magnetised collisional plasma. PhD thesis, Imperial College London.Google Scholar
Russell, D.R., Burdiak, G.C., Carroll-Nellenback, J.J., Halliday, J.W.D., Hare, J.D., Merlini, S., Suttle, L.G., Valenzuela-Villaseca, V., Eardley, S.J., Fullalove, J.A., et al. 2022 Perpendicular subcritical shock structure in a collisional plasma experiment. Phys. Rev. Lett. 129, 225001.CrossRefGoogle Scholar
Ryutov, D.D., Drake, R.P., Kane, J., Liang, E., Remington, B.A. & Wood-Vasey, W.M. 1999 Similarity criteria for the laboratory simulation of supernova hydrodynamics. Astrophys. J. 518, 821832.CrossRefGoogle Scholar
Sadler, J.D., Walsh, C.A. & Li, H. 2021 Symmetric set of transport coefficients for collisional magnetized plasma. Phys. Rev. Lett. 126, 075001.CrossRefGoogle ScholarPubMed
Schaeffer, D.B., Everson, E.T., Bondarenko, A.S., Clark, S.E., Constantin, C.G., Winske, D., Gekelman, W. & Niemann, C. 2015 Experimental study of subcritical laboratory magnetized collisionless shocks using a laser-driven magnetic piston. Phys. Plasmas 22, 113101.CrossRefGoogle Scholar
Simakov, A.N. 2022 Electron transport in a collisional plasma with multiple ion species in the presence of a magnetic field. Phys. Plasmas 29, 022304.CrossRefGoogle Scholar
Sinars, D.B., Sweeney, M.A., Alexander, C.S., Ampleford, D.J., Ao, T., Apruzese, J.P., Aragon, C., Armstrong, D.J., Austin, K.N., Awe, T.J., et al. 2020 Review of pulsed power-driven high energy density physics research on z at sandia. Phys. Plasmas 27, 070501.CrossRefGoogle Scholar
Slutz, S.A., Herrmann, M.C., Vesey, R.A., Sefkow, A.B., Sinars, D.B., Rovang, D.C., Peterson, K.J. & Cuneo, M.E. 2010 Pulsed-power-driven cylindrical liner implosions of laser preheated fuel magnetized with an axial field. Phys. Plasmas 17, 056303.CrossRefGoogle Scholar
Sutherland, R.S. & Dopita, M.A. 1993 Cooling functions for low-density astrophysical plasmas. The Astrophysical Journal Supplement Series 88, 253327.CrossRefGoogle Scholar
Suttle, L.G., Burdiak, G.C., Cheung, C.L., Clayson, T., Halliday, J.W.D., Hare, J.D., Rusli, S., Russell, D.R., Tubman, E.R., Ciardi, A., et al. 2020 Interactions of magnetized plasma flows in pulsed-power driven experiments. Plasma Phys. Control. Fusion 62, 014020.CrossRefGoogle Scholar
Suttle, L.G., Hare, J.D., Halliday, J.W.D., Merlini, S., Russell, D.R., Tubman, E.R., Valenzuela-Villaseca, V., Rozmus, W., Bruulsema, C. & Lebedev, S.V. 2021 Collective optical Thomson scattering in pulsed-power driven high energy density physics experiments (invited). Review of Scientific Instruments 92, 033542.CrossRefGoogle ScholarPubMed
Suzuki-Vidal, F., Lebedev, S.V., Ciardi, A., Pickworth, L.A., Rodriguez, R., Gil, J.M., Espinosa, G., Hartigan, P., Swadling, G.F., Skidmore, J., et al. 2015 Bow shock fragmentation driven by a thermal instability in laboratory astrophysics experiments. Astrophys. J. 815, 96.CrossRefGoogle Scholar
Swadling, G.F., Lebedev, S.V., Hall, G.N., Patankar, S., Stewart, N.H., Smith, R.A., Harvey-Thompson, A.J., Burdiak, G.C., Grouchy, P.D., Skidmore, J., et al. 2014 Diagnosing collisions of magnetized, high energy density plasma flows using a combination of collective Thomson scattering, faraday rotation, and interferometry (invited). Rev. Sci. Instrum. 85, 11E502.CrossRefGoogle ScholarPubMed
Swadling, G.F., Lebedev, S.V., Niasse, N., Chittenden, J.P., Hall, G.N., Suzuki-Vidal, F., Burdiak, G., Harvey-Thompson, A.J., Bland, S.N., Grouchy, P.D., et al. 2013 Oblique shock structures formed during the ablation phase of aluminium wire array z-pinches. Phys. Plasmas 20, 022705.CrossRefGoogle Scholar
Treumann, R.A. 2009 Fundamentals of collisionless shocks for astrophysical application. 1. Non-relativistic shocks. Astron. Astrophys. Rev. 17, 409435.CrossRefGoogle Scholar
Walsh, C.A., O'Neill, S., Chittenden, J.P., Crilly, A.J., Appelbe, B., Strozzi, D.J., Ho, D., Sio, H., Pollock, B., Divol, L., et al. 2022 Magnetized ICF implosions: scaling of temperature and yield enhancement. Phys. Plasmas 29, 042701.CrossRefGoogle Scholar
Wurden, G.A., Hsu, S.C., Intrator, T.P., Grabowski, T.C., Degnan, J.H., Domonkos, M., Turchi, P.J., Campbell, E.M., Sinars, D.B., Herrmann, M.C., et al. 2015 Magneto-inertial fusion. J. Fusion Energy 35, 6977.CrossRefGoogle Scholar
Yu, E.P., Velikovich, A.L. & Maron, Y. 2014 Application of one-dimensional stagnation solutions to three-dimensional simulation of compact wire array in absence of radiation. Phys. Plasmas 21, 082703.CrossRefGoogle Scholar