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The structure of 3-D collisional magnetized bow shocks in pulsed-power-driven plasma flows

Published online by Cambridge University Press:  11 November 2022

R. Datta
Affiliation:
Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
D.R. Russell
Affiliation:
Blackett Laboratory, Imperial College London, London SW7 2BW, UK
I. Tang
Affiliation:
Blackett Laboratory, Imperial College London, London SW7 2BW, UK
T. Clayson
Affiliation:
Blackett Laboratory, Imperial College London, London SW7 2BW, UK
L.G. Suttle
Affiliation:
Blackett Laboratory, Imperial College London, London SW7 2BW, UK
J.P. Chittenden
Affiliation:
Blackett Laboratory, Imperial College London, London SW7 2BW, UK
S.V. Lebedev
Affiliation:
Blackett Laboratory, Imperial College London, London SW7 2BW, UK
J.D. Hare*
Affiliation:
Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
Email address for correspondence: jdhare@mit.edu

Abstract

We investigate three-dimensional (3-D) bow shocks in a highly collisional magnetized aluminium plasma, generated during the ablation phase of an exploding wire array on the MAGPIE facility (1.4 MA, 240 ns). Ablation of plasma from the wire array generates radially diverging, supersonic ($M_S \sim 7$), super-Alfvénic ($M_A > 1$) magnetized flows with frozen-in magnetic flux ($R_M \gg 1$). These flows collide with an inductive probe placed in the flow, which serves both as the obstacle that generates the magnetized bow shock, and as a diagnostic of the advected magnetic field. Laser interferometry along two orthogonal lines of sight is used to measure the line-integrated electron density. A detached bow shock forms ahead of the probe, with a larger opening angle in the plane parallel to the magnetic field than in the plane normal to it. Since the resistive diffusion length of the plasma is comparable to the probe size, the magnetic field decouples from the ion fluid at the shock front and generates a hydrodynamic shock, whose structure is determined by the sonic Mach number, rather than the magnetosonic Mach number of the flow. The 3-D simulations performed using the resistive magnetohydrodynamic (MHD) code Gorgon confirm this picture, but under-predict the anisotropy observed in the shape of the experimental bow shock, suggesting that non-MHD mechanisms may be important for modifying the shock structure.

Type
Research Article
Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

Ampleford, D.J., Jennings, C.A., Hall, G.N., Lebedev, S.V., Bland, S.N., Bott, S.C., Suzuki-Vidal, F., Palmer, J.B.A., Chittenden, J.P., Cuneo, M.E., et al. 2010 Bow shocks in ablated plasma streams for nested wire array $z$-pinches: a laboratory astrophysics testbed for radiatively cooled shocks. Phys. Plasmas 17 (5), 056315.CrossRefGoogle Scholar
Anderson, J.D. 2001 Fundamentals of Aerodynamics. McGraw-Hill.Google Scholar
Bott-Suzuki, S.C., Caballero Bendixsen, L.S., Cordaro, S.W., Blesener, I.C., Hoyt, C.L., Cahill, A.D., Kusse, B.R., Hammer, D.A., Gourdain, P.A., Seyler, C.E., et al. 2015 Investigation of radiative bow-shocks in magnetically accelerated plasma flows. Phys. Plasmas 22 (5), 052710.CrossRefGoogle 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 (7), 072713.CrossRefGoogle Scholar
Chen, F.F. 1974 Introduction to Plasma Physics. Plenum.Google Scholar
Chevalier, R.A. 1982 Are young supernova remnants interacting with circumstellar gas. Astrophys. J. 259 (1981), L85.CrossRefGoogle Scholar
Chittenden, J.P., Lebedev, S.V., Oliver, B.V., Yu, E.P. & Cuneo, M.E. 2004 Equilibrium flow structures and scaling of implosion trajectories in wire array Z pinches. Phys. Plasmas 11 (3), 1118.CrossRefGoogle Scholar
Choi, E., Wiita, P.J. & Ryu, D. 2007 Hydrodynamic interactions of relativistic extragalactic jets with dense clouds. Astrophys. J. 655 (2), 769.CrossRefGoogle Scholar
Chou, M. & Hau, L.N. 2004 Magnetohydrodynamic waves and instabilities in homogeneous gyrotropic ultrarelativistic plasma. Astrophys. J. 611 (2), 1200.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 (5), 056501.CrossRefGoogle Scholar
Coburn, J.T., Chen, C.H.K. & Squire, J. 2022 A measurement of the effective mean free path of solar wind protons. J. Plasma Phys. 88 (5), 175880502.CrossRefGoogle Scholar
Datta, R., Russell, D.R., Tang, I., Clayson, T., Suttle, L.G., Chittenden, J.P., Lebedev, S.V. & Hare, J.D. 2022 Time-resolved velocity and ion sound speed measurements from simultaneous bow shock imaging and inductive probe measurements. Rev. Sci. Instrum. 93 (10), 103530.CrossRefGoogle ScholarPubMed
De Sterck, H., Low, B.C. & Poedts, S. 1998 Complex magnetohydrodynamic bow shock topology in field-aligned low-$\beta$ flow around a perfectly conducting cylinder. Phys. Plasmas 5 (11), 4015.CrossRefGoogle Scholar
De Sterck, H. & Poedts, S. 2000 Intermediate shocks in three-dimensional magnetohydrodynamic bow-shock flows with multiple interacting shock fronts. Phys. Rev. Lett. 84 (24), 5524.CrossRefGoogle Scholar
Draine, B.T. 1980 Interstellar shock waves with magnetic precursors. Astrophys. J. 241, 1021.CrossRefGoogle Scholar
Draine, B.T., Roberge, W.G. & Dalgarno, A. 1983 Magnetohydrodynamic shock waves in molecular clouds. Astrophys. J. 264, 485.CrossRefGoogle Scholar
Drake, R.P. 2013 High-Energy-Density Physics. Fundamentals, Inertial Fusion and Experimental Analysis. Springer.Google Scholar
Drake, R.P., Glendinning, S.G., Estabrook, K., Remington, B.A., McCray, R., Wallace, R.J., Suter, L.J., Smith, T.B., Carroll, J.J., London, R.A., et al. 1998 Observation of forward shocks and stagnated ejecta driven by high-energy-density plasma flow. Phys. Rev. Lett. 81 (10), 2068.CrossRefGoogle Scholar
Duncan, G.C. & Hughes, P.A. 1994 Simulations of relativistic extragalactic jets. Astrophys. J. 436, L119.CrossRefGoogle Scholar
Dursi, L.J. & Pfrommer, C. 2008 Draping of cluster magnetic fields over bullets and bubbles—morphology and dynamic effects. Astrophys. J. 677 (2), 993.CrossRefGoogle Scholar
Eastwood, J.P., Bale, S.D., Mozer, F.S. & Hull, A.J. 2007 Contributions to the cross shock electric field at a quasiperpendicular collisionless shock. Geophys. Res. Lett. 34 (17), L17104.CrossRefGoogle Scholar
Everson, E.T., Pribyl, P., Constantin, C.G., Zylstra, A., Schaeffer, D., Kugland, N.L. & Niemann, C. 2009 Design, construction, and calibration of a three-axis, high-frequency magnetic probe (b-dot probe) as a diagnostic for exploding plasmas. Rev. Sci. Instrum. 80 (11), 113505.CrossRefGoogle ScholarPubMed
Foster, J.M., Wilde, B.H., Rosen, P.A., Williams, R.J.R., Blue, B.E., Coker, R.F., Drake, R.P., Frank, A., Keiter, P.A., Khokhlov, A.M., et al. 2005 High-energy-density laboratory astrophysics studies of jets and bow shocks. Astrophys. J. 634 (1), L77.CrossRefGoogle Scholar
Goedbloed, J.P., Keppens, R. & Poedts, S. 2010 Advanced Magnetohydrodynamics: with Applications to Laboratory and Astrophysical Plasmas. Cambridge University Press.CrossRefGoogle 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 (8), 085012.CrossRefGoogle Scholar
Hare, J.D., Suttle, L.G., Lebedev, S.V., Loureiro, N.F., Ciardi, A., Chittenden, J.P., Clayson, T., Eardley, S.J., Garcia, C., Halliday, J.W.D., et al. 2018 An experimental platform for pulsed-power driven magnetic reconnection. Phys. Plasmas 25 (5), 055703.CrossRefGoogle Scholar
Hartigan, P., Raymond, J. & Meaburn, J. 1990 Observations and shock models of the jet and Herbig-Haro objects HH 46/47. Astrophys. J. 362, 624.CrossRefGoogle Scholar
Hau, L.N. & Sonnerup, B.U.O. 1993 On slow mode waves in an anisotropic plasma. Geophys. Res. Lett. 20 (17), 1763.CrossRefGoogle Scholar
Hutchinson, I.H. 2002 Principles of Plasma Diagnostics. Cambridge.CrossRefGoogle Scholar
Kane, J., Arnett, D., Remington, B.A., Glendinning, S.G., Bazan, G., Drake, R.P., Fryxell, B.A., Teyssier, R. & Moore, K. 1999 Scaling supernova hydrodynamics to the laboratory. Phys. Plasmas 6 (5 I), 2065.CrossRefGoogle Scholar
Kennel, C.F., Edmiston, J.P. & Hada, T. 1985 A quarter century of collisionless shock research. Washington DC American Geophysical Union Geophysical Monograph Series 34, 1.Google Scholar
Kifonidis, K., Plewa, T., Janka, H.-Th. & Müller, E. 2003 Non-spherical core collapse supernovae. Astron. Astrophys. 408 (2), 621.CrossRefGoogle Scholar
Kundu, P.K., Cohen, I.M. & Dowling, D.R. (Eds.) 2012 Fluid Mechanics, 5th edn. Academic.Google 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 (8), 3734.CrossRefGoogle Scholar
Lebedev, S.V., Frank, A. & Ryutov, D.D. 2019 Exploring astrophysics-relevant magneto- hydrodynamics with pulsed-power laboratory facilities. Rev. Mod. Phys. 91 (2), 25002.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 (5), 056305.CrossRefGoogle Scholar
Levesque, J.M., Liao, A.S., Hartigan, P., Young, R.P., Trantham, M., Klein, S., Gray, W., Manuel, M., Fiksel, G., Katz, J. et al. 2022 Experimental observations of detached bow shock formation in the interaction of a laser-produced plasma with a magnetized obstacle. Phys. Plasmas 29 (1), 012106.CrossRefGoogle Scholar
Liao, A., Hartigan, P., Fiksel, G., Blue, B., Graham, P., Foster, J. & Kuranz, C. 2018 Using the ROSS optical streak camera as a tool to understand laboratory experiments of laser-driven magnetized shock waves. High Power Laser Sci. Engng 6, E22.CrossRefGoogle Scholar
Miley, G. 1980 The structure of extended extragalactic sources. Annu. Rev. Astron. Astrophys. 18, 165.CrossRefGoogle 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 (4), 1533.CrossRefGoogle Scholar
Mullan, D.J. 1971 The structure of transverse hydromagnetic shocks in regions of low ionization. Mon. Not. R. Astron. Soc. 153 (2), 145.CrossRefGoogle Scholar
Pilgram, J.J., Adams, M.B.P., Constantin, C.G., Heuer, P.V., Ghazaryan, S., Kaloyan, M., Dorst, R.S., Schaeffer, D.B., Tzeferacos, P. & Niemann, C. 2022 High repetition rate exploration of the biermann battery effect in laser produced plasmas over large spatial regions. High Power Laser Sci. Engng 10, E13.CrossRefGoogle Scholar
Remington, B.A., Drake, R.P. & Ryutov, D.D. 2006 Experimental astrophysics with high power lasers and Z pinches. Rev. Mod. Phys. 78 (3), 755.CrossRefGoogle Scholar
Remington, B.A., Kane, J., Drake, R.P., Glendinning, S.G., Estabrook, K., London, R., Castor, J., Wallace, R.J., Arnett, D., Liang, E., et al. 1997 Supernova hydrodynamics experiments on the Nova laser. Phys. Plasmas 4 (5/2), 19942003.CrossRefGoogle Scholar
Richardson, A.S. 2019 NRL plasma formulary. US Naval Research Laboratory.Google Scholar
Robey, H.F., Perry, T.S., Klein, R.I., Kane, J.O., Greenough, J.A. & Boehly, T.R. 2002 Experimental investigation of the three-dimensional interaction of a strong shock with a spherical density inhomogeneity. Phys. Rev. Lett. 89 (8), 085001.CrossRefGoogle Scholar
Rochau, G.A., Bailey, J.E. & Maron, Y. 2010 Applied spectroscopy in pulsed power plasmas. Phys. Plasmas 17 (5), 055501.CrossRefGoogle 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. Plasmas arXiv:2201.09039Google Scholar
Schaeffer, D.B., Cruz, F.D., Dorst, R.S., Cruz, F., Heuer, P.V., Constantin, C.G., Pribyl, P., Niemann, C., Silva, L.O. & Bhattacharjee, A. 2022 Laser-driven, ion-scale magnetospheres in laboratory plasmas. I. Experimental platform and first results. Phys. Plasmas 29 (4), 042901.CrossRefGoogle Scholar
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 (11), 113101.CrossRefGoogle Scholar
Schaeffer, D.B., Fox, W., Haberberger, D., Fiksel, G., Bhattacharjee, A., Barnak, D.H., Hu, S.X. & Germaschewski, K. 2017 Generation and evolution of high-Mach-number laser-driven magnetized collisionless shocks in the laboratory. Phys. Rev. Lett. 119 (2), 025001.CrossRefGoogle ScholarPubMed
Shaikhislamov, I.F., Antonov, V.M., Zakharov, Yu.P., Boyarintsev, E.L., Melekhov, A.V., Posukh, V.G. & Ponomarenko, A.G. 2013 Mini-magnetosphere: laboratory experiment, physical model and Hall MHD simulation. Adv. Space Res. 52 (3), 422.CrossRefGoogle Scholar
Smith, M.D. 2012 Astrophysical Jets and Beams. Cambridge University Press.CrossRefGoogle Scholar
Smith, M.D., Khanzadyan, T. & Davis, C.J. 2003 Anatomy of the Herbig–Haro object HH7 bow shock. R. Astron. Soc. 536, 524.CrossRefGoogle Scholar
Smith, M.D. & Norman, C.A. 1981 Extrastellar jets – trajectories. R. Astron. Soc. 148, 148.Google Scholar
Spreiter, J.R. & Stahara, S.S. 1985 Magnetohydrodynamic and gasdynamic theories for planetary bow waves. Collisionless Shocks Heliosphere: Rev. Curr. Res. (), .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. 2019 Interactions of magnetized plasma flows in pulsed-power driven experiments. Plasma Phys. Control. Fusion 62 (1), 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). Rev. Sci. Instrum. 92 (3), 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. 2015 Bow shock fragmentation driven by a thermal instability in laboratory astrophysics experiments. Astrophys. J. 815 (2), 96.CrossRefGoogle Scholar
Suzuki-Vidal, F., Lebedev, S.V., Krishnan, M., Bocchi, M., Skidmore, J., Swadling, G., Harvey-Thompson, A.J., Burdiak, G., de Grouchy, P., Pickworth, L., et al. 2012 Laboratory astrophysics experiments studying hydrodynamic and magnetically-driven plasma jets. J. Phys. Conf. Ser. 370 (1), 012002.CrossRefGoogle Scholar
Suzuki-Vidal, F., Lebedev, S.V., Krishnan, M., Skidmore, J., Swadling, G.F., Bocchi, M., Harvey-Thompson, A.J., Patankar, S., Burdiak, G.C., de Grouchy, P., et al. 2013 Interaction of radiatively cooled plasma jets with neutral gases for laboratory astrophysics studies. High Energy Density Phys. 9 (1), 141.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., de Grouchy, P., 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. Rev. Sci. Instrum. 85 (11), 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., De Grouchy, P., et al. 2013 Oblique shock structures formed during the ablation phase of aluminium wire array Z-pinches. Phys. Plasmas 20 (2), 022705.CrossRefGoogle Scholar
Velikovich, A.L., Sokolov, I.V. & Esaulov, A.A. 2002 Perfectly conducting incompressible fluid model of a wire array implosion. Phys. Plasmas 9 (4), 1366.CrossRefGoogle Scholar
Verigin, M., Kotova, G., Szabo, A., Slavin, J., Gombosi, T., Kabin, K., Shugaev, F. & Kalinchenko, A. 2001 Wind observations of the terrestrial bow shock: 3-D shape and motion. Earth Planet. Space 53 (10), 1001.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 (4), 042701.CrossRefGoogle Scholar
Zhao, X. & Seyler, C.E. 2015 Computational extended magneto-hydrodynamical study of shock structure generated by flows past an obstacle. Phys. Plasmas 22 (7), 072102.CrossRefGoogle Scholar