Abstract
A review of publications on the Rayleigh–Taylor instability arising during high-velocity implosion of liners is presented. Papers that describe experimental testing and numerical simulation of the development and suppression of this instability are also considered.
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R. E. Reinovsky, W. E. Anderson, W. L. Atchison, et al., “Pulsed Power Hydrodynamics: a New Application of High Magnetic Field,” in Proc. of the 9th Intern. Conf. on Megagauss Magnetic Field Generation and Related Topics, Moscow — St.-Petersburg, 2002 (Inst. Exp. Phys., Sarov, 2004), pp. 696–705.
R. E. Reinovsky, W. L. Atchison, C. Rousculp, and A. Kaul, “Pulsed High Magnetic Fields for Exploring the Dynamic Properties of Materials,” in Proc. of the 13th Intern. Conf. on Megagauss Magnetic Field Generation and Related Topics, Suzhou (China), July 6–9, 2010 (Nat. Univ. Defense Technol., Chángsha, 2012), pp. 44–45.
G. Boffetta and A. Mazzino, “Incompressible Rayleigh–Taylor Turbulence,” Annual Rev. Fluid Mech. 49, 119–143 (2017).
A. L. Velikovich, “Mitigation of Rayleigh–Taylor Instability in High-Energy Density Plasmas. A Personal Perspective,” in Abstr. book of the 42nd IEEE Intern. Conf. on Plasma Science, Belek, Antalya (Turkey), May 24–28, 2015 (IEEE, 2015), p. 621.
G. I. Taylor, “The Instability of Liquid Surfaces when Accelerated in a Direction Perpendicular to their Planes. 1,” Proc. Roy. Soc. London. Ser. A 201 (1065), 192–196 (1950).
D. J. Lewis, “The Instability of Liquid Surfaces when Accelerated in a Direction Perpendicular to their Planes. 2,” Proc. Roy. Soc. London. Ser. A 202 (1068), 81–96 (1950).
L. D. Landau and E. M. Lifshits, Fluid Mechanics (Nauka, Moscow, 1986; Addison-Wesley, Reading, 1987).
E. G. Harris, “Rayleigh–Taylor Instabilities of a Collapsing Cylindrical Shell in a Magnetic Field,” Phys. Fluids 5 (9), 1057–1062 (1962).
S. F. Garanin, Physical Processes in the MAGO-MTF Systems (Inst. Exp. Phys., Sarov, 2012; Los Alamos, LA-UR-13-29094, 2013).
E. Ott, “Nonlinear Evolution of the Rayleigh–Taylor of Thin Layers,” Phys. Rev. Lett. 29 (21), 1429–1432 (1972).
P. B. Garabedian, “On Steady-State Bubbles Generated by Taylor Instability,” Proc. Roy. Soc. London. Ser. A 241 (1226), 423–431 (1957).
G. Birkhoff and D. Carter, “Rising Plane Bubbles,” J. Math. Mech. 6 (6), 769–779 (1957).
G. R. Baker, D. I. Meiron, and S. A. Orszag, “Vortex Simulations of the Rayleigh–Taylor Instability,” Phys. Fluids 23, 1485–1490 (1980).
C. L. Gardner, J. Glimm, O. McBryan, et al., “The Dynamics of Bubble Growth for Rayleigh–Taylor Unstable Interfaces,” Phys. Fluids 31 (3), 447–465 (1988).
S. W. Haan, “Onset of Nonlinear Saturation for Rayleigh–Taylor Growth in the Presence of a Full Spectrum of Modes,” Phys. Rev. A 39 (11), 5812–5825 (1989).
R. E. Reinovsky, W. E. Anderson, W. L. Atchison, et al., “Instability Growth in Magnetically Imploded High- Conductivity Cylindrical Liners with Material Strength,” IEEE Trans. Plasma Sci. 30 (5), 1764–1776 (2002).
D. B. Sinars, S. A. Slutz, M. C. Herrmann, et al., “Measurements of Magneto-Rayleigh–Taylor Instability Growth during the Implosion of Initially Solid Metal Liners,” Phys. Plasmas 18, 056301 (2011).
O. I. Volchenko, I. G. Zhidov, E. E. Meshkov, and V. G. Rogachev, “Development of Localized Perturbations on an Unstable Boundary of an Accelerated Liquid Layer,” Pis’ma v Zh. Tekh. Fiz. 15 (1), 47–51 (1989).
S. F. Garanin and A. I. Startsev, “Numerical Simulation of Nonlinear Growth of Localized Perturbations with Angles in the Case of the Rayleigh–Taylor Instability,” Vopr. Atom. Nauki Tekhniki, Ser. Teoret. Prikl. Fiz., No. 3, 6–9 (1992).
S. F. Garanin, “Self-Similar Evolution of Rayleigh–Taylor Instability in the Corner-Point Regions,” in Proc. of the 5th Intern. Workshop on Compressible Turbulent Mixing, Stony Brook, New York, 1995 (World Sci., Singapore–New Jersey–London–Hong Kong, 1995), pp. 33–39.
V. F. D’yachenko and V. S. Imshennik, “Two-Dimensional Magnetohydrodynamic Model of the Plasma Focus of the Z-Pinch,” in Issues of the Plasma Theory. Vol. 8 (Atomizdat, Moscow, 1974), pp. 164–246.
V. V. Vikhrev and S. I. Braginskii, “Dynamics of the Z-Pinch,” in Issues of the Plasma Theory, Vol. 10 (Atomizdat, Moscow, 1980), pp. 243–318.
S. F. Garanin, O. A. Amelicheva, O. M. Burenkov, et al., “Relaxation of a 3D MHD Flow across a Magnetic Field (2D Hydrodynamic Flow) in a Bounded Region,” Zh. Eksp. Teor. Fiz. 124 (1), 70–79 (2003) [J. Exp. Theor. Phys. 97 (1), 61–69 (2003)].
S. F. Garanin, E. M. Kravets, O. M. Pronina, and A. L. Stadnik, “Rayleigh–Taylor Instability in a Two- Dimensional Case,” in Problems of High Energy Density Physics, Proc. Intern. Conf. “12th Khariton’s Topical Scientific Readings,” Sarov, 2010 (Inst. Exp. Phys., Sarov, 2010), pp. 235–239.
V. K. Chernyshev, V. N. Mokhov, M. S. Protasov, et al., “Investigation of Liner Ponderomotive Units used as a Driver in a System with Magnetic Compression,” Vopr. Atom. Nauki Tekhniki. Ser. Mat. Model. Fiz. Prots., No. 4, 42–50 (1992).
A. M. Buyko, V. V. Zmushko, V. N. Mokhov, et al., “On Feasibility to Achieve High Longitudinal Symmetry of Cylindrical Metal Liners Compressed by Currents from Most Powerful Disk EMG,” in Digest of Tech. Papers 12th IEEE Intern. Pulsed Power Conf., Monterey (USA), June 27–30, 1999, pp. 1145–1148.
R. E. Reinovsky, “Pulsed Power Experiments in Hydrodynamics and Material Properties,” in Digest of Tech. Papers 12th IEEE Intern. Pulsed Power Conf., Monterey (USA), June 27–30, 1999, pp. 38–43.
A. M. Buyko, O. M. Burenkov, V. V. Zmushko, et al., “On the Feasibility to Achieve High Pressures with Disk EMG Driven Impacting Liners,” in Digest of Tech. Papers: Pulsed Power Plasma Science — 2001 (Inst. Electric. Electron. Engrs, Las Vegas, 2001), pp. 516–519.
R. K. Keinigs, W. L. Atchison, W. E. Anderson, et al., “Material Science Experiments on the Atlas Facility,” in Digest of Tech. Papers: Pulsed Power Plasma Science — 2001 (Inst. Electric. Electron. Engrs, Las Vegas, 2001), pp. 356–360.
S. F. Garanin, V. I. Mamyshev, and V. B. Yakubov, “The MAGO System: Current Status,” IEEE Trans. Plasma Sci. 34 (5), pt 3, 2273–2278 (2006).
J. H. Degnan, T. Cavazos, D. Clark, et al., “On Research on Magnetic Pressure Implosions of Long Cylindrical Liners, Suitable for Subsequent Compression of the Field Reversed Configuration Type of Compact Toroids,” in Proc. of the 9th Intern. Conf. on Megagauss Magnetic Field Generation and Related Topics, Moscow — St.-Petersburg, 2002 (Inst. Exp. Phys., Sarov, 2004), pp. 730–737.
D. B. Sinars, “Magneto-Inertial Fusion Research in the United States: A Promising Prospect,” in Abstracts of the 42nd IEEE Intern. Conf. on Plasma Science, Belek, Antalya (Turkey), May 24–28, 2015 (IEEE, 2015), p. 245.
S. F. Garanin, G. G. Ivanova, D. V. Karmishin, and V. N. Sofronov, “Diffusion of a Megagauss Field into a Metal,” Prikl. Mekh. Tekh. Fiz. 46 (2), 5–12 (2005) [J. Appl. Mech. Tech. Phys. 46 (2), 153–159 (2005)].
W. L. Atchison, R. J. Faehl, I. R. Lindemuth, et al., “Dependence of Solid Liner Stability on Drive Conditions during Magnetic Implosion,” in Proc. of the 9th Intern. Conf. on Megagauss Magnetic Field Generation and Related Topics, Moscow — St.-Petersburg, 2002 (Inst. Exp. Phys., Sarov, 2004), pp. 710–717.
A. M. Buyko, S. F. Garanin, D. V. Karmishin, et al., “Analysis of the Liner Stability in Various Experiments,” IEEE Trans. Plasma Sci. 36 (1), 4–9 (2008).
I. D. Sofronov, O. A. Vinokurov, V. V. Zmushko, et al., “MIMOZA Software Complex. Solution of Multidimensional Problems of Hydrodynamics,” in Issues of Mathematical modeling, Computational Mathematics, and Informatics (Inst. Exp. Phys., Moscow, Arzamas-16, 1994), pp. 94–96.
A. M. Buyko, S. F. Garanin, V. V. Zmushko, et al., “2D Computations for Perturbation Growth of Magnetically Driven Cylindrical Aluminum and Aluminum Alloy Liners,” in Proc. of the 7th Intern. Workshop Phys. Compressible Turbulent Mixing, St.-Petersburg (Russia), 1999 (Inst. Exp. Phys., Sarov, 2001), pp. 237–243.
V. A. Raevskii, A. I. Lebedev, P. N. Nizovtsev, et al., “Investigation of the Rayleigh–Taylor Instability in Copper and Aluminum at Pressures up to 45 GPa and Strain Rates of 105–108 s−1,” in Abstracts of Intern. Conf. “5th Khariton’s Topical Readings: Substances, Materials, and Structures under Intense Dynamic Actions” (Inst. Exp. Phys., Sarov, 2003, pp. 180–181).
Yu. V. Bat’kov, V. N. Knyazev, S. A. Novikov, et al., “Shear Strength of Aluminum upon Shockless Compression,” Fiz. Goreniya Vzryva 35 (6), 115–118 (1999) [Comb., Expl., Shock Waves 35 (6), 707–710 (1999)].
A. M. Buyko, S. F. Garanin, V. V. Zmushko, et al., “On Stabilization of Implosion of Condensed Liners,” Prikl. Mekh. Tekh. Fiz. 50 (3), 3–14 (2009) [J. Appl. Mech. Tech. Phys. 50 (3), 361–370 (2009)].
A. I. Pavlovskii, A. I. Bykov, M. I. Dolotenko, et al., “Cumulation of Superstrong Magnetic Fields,” in High Energy Densities (collected scientific papers) (Inst. Exp. Phys., Sarov, 1997, pp. 446–468).
J. Davis, N. A. Gondarenko, and A. L. Velikovich, “Fast Commutator of High Current in Double Wire Array Z-Pinch Loads,” Appl. Phys. Lett. 70, 170–172 (1997).
D. L. Book and P. J. Turchi, “Dynamics of Rotationally Stabilized Implosions of Compressible Liquid Shells,” Phys. Fluids 22, 68–78 (1979).
K. J. Peterson, T. J. Awe, E. P. Yu, et al., “Electrothermal Instability Mitigation by Using Thick Dielectric Coatings on Magnetically Imploded Conductors,” Phys. Rev. Lett. 112, 135002(5) (2014).
S. F. Garanin, S. D. Kuznetsov, V. N. Mokhov, et al., “On Feasibility of Rayleigh–Taylor Instability Magnetic Stabilization of Liner Implosions,” in Proc. of the 8th Intern. Conf. on Megagauss Magnetic Field Generation and Related Topics, Tallahassee (USA), 1998 (World. Sci., Singapore, 2004), pp. 563–567.
B. G. Anderson, W. E. Anderson, W. L. Atchison, et al., “Liner Experiment on Verification of Rayleigh–Taylor Instability Magnetic Stabilization Effect (Joint LANL/VNIIEF Experiment Pegasus-2),” in Digest Tech. Papers: Pulsed Power Plasma Science — 2001 (Inst. Electric. Electron. Engrs, Las Vegas, 2001), pp. 354–355.
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Original Russian Text © S.F. Garanin, A.M. Buyko, V.B. Yakubov.
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 58, No. 5, pp. 26–43, September–October, 2017.
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Garanin, S.F., Buyko, A.M. & Yakubov, V.B. Rayleigh–Taylor instability of high-velocity condensed-matter liners. J Appl Mech Tech Phy 58, 779–793 (2017). https://doi.org/10.1134/S0021894417050030
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DOI: https://doi.org/10.1134/S0021894417050030