Temporal evolution of surface ripples on a finite plasma slab subject to the magneto-Rayleigh-Taylor instability

Weis, M. R.; Zhang, P.; Rittersdorf, I. M.; Zier, J. C.; Gilgenbach, R. M.; Hess, M. H.; Peterson, K. J.

doi:10.1063/1.4904210

Title: Temporal evolution of surface ripples on a finite plasma slab subject to the magneto-Rayleigh-Taylor instability

Journal Article · Mon Dec 15 00:00:00 EST 2014 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.4904210· OSTI ID:22407917

Weis, M. R.; Zhang, P.; Rittersdorf, I. M.; Zier, J. C.; Gilgenbach, R. M. ^[1]; Hess, M. H.; Peterson, K. J. ^[2]

Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, Michigan 48109-2104 (United States)
Sandia National Laboratories, Albuquerque, New Mexico 87185 (United States)

Using the ideal magnetohydrodynamic model, we calculate the temporal evolution of initial ripples on the boundaries of a planar plasma slab that is subjected to the magneto-Rayleigh-Taylor instability. The plasma slab consists of three regions. We assume that in each region the plasma density is constant with an arbitrary value and the magnetic field is also constant with an arbitrary magnitude and an arbitrary direction parallel to the interfaces. Thus, the instability may be driven by a combination of magnetic pressure and kinetic pressure. The general dispersion relation is derived, together with the feedthrough factor between the two interfaces. The temporal evolution is constructed from the superposition of the eigenmodes. Previously established results are recovered in the various limits. Numerical examples are given on the temporal evolution of ripples on the interfaces of the finite plasma slab.

Cite

Export

Save

OSTI ID:: 22407917

Journal Information:: Physics of Plasmas, Vol. 21, Issue 12; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 1070-664X

Country of Publication:: United States

Language:: English

References (33)

Properties of a planar wire arrays Z-pinch source and comparisons with cylindrical arrays Kantsyrev, V. L.; Rudakov, L. I.; Safronova, A. S. High Energy Density Physics, Vol. 3, Issue 1-2 https://doi.org/10.1016/j.hedp.2007.02.009	journal	May 2007
SPECT3D – A multi-dimensional collisional-radiative code for generating diagnostic signatures based on hydrodynamics and PIC simulation output MacFarlane, J. J.; Golovkin, I. E.; Wang, P. High Energy Density Physics, Vol. 3, Issue 1-2 https://doi.org/10.1016/j.hedp.2007.02.016	journal	May 2007
Triple-threat method sparks hope for fusion Gibbs, W. Wayt Nature, Vol. 505, Issue 7481 https://doi.org/10.1038/505009a	journal	December 2013
Three-dimensional HYDRA simulations of National Ignition Facility targets Marinak, M. M.; Kerbel, G. D.; Gentile, N. A. Physics of Plasmas, Vol. 8, Issue 5 https://doi.org/10.1063/1.1356740	journal	May 2001
Effect of discrete wires on the implosion dynamics of wire array Z pinches Lebedev, S. V.; Beg, F. N.; Bland, S. N. Physics of Plasmas, Vol. 8, Issue 8 https://doi.org/10.1063/1.1385373	journal	August 2001
Characterization of magnetically accelerated flyer plates Lemke, R. W.; Knudson, M. D.; Hall, C. A. Physics of Plasmas, Vol. 10, Issue 4 https://doi.org/10.1063/1.1554740	journal	April 2003
Self-consistent, two-dimensional, magnetohydrodynamic simulations of magnetically driven flyer plates Lemke, R. W.; Knudson, M. D.; Robinson, A. C. Physics of Plasmas, Vol. 10, Issue 5 https://doi.org/10.1063/1.1557530	journal	May 2003
Finite-Resistivity Instabilities of a Sheet Pinch Furth, Harold P.; Killeen, John; Rosenbluth, Marshall N. Physics of Fluids, Vol. 6, Issue 4 https://doi.org/10.1063/1.1706761	journal	January 1963
On the Stability of Fluid Flows with Spherical Symmetry Plesset, M. S. Journal of Applied Physics, Vol. 25, Issue 1 https://doi.org/10.1063/1.1721529	journal	January 1954
Rayleigh-Taylor Instabilities of a Collapsing Cylindrical Shell in a Magnetic Field Harris, E. G. Physics of Fluids, Vol. 5, Issue 9 https://doi.org/10.1063/1.1724473	journal	January 1962
Three-dimensional effects in trailing mass in the wire-array Z pinch Yu, Edmund P.; Cuneo, M. E.; Desjarlais, M. P. Physics of Plasmas, Vol. 15, Issue 5 https://doi.org/10.1063/1.2837050	journal	May 2008
2–20ns interframe time 2-frame 6.151keV x-ray imaging on the recently upgraded Z Accelerator: A progress report Bennett, G. R.; Smith, I. C.; Shores, J. E. Review of Scientific Instruments, Vol. 79, Issue 10 https://doi.org/10.1063/1.2956823	journal	October 2008
Pulsed-power-driven cylindrical liner implosions of laser preheated fuel magnetized with an axial field Slutz, S. A.; Herrmann, M. C.; Vesey, R. A. Physics of Plasmas, Vol. 17, Issue 5 https://doi.org/10.1063/1.3333505	journal	May 2010
Measurements of magneto-Rayleigh–Taylor instability growth during the implosion of initially solid metal liners Sinars, D. B.; Slutz, S. A.; Herrmann, M. C. Physics of Plasmas, Vol. 18, Issue 5 https://doi.org/10.1063/1.3560911	journal	May 2011
Liner-on-plasma system near stagnation: Stabilizing effect of a magnetic cushion Ryutov, D. D. Physics of Plasmas, Vol. 18, Issue 6 https://doi.org/10.1063/1.3596541	journal	June 2011
Effects of magnetic shear on magneto-Rayleigh-Taylor instability Zhang, Peng; Lau, Y. Y.; Rittersdorf, I. M. Physics of Plasmas, Vol. 19, Issue 2 https://doi.org/10.1063/1.3680646	journal	February 2012
Magneto-Rayleigh-Taylor experiments on a MegaAmpere linear transformer driver Zier, J. C.; Gilgenbach, R. M.; Chalenski, D. A. Physics of Plasmas, Vol. 19, Issue 3 https://doi.org/10.1063/1.3690088	journal	March 2012
Solid liner implosions on Z for producing multi-megabar, shockless compressions Martin, M. R.; Lemke, R. W.; McBride, R. D. Physics of Plasmas, Vol. 19, Issue 5 https://doi.org/10.1063/1.3694519	journal	May 2012
Simulating the magnetized liner inertial fusion plasma confinement with smaller-scale experiments Ryutov, D. D.; Cuneo, M. E.; Herrmann, M. C. Physics of Plasmas, Vol. 19, Issue 6 https://doi.org/10.1063/1.4729726	journal	June 2012
Electrothermal instability growth in magnetically driven pulsed power liners Peterson, Kyle J.; Sinars, Daniel B.; Yu, Edmund P. Physics of Plasmas, Vol. 19, Issue 9 https://doi.org/10.1063/1.4751868	journal	September 2012
Simulations of electrothermal instability growth in solid aluminum rods Peterson, Kyle J.; Yu, Edmund P.; Sinars, Daniel B. Physics of Plasmas, Vol. 20, Issue 5 https://doi.org/10.1063/1.4802836	journal	May 2013
Modified helix-like instability structure on imploding z-pinch liners that are pre-imposed with a uniform axial magnetic field Awe, T. J.; Jennings, C. A.; McBride, R. D. Physics of Plasmas, Vol. 21, Issue 5 https://doi.org/10.1063/1.4872331	journal	May 2014
A heuristic model for the nonlinear Rayleigh–Taylor instability in fast Z pinches Hussey, T. W.; Roderick, N. F.; Shumlak, U. Physics of Plasmas, Vol. 2, Issue 6 https://doi.org/10.1063/1.871292	journal	June 1995
Two‐dimensional modeling of x‐ray output from switched foil implosions on Procyon Bowers, R. L.; Nakafuji, G.; Greene, A. E. Physics of Plasmas, Vol. 3, Issue 9 https://doi.org/10.1063/1.871594	journal	September 1996
Insights and applications of two-dimensional simulations to Z-pinch experiments Peterson, D. L.; Bowers, R. L.; Matuska, W. Physics of Plasmas, Vol. 6, Issue 5 https://doi.org/10.1063/1.873469	journal	May 1999
WFPC2 Studies of the Crab Nebula. III. Magnetic Rayleigh-Taylor Instabilities and the Origin of the Filaments Hester, J. Jeff; Stone, James M.; Scowen, Paul A. The Astrophysical Journal, Vol. 456 https://doi.org/10.1086/176643	journal	January 1996
Parameter space for magnetized fuel targets in inertial confinement fusion Lindemuth, I. R.; Kirkpatrick, R. C. Nuclear Fusion, Vol. 23, Issue 3 https://doi.org/10.1088/0029-5515/23/3/001	journal	March 1983
Experimental measurements of a converging flux conserver suitable for compressing a field reversed configuration for magnetized target fusion Intrator, T.; Taccetti, M.; Clark, D. A. Nuclear Fusion, Vol. 42, Issue 2 https://doi.org/10.1088/0029-5515/42/2/313	journal	February 2002
The Physics of Inertial Fusion Atzeni, Stefano; Meyer-ter-Vehn, Jürgen https://doi.org/10.1093/acprof:oso/9780198562641.001.0001	book	January 2004
The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I Taylor, Geoffrey Ingram Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 201, Issue 1065, p. 192-196 https://doi.org/10.1098/rspa.1950.0052	journal	March 1950
Some instabilities of a completely ionized plasma Kruskal, Martin DAvid; Schwarzschild, Martin Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 223, Issue 1154, p. 348-360 https://doi.org/10.1098/rspa.1954.0120	journal	May 1954
Fundamentals of Plasma Physics Cargill, P. J. Plasma Physics and Controlled Fusion, Vol. 49, Issue 2 https://doi.org/10.1088/0741-3335/49/2/b01	journal	January 2007
Fundamentals of Plasma Physics Schmidt, George Nuclear Science and Engineering, Vol. 79, Issue 4 https://doi.org/10.13182/nse81-a21396	journal	December 1981

Cited By (6)

Coupling of sausage, kink, and magneto-Rayleigh-Taylor instabilities in a cylindrical liner Weis, M. R.; Zhang, P.; Lau, Y. Y. Physics of Plasmas, Vol. 22, Issue 3 https://doi.org/10.1063/1.4915520	journal	March 2015
Discrete helical modes in imploding and exploding cylindrical, magnetized liners Yager-Elorriaga, D. A.; Zhang, P.; Steiner, A. M. Physics of Plasmas, Vol. 23, Issue 12 https://doi.org/10.1063/1.4969082	journal	December 2016
Evolution of sausage and helical modes in magnetized thin-foil cylindrical liners driven by a Z-pinch Yager-Elorriaga, D. A.; Lau, Y. Y.; Zhang, P. Physics of Plasmas, Vol. 25, Issue 5 https://doi.org/10.1063/1.5017849	journal	May 2018
Study of stability in a liner-on-target gas puff Z-pinch as a function of pre-embedded axial magnetic field Conti, F.; Aybar, N.; Narkis, J. Physics of Plasmas, Vol. 27, Issue 1 https://doi.org/10.1063/1.5131170	journal	January 2020
Magneto-Rayleigh–Taylor instability in compressible Z-pinch liner plasmas Yang, Xue; Xiao, De-Long; Ding, Ning Chinese Physics B, Vol. 26, Issue 7 https://doi.org/10.1088/1674-1056/26/7/075202	journal	June 2017
Rayleigh-Taylor instability in accelerated elastic-solid slabs Piriz, S. A.; Piriz, A. R.; Tahir, N. A. Physical Review E, Vol. 96, Issue 6 https://doi.org/10.1103/physreve.96.063115	journal	December 2017

Similar Records

Temporal evolution of surface ripples on a finite plasma slab subject to the magneto-Rayleigh-Taylor instability

Journal Article · Wed Dec 17 00:00:00 EST 2014 · Physics of Plasmas · OSTI ID:22407917

Weis, Matthew Robert; Zhang, Peng; Lau, Yue Ying; +4 more

Anisotropy and feedthrough in magneto-Rayleigh-Taylor instability

Journal Article · Wed Jun 15 00:00:00 EDT 2011 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print) · OSTI ID:22407917

Lau, Y Y; Zier, J C; Rittersdorf, I M; +2 more

Theoretical and Experimental Studies of Magneto-Rayleigh-Taylor Instabilities

Technical Report · Sun Jul 07 00:00:00 EDT 2013 · OSTI ID:22407917

Lau, Yue Ying; Gilgenbach, Ronald

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
DISPERSION RELATIONS
MAGNETIC FIELDS
PLASMA DENSITY
RAYLEIGH-TAYLOR INSTABILITY
SLABS
SURFACES
TIME DEPENDENCE

Title: Temporal evolution of surface ripples on a finite plasma slab subject to the magneto-Rayleigh-Taylor instability

Citation Formats

References (33)

Cited By (6)

Similar Records

Related Subjects