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Title: Linear and nonlinear evolution of azimuthal clumping instabilities in a Z-pinch wire array

Abstract

This study presents an analytic theory on the linear and nonlinear evolution of the most unstable azimuthal clumping mode, known as the pi-mode, in a discrete wire array. In the pi-mode, neighboring wires of the array pair-up as a result of the mutual attraction of the wires which carry current in the same direction. The analytic solution displays two regimes, where the collective interactions of all wires dominate, versus where the interaction of the neighboring, single wire dominates. This solution was corroborated by two vastly different numerical codes which were used to simulate arrays with both high wire numbers (up to 600) and low wire number (8). All solutions show that azimuthal clumping of discrete wires occurs before appreciable radial motion of the wires. Thus, absence of azimuthal clumping of wires in comparison with the wires’ radial motion may imply substantial lack of wire currents. Finally, while the present theory and simulations have ignored the plasma corona and axial variations, it is argued that their effects, and the complete account of the three-dimensional feature of the pi-mode, together with a scaling study of the wire number, may be expediently simulated by using only one single wire in an annular wedgemore » with a reflection condition imposed on the wedge’s boundary.« less

Authors:
 [1];  [1];  [1];  [1];  [1];  [1];  [2];  [2];  [2];  [2]
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  1. Univ. of Michigan, Ann Arbor, MI (United States). Dept. of Nuclear Engineering and Radiological Sciences
  2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Univ. of Michigan, Ann Arbor, MI (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1427015
Report Number(s):
SAND2007-0206J
Journal ID: ISSN 1070-664X; 524280
Grant/Contract Number:  
AC04-94AL85000
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 14; Journal Issue: 1; Journal ID: ISSN 1070-664X
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 97 MATHEMATICS AND COMPUTING; plasma pinch; Lagrangian mechanics; classical field theory; Z pinch; wire array Z pinches; plasma confinement; differential equations; plasma instabilities; calculus; classical electromagnetism

Citation Formats

Tang, Wilkin, Strickler, T. S., Lau, Y. Y., Gilgenbach, R. M., Zier, Jacob, Gomez, M. R., Yu, Edmund, Garasi, Chris, Cuneo, M. E., and Mehlhorn, T. A. Linear and nonlinear evolution of azimuthal clumping instabilities in a Z-pinch wire array. United States: N. p., 2007. Web. doi:10.1063/1.2434794.
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Tang, Wilkin, Strickler, T. S., Lau, Y. Y., Gilgenbach, R. M., Zier, Jacob, Gomez, M. R., Yu, Edmund, Garasi, Chris, Cuneo, M. E., & Mehlhorn, T. A. Linear and nonlinear evolution of azimuthal clumping instabilities in a Z-pinch wire array. United States. https://doi.org/10.1063/1.2434794
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Tang, Wilkin, Strickler, T. S., Lau, Y. Y., Gilgenbach, R. M., Zier, Jacob, Gomez, M. R., Yu, Edmund, Garasi, Chris, Cuneo, M. E., and Mehlhorn, T. A. Wed . "Linear and nonlinear evolution of azimuthal clumping instabilities in a Z-pinch wire array". United States. https://doi.org/10.1063/1.2434794. https://www.osti.gov/servlets/purl/1427015.
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@article{osti_1427015,
title = {Linear and nonlinear evolution of azimuthal clumping instabilities in a Z-pinch wire array},
author = {Tang, Wilkin and Strickler, T. S. and Lau, Y. Y. and Gilgenbach, R. M. and Zier, Jacob and Gomez, M. R. and Yu, Edmund and Garasi, Chris and Cuneo, M. E. and Mehlhorn, T. A.},
abstractNote = {This study presents an analytic theory on the linear and nonlinear evolution of the most unstable azimuthal clumping mode, known as the pi-mode, in a discrete wire array. In the pi-mode, neighboring wires of the array pair-up as a result of the mutual attraction of the wires which carry current in the same direction. The analytic solution displays two regimes, where the collective interactions of all wires dominate, versus where the interaction of the neighboring, single wire dominates. This solution was corroborated by two vastly different numerical codes which were used to simulate arrays with both high wire numbers (up to 600) and low wire number (8). All solutions show that azimuthal clumping of discrete wires occurs before appreciable radial motion of the wires. Thus, absence of azimuthal clumping of wires in comparison with the wires’ radial motion may imply substantial lack of wire currents. Finally, while the present theory and simulations have ignored the plasma corona and axial variations, it is argued that their effects, and the complete account of the three-dimensional feature of the pi-mode, together with a scaling study of the wire number, may be expediently simulated by using only one single wire in an annular wedge with a reflection condition imposed on the wedge’s boundary.},
doi = {10.1063/1.2434794},
journal = {Physics of Plasmas},
number = 1,
volume = 14,
place = {United States},
year = {Wed Jan 31 00:00:00 EST 2007},
month = {Wed Jan 31 00:00:00 EST 2007}
}
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https://doi.org/10.1063/1.2434794
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Works referenced in this record:

Characteristics and scaling of tungsten-wire-array z -pinch implosion dynamics at 20 MA
journal, April 2005

Efficient computation of current in multiwire Z-pinch arrays
journal, December 2003

  • Strickler, T. S.; Gilgenbach, R. M.; Johnston, M. D.
  • IEEE Transactions on Plasma Science, Vol. 31, Issue 6
  • DOI: 10.1109/TPS.2003.821357

The relationship between exploding wire expansion rates and wire material properties near the boiling temperature
journal, April 2002

  • Chandler, K. M.; Hammer, D. A.; Sinars, D. B.
  • IEEE Transactions on Plasma Science, Vol. 30, Issue 2
  • DOI: 10.1109/TPS.2002.1024292

Kink and displacement instabilities in imploding wire arrays
journal, January 1981

Azimuthal clumping instabilities in a Z-pinch wire array
journal, May 2005

  • Strickler, Trevor; Lau, Y. Y.; Gilgenbach, R. M.
  • Physics of Plasmas, Vol. 12, Issue 5
  • DOI: 10.1063/1.1886828

An electron conductivity model for dense plasmas
journal, January 1984

  • Lee, Y. T.; More, R. M.
  • Physics of Fluids, Vol. 27, Issue 5
  • DOI: 10.1063/1.864744

Enhancement of X-Ray Power from a Z Pinch Using Nested-Wire Arrays
journal, November 1998

Multi-dimensional high energy density physics modeling and simulation of wire array Z-pinch physics
journal, May 2004

  • Garasi, C. J.; Bliss, D. E.; Mehlhorn, T. A.
  • Physics of Plasmas, Vol. 11, Issue 5
  • DOI: 10.1063/1.1683506

Fast commutation of high current in double wire array Z-pinch loads
journal, January 1997

  • Davis, J.; Gondarenko, N. A.; Velikovich, A. L.
  • Applied Physics Letters, Vol. 70, Issue 2
  • DOI: 10.1063/1.118339

A review of long-implosion-time z pinches as efficient and high-power radiation sources
journal, July 2001

Plasma formation in metallic wire Z pinches
journal, April 2000

Theory of wire number scaling in wire-array Z pinches
journal, May 1999

  • Desjarlais, M. P.; Marder, B. M.
  • Physics of Plasmas, Vol. 6, Issue 5
  • DOI: 10.1063/1.873460

High yield inertial confinement fusion target design for a z -pinch-driven hohlraum
journal, May 1999

  • Hammer, James H.; Tabak, Max; Wilks, Scott C.
  • Physics of Plasmas, Vol. 6, Issue 5
  • DOI: 10.1063/1.873464

Stability of symmetrical compression of a cylindrical liner modeling a system of wires
journal, January 1988

  • Samokhin, A. A.
  • Journal of Applied Mechanics and Technical Physics, Vol. 29, Issue 2
  • DOI: 10.1007/BF00908589

Physics of wire array Z-pinch implosions: experiments at Imperial College
journal, April 2005

  • Lebedev, S. V.; Ampleford, D. J.; Bland, S. N.
  • Plasma Physics and Controlled Fusion, Vol. 47, Issue 5A
  • DOI: 10.1088/0741-3335/47/5A/009

Measurements of the mass distribution and instability growth for wire-array Z-pinch implosions driven by 14–20 MA
journal, May 2005

  • Sinars, D. B.; Cuneo, M. E.; Jones, B.
  • Physics of Plasmas, Vol. 12, Issue 5
  • DOI: 10.1063/1.1876272

Implosion dynamics of wire array Z-pinches: experiments at Imperial College
journal, November 2004

Azimuthal structure in wire-array Z pinch experiments
journal, April 2002

  • Sanford, T. W. L.; Roderick, N. F.; Mock, R. C.
  • IEEE Transactions on Plasma Science, Vol. 30, Issue 2
  • DOI: 10.1109/TPS.2002.1024287

On the gravitational stability of a disk of stars
journal, May 1964

Development and characterization of a Z-pinch-driven hohlraum high-yield inertial confinement fusion target concept
journal, May 2001

  • Cuneo, Michael E.; Vesey, Roger A.; Porter, John L.
  • Physics of Plasmas, Vol. 8, Issue 5
  • DOI: 10.1063/1.1348328

Practical Improvements to the Lee-More Conductivity Near the Metal-Insulator Transition
journal, March 2001

Dynamics of the anode plasma in the magnetically insulated diode of the COBRA ion accelerator by modified laser deflectometry
journal, May 1997

  • Knyazev, B. A.; Greenly, J. B.; Hammer, D. A.
  • Technical Physics Letters, Vol. 23, Issue 5
  • DOI: 10.1134/1.1261695

Wire number breakthrough for high-power annular z pinches and some characteristics at high wire number
journal, October 2001

Tungsten wire number dependence of the implosion dynamics at the Z-accelerator
journal, June 2005

  • Mazarakis, M. G.; Deeney, C. E.; Douglas, M. R.
  • Plasma Devices and Operations, Vol. 13, Issue 2
  • DOI: 10.1080/10519990500058339

Mass-Profile and Instability-Growth Measurements for 300-Wire Z -Pinch Implosions Driven by 14–18 MA
journal, September 2004

Tungsten wire-array Z-pinch experiments at 200 TW and 2 MJ
journal, May 1998

  • Spielman, R. B.; Deeney, C.; Chandler, G. A.
  • Physics of Plasmas, Vol. 5, Issue 5
  • DOI: 10.1063/1.872881

Density measurements in exploding wire-initiated plasmas using tungsten wires
journal, November 1999

  • Pikuz, S. A.; Shelkovenko, T. A.; Mingaleev, A. R.
  • Physics of Plasmas, Vol. 6, Issue 11
  • DOI: 10.1063/1.873695

Linear stability of an accelerated, current carrying wire array
journal, August 1999

  • Hammer, J. H.; Ryutov, D. D.
  • Physics of Plasmas, Vol. 6, Issue 8
  • DOI: 10.1063/1.873598

Pulsed-power-driven high energy density physics and inertial confinement fusion research
journal, May 2005

  • Matzen, M. Keith; Sweeney, M. A.; Adams, R. G.
  • Physics of Plasmas, Vol. 12, Issue 5
  • DOI: 10.1063/1.1891746

Caterpillar structures in single-wire Z-pinch experiments
journal, December 2003

  • Johnston, M. D.; Lau, Y. Y.; Gilgenbach, R. M.
  • Applied Physics Letters, Vol. 83, Issue 24
  • DOI: 10.1063/1.1632535

Theoretical equation of state for aluminum
journal, January 1987

Improved Symmetry Greatly Increases X-Ray Power from Wire-Array Z -Pinches
journal, December 1996

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