This paper 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. 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.
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January 2007
Research Article|
January 31 2007
Linear and nonlinear evolution of azimuthal clumping instabilities in a Z-pinch wire array
Wilkin Tang;
Wilkin Tang
Department of Nuclear Engineering and Radiological Sciences,
University of Michigan
, Ann Arbor, Michigan 48109-2104
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T. S. Strickler;
T. S. Strickler
Department of Nuclear Engineering and Radiological Sciences,
University of Michigan
, Ann Arbor, Michigan 48109-2104
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Y. Y. Lau;
Y. Y. Lau
Department of Nuclear Engineering and Radiological Sciences,
University of Michigan
, Ann Arbor, Michigan 48109-2104
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R. M. Gilgenbach;
R. M. Gilgenbach
Department of Nuclear Engineering and Radiological Sciences,
University of Michigan
, Ann Arbor, Michigan 48109-2104
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Jacob Zier;
Jacob Zier
Department of Nuclear Engineering and Radiological Sciences,
University of Michigan
, Ann Arbor, Michigan 48109-2104
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M. R. Gomez;
M. R. Gomez
Department of Nuclear Engineering and Radiological Sciences,
University of Michigan
, Ann Arbor, Michigan 48109-2104
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Edmund Yu;
Edmund Yu
Sandia National Laboratories
, Albuquerque, New Mexico 87185
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Chris Garasi;
Chris Garasi
Sandia National Laboratories
, Albuquerque, New Mexico 87185
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M. E. Cuneo;
M. E. Cuneo
Sandia National Laboratories
, Albuquerque, New Mexico 87185
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T. A. Mehlhorn
T. A. Mehlhorn
Sandia National Laboratories
, Albuquerque, New Mexico 87185
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Phys. Plasmas 14, 012706 (2007)
Article history
Received:
September 14 2006
Accepted:
December 19 2006
Citation
Wilkin Tang, T. S. Strickler, Y. Y. Lau, R. M. Gilgenbach, Jacob Zier, M. R. Gomez, Edmund Yu, Chris Garasi, M. E. Cuneo, T. A. Mehlhorn; Linear and nonlinear evolution of azimuthal clumping instabilities in a Z-pinch wire array. Phys. Plasmas 1 January 2007; 14 (1): 012706. https://doi.org/10.1063/1.2434794
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