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

Abstract

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 withmore » a reflection condition imposed on the wedge's boundary.« less

Authors:
; ; ; ; ; ; ; ; ;  [1];  [2]
  1. Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, Michigan 48109-2104 (United States)
  2. (United States)
Publication Date:
OSTI Identifier:
20960111
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 14; Journal Issue: 1; Other Information: DOI: 10.1063/1.2434794; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ANALYTICAL SOLUTION; BOUNDARY LAYERS; CURRENTS; NONLINEAR PROBLEMS; NUMERICAL ANALYSIS; PLASMA; PLASMA INSTABILITY; PLASMA SIMULATION; THREE-DIMENSIONAL CALCULATIONS; WIRES

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., Mehlhorn, T. A., and Sandia National Laboratories, Albuquerque, New Mexico 87185. 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.
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., & Sandia National Laboratories, Albuquerque, New Mexico 87185. Linear and nonlinear evolution of azimuthal clumping instabilities in a Z-pinch wire array. United States. doi:10.1063/1.2434794.
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., and Sandia National Laboratories, Albuquerque, New Mexico 87185. Mon . "Linear and nonlinear evolution of azimuthal clumping instabilities in a Z-pinch wire array". United States. doi:10.1063/1.2434794.
@article{osti_20960111,
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. and Sandia National Laboratories, Albuquerque, New Mexico 87185},
abstractNote = {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.},
doi = {10.1063/1.2434794},
journal = {Physics of Plasmas},
number = 1,
volume = 14,
place = {United States},
year = {Mon Jan 15 00:00:00 EST 2007},
month = {Mon Jan 15 00:00:00 EST 2007}
}