Linear and nonlinear evolution of azimuthal clumping instabilities in a Zpinch 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 pimode, in a discrete wire array. In the pimode, neighboring wires of the array pairup 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 threedimensional feature of the pimode, together with a scaling study of the wire number, may be expediently simulated by using only one single wire in an annular wedge withmore »
 Authors:
 Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, Michigan 481092104 (United States)
 (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; THREEDIMENSIONAL 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 Zpinch 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 Zpinch 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 Zpinch wire array". United States.
doi:10.1063/1.2434794.
@article{osti_20960111,
title = {Linear and nonlinear evolution of azimuthal clumping instabilities in a Zpinch 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 pimode, in a discrete wire array. In the pimode, neighboring wires of the array pairup 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 threedimensional feature of the pimode, 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}
}

This study presents an analytic theory on the linear and nonlinear evolution of the most unstable azimuthal clumping mode, known as the pimode, in a discrete wire array. In the pimode, neighboring wires of the array pairup 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 (upmore »Cited by 1

Azimuthal clumping instabilities in a Zpinch wire array
A simple model is constructed to evaluate the temporal evolution of azimuthal clumping instabilities in a cylindrical array of currentcarrying wires. An analytic scaling law is derived, which shows that randomly seeded perturbations evolve at the rate of the fastest unstable mode, almost from the start. This instability is entirely analogous to the Jeans instability in a selfgravitating disk, where the mutual attraction of gravity is replaced by the mutual attraction among the currentcarrying wires. 
Hybrid simulation of the Zpinch instabilities for profiles generated in the process of wire array implosion in the Saturn pulsed power generator.
Experimental evidence suggests that the energy balance between processes in play during wire array implosions is not well understood. In fact the radiative yields can exceed by several times the implosion kinetic energy. A possible explanation is that the coupling from magnetic energy to kinetic energy as magnetohydrodynamic plasma instabilities develop provides additional energy. It is thus important to model the instabilities produced in the after implosion stage of the wire array in order to determine how the stored magnetic energy can be connected with the radiative yields. To this aim threedimensional hybrid simulations have been performed. They are initializedmore » 
Hybrid simulation of the Zpinch instabilities for profiles generated during wire array implosion in the Saturn pulsed power generator
Experimental evidence suggests that the energy balance between processes in play during wire array implosions is not well understood. In fact the radiative yields can exceed by several times the implosion kinetic energy. A possible explanation is that the coupling from magnetic energy to kinetic energy as magnetohydrodynamic plasma instabilities develop provides additional energy. It is thus important to model the instabilities produced in the after implosion stage of the wire array in order to determine how the stored magnetic energy can be connected with the radiative yields. To this aim threedimensional hybrid simulations have been performed. They are initializedmore »