Historical research guide · 1110 · 2002
Perfectly conducting incompressible fluid model of a wire array implosion
Alexander L. Velikovich · Igor V. Sokolov · Andrey A. Esaulov
In one minute
A wire-array Z-pinch begins as a cage of fine wires around a common axis. A colossal current explodes each wire into plasma, and the magnetic field then drives the whole cage inward. Whether that cage behaves as many separate columns or as one continuous shell decides how the implosion goes, and Velikovich, Sokolov and Esaulov answer it analytically. Treat each plasma column as an incompressible, perfectly conducting fluid, and the two-dimensional problem of columns that move and change shape collapses into one-dimensional equations written for the boundaries of those columns alone. Two pressures then compete. One drives the array toward the axis as a set of individual columns; the other, which the authors call a tidal pressure, pulls neighbours together into an annular conducting shell before anything converges. Which one wins is set by a single number, the gap between wires measured against their diameter. The model also names its own limit: it cannot produce the precursor plasma streams the experiments see.
Connection
Chapter 9 is about plasma that organises itself into structures that hold together and carry current, and this paper gives the arithmetic for when a ring of separate current-carrying columns stops being separate and becomes a single shell. Chapter 12 depends on the same machines, because wire arrays are the drivers behind the largest laboratory X-ray sources built for fusion, and the array’s geometry is the part the designer actually chooses.
From the source
An incompressible, perfectly conducting magnetohydrodynamic model can describe a multiwire array implosion in the plane transverse to the axis, using the theory of analytic functions: the plasma columns left by the electrical explosion of the individual wires move and change the shape of their cross section in the magnetic field produced by the currents flowing on the surfaces of the columns and closing through a cylindrical return-current can.Abstract, opening sentences
The model solves the field geometry for an arbitrary array. The geometry of both the global and the private magnetic fields, and the self-consistent distributions of electric current on the conducting surfaces, are determined for any wire array configuration — including nested wire arrays and wires placed close to the return-current can.Abstract
The problem reduces in dimension. The coupled equations of motion and magnetostatics for what is essentially a two-dimensional problem are reduced to one-dimensional parametric governing equations, written for the boundary of the fluid contours rather than for their interiors.Abstract
The implosion is a competition between two pressures: an implosion pressure that makes the array converge to the axis as a set of individual plasma columns, and a tidal pressure that makes the wires merge and form an annular conducting shell.Abstract
One ratio decides which pressure wins — the gap-to-diameter ratio, pi times the array radius divided by the number of wires times the wire radius, both taken as functions of time. If that ratio is large at early time the array implodes as a set of individual plasma columns; when it falls to about pi or less the tidal forces prevail and the columns tend to form a shell-like configuration before they start converging on the axis.Abstract
The model states its own boundary. It does not allow the precursor plasma streams to be ejected from the wires toward the axis, which the authors read as an indication that this process is governed by the finite plasma conductivity and could only be described with a proper conductivity model.Abstract, closing sentences
The way in
https://doi.org/10.1063/1.1452104How to cite it
Alexander L. Velikovich, Igor V. Sokolov, Andrey A. Esaulov (2002) Perfectly conducting incompressible fluid model of a wire array implosion doi:10.1063/1.1452104