Perfectly conducting incompressible fluid model of a wire array implosion

Abstract

An incompressible perfectly conducting magnetohydrodynamic model is applied to describe a multiwire array implosion on the (r,θ) plane using the theory of analytic functions. The plasma columns emerging from the electrical explosion of 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. Geometry of both the “global” and “private” magnetic fields and self-consistent distributions of the electric currents on the conducting surfaces are determined for any wire array configuration including nested wire arrays, wires close to the return current can, etc. The coupled equations of motion and magnetostatics for an essentially two-dimensional problem are reduced to one-dimensional parametric governing equations, written for the boundary of the fluid contours. The implosion dynamics is shown to be driven by a competition between the implosion pressure, making the array converge to the axis as a set of individual plasma columns, and the tidal pressure that makes the wires merge, forming an annular conducting shell. Their relative roles are determined by the gap-to-diameter ratio πRc(t)/NRw(t). If this ratio is large at early time, then the array implodes as a set of individual plasma columns. Otherwise, when the ratio is about π or less, the tidal forces prevail, and the plasma columns tend to form a shell-like configuration before they start converging to the axis of the array. The model does not allow the precursor plasma streams to be ejected from the wires to the axis, indicating that this process is governed by the finite plasma conductivity and could only be described with a proper conductivity model.