Effects of various inductances on the dynamic models of the Z-pinch implosion of nested wire arrays

Z-pinch experiments have demonstrated that the soft X-ray power increases 40% with a nested-wire array compared with that with a single-layered wire array. However, the development of the technique of obtaining higher X-ray power using nested wire array configurations has been largely empirical. This has, in part, been due to the absence of adequate theoretical models to describe the mechanism of interaction of the two arrays. As is well known, 2D MHD modeling of nested wire array implosions is difficult, and is very inconvenient to optimize the design of nested-wire arrays. In this paper, the Z-pinch implosion dynamics of nested wire array has been described by its equivalent electric circuit and by solving the corresponding circuit equation. The currents flowing through the outer and inner arrays in the initial stage of implosion depend on the array dimensions, especially on the array inductances. The analysis indicates that the arrays inductance variation can result in four dynamic models of the Z-pinch implosion of nested wire arrays, which is the same as that predicted by previous works. Fast and inexpensive 0D modeling can predict the implosion time and the rate of thermalization of the kinetic energy of the nested-wire array at Qingguang-1 facility, and estimate the implosion model that the inner array wires remain discrete until the outer array material has passed through their gaps. The full current is then transferred rapidly to what was initially the inner, imploding it rapidly onto the outer array material on the axis. Some suggestions are put forward which may be helpful in the nested-wire array design for Z-pinch experiments.