A heuristic model of the wire array Z-pinch

Summary form only given, as follows. A heuristic model of a wire array Z-pinch has been developed in which the behaviour is divided into four distinct phases. In phase one, the individual wires behave independently, each having an expanding plasma and subject to m=0 MHD instabilities. The velocity of expansion and the rate of rise of current are input parameters for the model, together with the instability growth and are based on single wire experimental data. Phase two is the merger of the expanding plasmas to form a continuous conducting plasma shell. Throughout phases one and two, the plasmas are accelerated towards the axis, but the time of merger compared to the pinch time is a very non-linear function of the number of wires (n) or the wire separation. At phase two, the shell thickness is determined and the assumed uncorrelated instabilities in the individual wires lead to an initial seed perturbation in line density N of /spl delta/N/N=n/sup -1/2/ /spl delta/~N/sub i//N/sub i/ where /spl delta/~6N/sub i//Ni is the mean relative perturbation in a single wire. Thus for larger n, the initial perturbation is lower. Phase three is the inward pinch collapse to the axis. This is subject to Rayleigh-Taylor growth from the seed level determined in phase two. Linear growth develops to non-linear algebraic growth when the amplitude of the mode exceeds either a fraction of the wavelength of the mode or the shell thickness. At any later time, for example, at the pinch time, it is possible to calculate the largest amplitude mode and compare this wavelength to the experiment and to estimate from the initial shell thickness and the Rayleigh-Taylor amplitude what the pinch radius is. At phase four, the plasma is pinches and initially most of the energy is in kinetic energy of the ions, viscous heating rapidly converts this to an ion temperature, but equipartition to the electrons and further ionisation to high Z occurs on a time-scale comparable to the pinch bounce time. The latter can thus determine the pulse width of the X-ray pulse. Thus with very few input parameters an analytic, physical model of the behaviour of a wire array implosion can be constructed. Good agreement with experimental results has been found.