A review of the dense Z-pinch

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Plasma Phys. Control. Fusion 53 (2011) 093001 Topical Review the aluminium or tungsten. The prepulse current supply can rise to 10 kA. By varying the time of the main LTD 5 MA current an optimum value of ∼7 µs delay was found. Amazingly the cathode bubble disappeared, and an almost 1D snowplough-like and reproducible implosion with no zipper occurred. The x-ray pulse is reduced to 20 ns (a quarter of its previous value) and the peak power was increased by a factor of six to 1.5 TW cm −1 , with 25% conversion efficiency. Single arrays performed as well as nested arrays, thus simplifying future loads. Finally the design of petawatt-class pulsed-power accelerators has been considered by Welch et al [472] and Stygar et al [473]. In [473] a comparison between Marx/pulse-forming line and LTD is made, favouring the latter. Both systems require a magnetically insulated transfer line (MITL), and Stygar et al [474] have studied in a relativistic model the critical issue of electron current shorting here. By varying the charging voltage of the module cavities and the timing, Stygar et al [475] have shown how the output current pulse of a LTD can be shaped. A LTD is compact and can be rep-rated. These features are discussed by Mazarakis et al [476]. Already small LTD experiments are being undertaken in universities: Bott et al [477] have made ablation studies of low number wire arrays at currents of 200 kA employing laser imaging techniques to measure the wavelength of the axial density variations and ablation velocities. A larger LTD-driven Z-pinch is being commissioned at the University of Michigan [478], while a load current multiplier is being tested at the University of Nevada [479]. 7. Other experimental configurations of the Z-pinch As earlier discussed and illustrated in figure 3, there are many configurations of Z-pinches. The experimental results from these will be reviewed, and interpreted using the theory developed in earlier sections. 7.1. Compressional Z-pinch Most of the earliest Z-pinch experiments were compressional Z-pinches in which there is initially a uniform fill of gas inside an insulating cylinder, at the ends of which are the two electrodes. In section 1.2 and [29–36] we reported some of these early experiments. They are characterized by the formation through the skin effect of a current sheet adjacent to the insulating wall, followed by an implosion. Whilst experiments were often interpreted using the snowplough model, section 4.1 (which requires radiated energy loss for energy conservation), it was soon found experimentally that preceding the magnetic piston was a shock wave [257, 258] which caused dissociation and ionization [260] as discussed in section 4.2. A direct experimental verification of the presence of the shock was published by Folkierski and Latham [300]. Earlier, radiating luminous fronts were detected by Heflinger and Leonard [480] using a streak camera, and attributed to a shock. At this stage there is no sign of an instability. Only after the first pinch and a subsequent bounce with inward acceleration caused by the J ×B force is the magneto- MRT instability observed and growth rates measured [39]. These instabilities in the form of m = 0 constrictions are found to occur first in the vicinity of the electrodes, and lead to axially moving luminous fronts which could be shocks [481]. These could be similar to the end effects found more recently in wire-array pinch experiments (see section 5.10). A theory of ionizing strong shocks was developed by Gross [482] and compared with experiments. Further experiments on radially converging cylindrical shocks in various gases by Kogelschatz et al [483] and Kleist et al [484] confirm several aspects of Potter’s slug model [261] (see section 4.3), namely very little current travels with the shock wave, and the gas pressure between the shock and piston is approximately uniform. However at higher filling pressures significant current has been found to flow even ahead of the shock [483]. 107
Plasma Phys. Control. Fusion 53 (2011) 093001 Topical Review The development of high voltage pulsed power technology [6] led to compressional Z-pinches with current rising at 10 13 As −1 or higher. Early experiments by Choi et al [485] using 100 kA from a 600 kV storage line produced a stationary pinch in 100 ns at about 0.3 of the pinch radius, as predicted by the slug model. There was no bounce or oscillation for times of interest. Later, end-on interferometry by Baldock et al [486] demonstrated a stable, cylindrical plasma column while side-on framing images were obtained by Bayley et al [131]. Recent work by Davies et al [14] shows that the enhanced stability is due to large ion Larmor radius effects, but there still is a slowly growing m = 0 instability as shown in figure 26. A simple model of how to attain LLR conditions in a compressional pinch is presented in [183]. However, if the aim of the experiment is to form a dense, high temperature pinch for fusion studies, a smaller final radius is needed. This could be obtained using a hollow, and hence dynamic, gas pinch which we consider next. 7.2. Gas-puff Z-pinch The hollow gas puff is well suited for pulsed power as it removes the need for an insulating wall and its concomitant plasma–wall and radiation driven interactions. It also acts as an accelerating shell, rather than a snowplough, allowing the ions to be accelerated to higher energy before stagnation closer to the axis. The gas-puff is formed by releasing gas stored in a subsidiary chamber at high pressure, using a fast acting valve. The gas flows through a nozzle, and the resulting supersonic jet should have very little transverse motion. It is possible to use a ‘solid’ fill or a hollow fill, and, currently up to three separate, concentric jets have been employed [487–489], thus allowing great control of the initial neutral gas density profile and composition and so minimizing MRT growth (see section 4.7). The fast-rising current from a pulsed power generator is applied when the gas has reached the second electrode, which is usually in the form of crossed wires to enable the gas flow to continue without a reflected shock. The three shells of gas can be considered as pusher (outermost), stabilizer (middle) and radiator [489]. In this way MRT instability can be mitigated and optimal radiation power obtained. One of the earliest experimental studies was a PhD Thesis by Shiloh at Irvine in 1978 [490] who studied both solid and hollow gas jets in deuterium and in high Z gases (argon and krypton) as a radiative source. Highest temperatures were obtained with a hollow jet, and he found that its implosion had similar phenomena to the collapse phase of a compressional pinch or plasma focus namely sausage instabilities, energetic electron and ion beams, and non-thermal neutrons. The instabilities were more slowly growing than given by ideal MHD. The current used here was generally a maximum of 300 kA from 5.4 kJ of a 30 kV capacitor bank. Deuterium gas experiments were carried out on the Saturn generator at Sandia by Spielman et al [491] with currents up to 10 MA. The gas load was produced by a supersonic nozzle (Mach 6) tilted at 5 ◦ to eliminate the zippering effect. Up to 3 × 10 12 DD neutrons were measured in a then unexplained extra apparent resistive heating of the pinched plasma. Very recent gas-puff experiments carried out on Z at Sandia by Coverdale et al [492, 493] have taken a deuterium gas-puff pinch to 17.71 MA current and measured a neutron yield of 3.9 × 10 13 . In contrast to earlier Z-pinch and plasma focus experiments these neutrons are probably not the result of ion beam formation followed by beam–plasma nuclear reactions, but mainly thermonuclear neutrons. This is because they appeared to be isotropic as far as limited measurements could conclude. A detailed discussion of the possibility that ion beams could be generated is to be found in Velikovich et al [494] and they conclude that the neutron yield in [492] is mainly thermonuclear and consistent with analytic theory and oneand two-dimensional simulations. They point out that this yield is several orders of magnitude 108
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