A review of the dense Z-pinch

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Plasma Phys. Control. Fusion 53 (2011) 093001 Topical Review Figure 71. Radiation temperature as a function of time for the Z-pinch baseline design at Sandia. Reprinted with permission from [455]. Copyright 2007, American Institute of Physics. Figure 72. Conceptual design of Z-pinch reactor based on the vacuum hohlraum, ZP3 elliptical IFE chamber [463]. Copyright 2003 by the American Nuclear Society, La Grange Park, Illinois. Various simplified models of hohlraums have been developed. Cuneo et al [459] considered 0D models for four configurations and found consistency with measured x-ray powers and wall temperatures. Stygar et al [460] proposed analytic models coupling x-ray sources to hohlraums and capsules in a more general way, but gave special attention to the Z-pinch source. Lastly, numerical simulations have been used to examine fast ignition [19] and the scaling of hot-spot break-even in both tamped and untamped compressed fuel [461]. The subject is discussed in a review by Cuneo et al [462]. 6.4. Z-pinch hohlraum reactor Figure 72 illustrates the conceptual design of Sandia’s ZP3 fusion reactor [463, 464] based on the vacuum hohlraum. It is to be repetitively operated at about 0.1 Hz. In each cycle about 3 GJ is released mainly as 14 MeV neutrons and x-rays. This energy is planned to be absorbed by thick curtains of flowing flibe molten salt (BeF 2 –LiF), which acts both as a tritium breeder (from the lithium) and as a heat transfer agent. The current from the repetitively pulsed power source is coupled to the Z-pinch load through a recyclable transmission line (RTL). 105
Plasma Phys. Control. Fusion 53 (2011) 093001 Topical Review This alleviates the need for complex liquid–vacuum geometry, as the pulsed power energy is coupled to the Z-pinch by direct contact. It also eases the vacuum requirements in the chamber which will have a 10 Torr pressure background of argon. However the inner gap of the RTL must operate in high vacuum to prevent electric breakdown, and a sliding seal arrangement has been devised to allow the pre-pumped RTLs to be inserted and connected to the pulsed power source, without opening the full chamber to high vacuum between each shot. After that the RTL will be destroyed, and a new RTL inserted. Therefore the RTL can be built either of frozen flibe which will melt in the coolant, or of a material immiscible in the molten salt which could then be separated and recycled. To alleviate shock generation arising from the pulsed energy absorption the flibe is in the form of curtains, with voids between, and the bubbling pool at the bottom of the chamber is two phase. Aspects of the nuclear technology involved are being studied in separate experiments. One of these considers low mass recyclable transmission lines theoretically and experimentally to determine the ability of the electrodes to carry the current required as a function of electrode thickness [465]. It was concluded that a transmission line of only a few tens of kilograms of material could carry the large currents require for fusion. 6.5. Technology of pulsed power; longer pulses The further development of pulsed power to achieve more powerful x-ray sources and ignition of indirect drive ICF requires a greater understanding of the present technological approach and its limitations, together with the development of alternative techniques such as linear transformer drivers (LTDs) pioneered at Tomsk. In brief LTD accelerating cavities contain the pulse-forming capacitors. These are switched at low voltage, inductively adding the pulses and using soft iron-core isolation. Higher currents can be obtained by employing many capacitors in parallel, while higher voltage can be achieved by inductively adding the output voltage of several cavities in series. In addition the scaling of the Z-pinch itself to higher currents and the trade-off of longer current pulses with lower voltages should be explored. A three-dimensional e.m. model of pulsed power has been developed recently by Rose et al [466]. It has been applied to the new ZR-accelerator at Sandia which is designed to give 27 MA. This represents a major computational step compared with the earlier development of the Z-accelerator [467]. Extrapolating to new designs however assumes a knowledge of the scaling laws of the Z-pinch itself. Empirical scaling relations have been developed by Stygar et al [468], but these ignore the fact that the radiated energy can be three or four times the kinetic energy of the implosion, which is discussed in sections 5.8 and 7.2. Indeed the analysis assumes competition between ablation-dominated and RT-dominated pinches, each of which has its own scaling law, and concludes that a decrease in implosion time is preferential. In contrast, experiments were undertaken ten years ago by Deeney et al [386] and Douglas et al [469] to see if x-ray powers could be maintained with a longer current rise-time (∼250 ns), implying a lower voltage and fewer insulator problems. These were surprisingly successful. Characteristics of wire-array implosions on the longer 1 µs time scale are being carried out on the SPHINX machine at CEA, Gramat [470]. This leads to a longer x-ray pulse, dominated by a large plasma bubble at the cathode and the associated zippering along the axis. However there has been a dramatic improvement in the performance of SPHINX by employing a microsecond prepulse [471]. Previously the long x-ray pulse [470] was a result of a cathode bubble (see section 5.10) which collapsed onto the axis first, starting the main x-ray pulse. During the prepulse the wires are heated, but after ∼4 µs at 400 V there occurs plasma breakdown, presumably of vaporized low Z impurities, dropping the voltage to 40 V. The current at this time is 1750 or 8 A per wire and the deposited energy is far below that needed to cause melting of 106
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A review of the dense Z-pinch

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