A review of the dense Z-pinch

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IOP PUBLISHING Plasma Phys. Control. Fusion 53 (2011) 093001 (168pp) PLASMA PHYSICS AND CONTROLLED FUSION doi:10.1088/0741-3335/53/9/093001 TOPICAL REVIEW A review of the dense Z-pinch M G Haines Blackett Laboratory, Imperial College, London SW7 2BW, UK Received 15 October 2009, in final form 31 January 2011 Published 2 June 2011 Online at stacks.iop.org/PPCF/53/093001 Abstract The Z-pinch, perhaps the oldest subject in plasma physics, has achieved a remarkable renaissance in recent years, following a few decades of neglect due to its basically unstable MHD character. Using wire arrays, a significant transition at high wire number led to a great improvement in both compression and uniformity of the Z-pinch. Resulting from this the Z-accelerator at Sandia at 20 MA in 100 ns has produced a powerful, short pulse, soft x-ray source >230 TW for 4.5 ns) at a high efficiency of ∼15%. This has applications to inertial confinement fusion. Several hohlraum designs have been tested. The vacuum hohlraum has demonstrated the control of symmetry of irradiation on a capsule, while the dynamic hohlraum at a higher radiation temperature of 230 eV has compressed a capsule from 2 mm to 0.8 mm diameter with a neutron yield >3 × 10 11 thermal DD neutrons, a record for any capsule implosion. World record ion temperatures of >200 keV have recently been measured in a stainless-steel plasma designed for Kα emission at stagnation, due, it was predicted, to ion-viscous heating associated with the dissipation of fast-growing short wavelength nonlinear MHD instabilities. Direct fusion experiments using deuterium gas-puffs have yielded 3.9×10 13 neutrons with only 5% asymmetry, suggesting for the first time a mainly thermal source. The physics of wire-array implosions is a dominant theme. It is concerned with the transformation of wires to liquid-vapour expanding cores; then the generation of a surrounding plasma corona which carries most of the current, with inward flowing low magnetic Reynolds number jets correlated with axial instabilities on each wire; later an almost constant velocity, snowplough-like implosion occurs during which gaps appear in the cores, leading to stagnation on the axis, and the production of the main soft-x-ray pulse. These studies have been pursued also with smaller facilities in other laboratories around the world. At Imperial College, conical and radial wire arrays have led to highly collimated tungsten plasma jets with a Mach number of >20, allowing laboratory astrophysics experiments to be undertaken. These highlights will be underpinned in this review with the basic physics of Z-pinches including stability, kinetic effects, and finally its applications. (Some figures in this article are in colour only in the electronic version) 0741-3335/11/093001+168$33.00 © 2011 IOP Publishing Ltd Printed in the UK & the USA 1
Plasma Phys. Control. Fusion 53 (2011) 093001 Topical Review Contents 1. Introduction 3 1.1. History 5 1.2. Various Z-pinch configurations 8 1.3. Outline of the review 10 2. Physics of the equilibrium Z-pinch 11 2.1. Bennett relation 11 2.2. Particle orbits 12 2.3. Axial heat loss to electrodes 16 2.4. Fusion conditions if magnetically confined and stable 20 2.5. Self-similar solutions and radial heat loss 22 2.6. Nernst and Ettingshausen effects 26 2.7. Runaway electrons 27 2.8. The Pease–Braginskii current and radiative collapse 28 3. Stability of an equilibrium Z-pinch 31 3.1. Regimes for stability models 31 3.2. Ideal MHD stability 34 3.3. Resistive MHD stability 38 3.4. Visco-resistive models of stability 39 3.5. The stress tensor; axial differential flow and strong curvature 40 3.6. Anisotropic pressure effects 42 3.7. Hall fluid model of stability 43 3.8. Large ion Larmor radius (LLR) effects 43 3.9. Effect of sheared axial flow 44 3.10. Addition of axial magnetic field 46 3.11. Nonlinear growth of MHD modes 47 3.12. Electrothermal instability and the heat-flow instability 50 3.13. Micro-instabilities and anomalous resistivity 52 3.14. Disruptions; ion beams and neutrons 54 4. Dynamic Z-pinch 57 4.1. The snowplough model 57 4.2. The shock model 58 4.3. The slug model 58 4.4. Accelerating hollow shell 60 4.5. Early work on numerical simulations of Z-pinches 62 4.6. The skin effect and inverse skin effect 63 4.7. The Rayleigh–Taylor instability 63 4.8. Nonlinear Rayleigh–Taylor instabilities 66 5. The wire-array Z-pinch 67 5.1. Overview 67 5.2. Melting and vaporizing wire cores; plasma formation 72 5.3. Ablation phase and the precursor plasma 76 5.4. Axial structures on wires 84 5.5. Main implosion 87 5.6. Nested arrays 89 5.7. Stagnation on the axis 90 5.8. m = 0 instabilities and ion-viscous heating 92 5.9. Atomic physics 94 2
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A review of the dense Z-pinch

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