A review of the dense Z-pinch

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Plasma Phys. Control. Fusion 53 (2011) 093001 Topical Review Figure 52. A radial streak picture of a typical wire array on MAGPIE. Reprinted with permission from [65]. Copyright 2001, American Institute of Physics. Figure 53. Gated soft x-ray images of the precursor column in carbon, aluminium and tungsten taken on MAGPIE. Reprinted with permission from [65]. Copyright 2001, American Institute of Physics. the precursor streams impinging on it. Because of radiative cooling of the higher Z plasma there is a radial contraction of the column in W; the diameters of the columns in MAGPIE are 3 mm for C, 1.25 for Al and 0.2 mm for W. Benjamin et al [350] and Aivazov et al [319] earlier had shown the formation of a precursor column. In a hybrid r −θ Monte Carlo treatment of the Fokker–Planck equation Sherlock et al [351] show that for tungsten the precursor flow is relatively collisionless, while for aluminium it becomes collisional almost immediately a significant amount of plasma arrives on axis. The precursor column forms after a critical density occurs on axis through convergence, allowing a nonlinear compression by collisional interaction with the incoming streams. The W ions are more collisionless than Al ions because the W ions have a higher kinetic energy (because of their higher atomic mass), causing an increase in the mean-free path not compensated by the higher Z value. Figure 54 shows the evolution of ion number density profile with time and also the ion–ion mean-free path and ion temperature. In contrast as shown by experimental end-on laser probing by Lebedev et al [352] in figure 55, the Al is more collisional and shock interactions between individual streams can be seen. The low magnetic Reynolds number in the ablation zone was first shown by Haines [230] in a 3D analytic model of the ablation process in the presence of localized m = 0 necks in which Joule heating was concentrated. This led to flux limited heat flow to the cores, this providing the energy for ionization and ablation. (It should be noted that while radiation transport is dominant in the outer regions, the final heat flow to the cold cores is thermal transport.) 79
Plasma Phys. Control. Fusion 53 (2011) 093001 Topical Review Figure 54. The precursor W ion density radial profiles at successive times, showing column formation at 200 ns, (b) the ion–ion mean-free path to be compared with the typical 1–4 mm scale length and (c) the ion temperature showing a drop on axis is at late times. Reprinted with permission from [351]. Copyright 2004, American Institute of Physics. This plasma flows axially to the lobe regions where the global J × B force accelerates the jetting plasma to the axis by rocket action. It is the cooling of the Joule heated plasma by the energy flow to the cores which leads to a low magnetic Reynolds number R m both here and in [338]. In contrast Ratakhin and Baksht [353] propose a higher current in the precursor. Currently miniature magnetic probe measurements are being undertaken at Cornell University and Imperial College. Estimates of the maximum current that could flow yet yield less than 1 e-folding time for any m = 0orm = 1 MHD instability have been carried out by Bott 80
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A review of the dense Z-pinch

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