A review of the dense Z-pinch

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Plasma Phys. Control. Fusion 53 (2011) 093001 Topical Review ions leaving the core with a large component of velocity in the −z-direction (i.e. towards the anode) will almost complete a Larmor orbit before returning. Thus the cores will receive momentum in the +z-direction for one Larmor period, while, by conservation, the precursor plasma will acquire momentum in the −z-direction, i.e. towards the anode. Collisions in the precursor plasma might reduce this effect. Furthermore 3D effects will especially cause the ions with initial components of velocity in the −z-direction together with a θ-component to miss the core and join preferentially the precursor flow towards the axis. This is essentially a finite ion Larmor radius (FLR) effect, and will lead to a component of the inward precursor plasma flow towards the anode, regardless of the position of the power feed. It is an adaptation of a theory of the origin of rotation of theta pinches [93] in which ions leaving the vessel-wall exchange angular momentum with the wall. Experimental data at the present time show an axial component of precursor flow towards the anode and away from the power-feed, which is at the cathode. It will be interesting when experiments with the power-feed at the anode end are undertaken: Then any shorting process will be electron emission, not from the wires, but from the return conductor. The J × B force will have a component driving flow away from the power-feed, i.e. towards the cathode. The FLR mechanism will continue to lead to a component of flow towards the anode. 5.11. Trailing mass and current re-strike The implosion phase commences when there are gaps in the wire cores. As discussed above, it could be theorized that the plasma in the gaps, being no longer cooled by the heat flow to the cores necessary to cause ablation, heats up sufficiently for the magnetic Reynolds’ number to exceed unity. Thus, this plasma together with the current and associated magnetic field implodes under the action of the global J × B force. This is illustrated in figure 61 taken from Lebedev et al [363] for an 8×10 µm Cu wire array. The characteristic wavelength of ∼0.5 mm of the modulation is seen in the x-ray image at 185 ns. The precursor plasma arrived on the axis earlier at 130 ns. At 215 ns the implosion has already started, the current sheath being formed by a large number of magnetic bubbles, moving towards the axis, snowploughing up previously launched precursor plasma, and now has ∼2 mm wavelength. At 245 ns the imploding plasma has stagnated leaving behind characteristic trailing mass which has a global m = 0 structure. Later, these fingers of trailing mass also pinch to the axis, and this is the cause of later x-ray emission. The peak x-ray emission in this 32 × 10 µm Al wire array occurs at 265 ns, and so the trailing mass does not contribute to the main x-ray pulse, and indeed could deprive the stagnated column of some of the current. Figure 69 shows grated x-ray images 2.3 ns before and 3.2 ns after peak x-ray emission on Z, illustrating the later implosion of the trailing mass and the relative uniformity of the pinch column. From analysis of the trajectories it would appear that about 30% of the original mass of the wires is in the trailing mass [65] though fringe shifts from laser interferograms would merely estimate that this trailing mass is greater than 7% [363]. After stagnation there is evidence of a m = 1 component to the dominantly m = 0 stagnated pinch. Bland et al [413] have compared the evolution of filaments and precursor bubbles for low (8) and high (32) wire number aluminium wire-array implosions, showing correlation and merging of bubbles in the latter case. For arrays of ∼300 wires Sinars et al [414] have shown a similar evolution of trailing mass on Z using x-ray radiography. Recently, Yu et al [415] have simulated the current trajectories in 3D in the trailing mass. They find that the growth of bubbles (in the sense of bubble and spike of RT) is reduced compared with 2D simulations. The trailing mass evolves towards a force-free structure, implying the presence of significant axial magnetic fields. The azimuthal perturbations and 101
Plasma Phys. Control. Fusion 53 (2011) 093001 Topical Review Figure 69. False colour composite 1 ns. Gated images from Al shot 1519 on Z-accelerator 2.3 ns before and 3.2 ns after peak x-ray power [739, figure 3]. Copyright © 2000 IEEE. Figure 70. Three designs for hohlraums for Z-pinch driven inertial confinement fusion at Sandia: (a) the dynamic hohlraum, (b) the static-walled hohlraum and (c) the vacuum hohlraum. Courtesy of Sandia National Laboratory. correlations introduced initially will, however, strongly affect the result, and whether this occurs in experiments conducted with a high degree of azimuthal symmetry is an open question. 5.12. Planar arrays Recently some small scale experiments have been undertaken with planar arrays [416] which showed that current stays on edge wires and cascades inwards from wire to wire, giving an implosion at the centre of the array with significant x-ray yield [417]. Ivanov et al [418, 419] have extended the data and given a more thorough review of planar arrays. Their application to larger-scale experiments was undertaken by Jones et al [420] at currents of 3–6 MA. There is a significant amount of trailing mass here, and there appears to be saturation of peak x-ray power. Double planar arrays were explored by Kantsyrev et al [421, 422], for Mo and W at ∼1MA and gave increased x-ray yield. Star arrays have also given interesting results in experiments 102
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A review of the dense Z-pinch

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