A review of the dense Z-pinch

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Plasma Phys. Control. Fusion 53 (2011) 093001 Topical Review Figure 60. A sequence of side-on soft x-ray images on MAGPIE for an array of 16 wires at 155, 164, 238 and 247 ns. Reprinted figure with permission from [314, figure 4]. Copyright 1998 by the American Physical Society. Novel experiments have been carried out using coiled or helical Al wires in an array by Hall et al [295]. The complex 3D Lorentz forces were modelled by MHD simulations. It was found that outside the diameter of each helix the flow of ablated plasma is now modulated at the wavelength of the coils rather than at the fundamental wavelength. Furthermore with only eight helical wires the resulting x-ray power at stagnation was surprisingly increased to that of a 32 wire implosion on MAGPIE. However more recently Hall et al [374] have shown that the fundamental mode does occur initially close to the wire cores. Further details of an experiment with etched wires can be found in [375]. 5.5. Main implosion The ablation of the wire cores is axially non-uniform due to the occurrence of the instability, discussed in the previous section and an early implosion adjacent to the cathode. At a certain stage, typically at a time of 80% of the total time to implosion, gaps appear in the necks of the instability on each wire, accompanied by correlated bright spots due to the development of the global MRT instability. A sequence of soft x-ray images is shown in figure 60 from [348]. With no wire cores in the gaps the plasma heats up; the magnetic Reynolds’ number can be inferred to exceed one, and the J × B global pinching force causes the main implosion. The implosion’s trajectory is shown in figure 40, and, as discussed in section 5.1, figure 41 illustrates the imploding current shell which acts to a good approximation as a snowplough, sweeping up the precursor plasma still in its path. This considerably reduces the growth of RT because the piston is forced to move at almost constant velocity. Lebedev et al [65, 376] estimated the radial mass distribution ρ(r,t) at a position r at a time t, taking into account the time delay required for the precursor material to reach the position r to be ρ(r,t) = µ 0 8π 2 R 0 rV 2 a [ I ( t − R 0 − r V a )] 2 , (5.7) where I(t − ((R 0 − r)/V a )) is the current in the array at the earlier time t − (R 0 − r)/V A . With r = R p , the radius of the precursor column, the total mass in the precursor column can be found by integrating equation (5.1) to the time t − (R 0 − R p )/V a . Using a snowplough model of the implosion as in section 4.1 with ρ(r,t)given by equation (5.7) and by varying the initial mass in the piston a fit can be made to the trajectory of the final implosion as shown in figure 40. Similar detailed fitting of Z data from Sandia can be found in Cuneo et al [323]. A small correction could be made for the motion of the gas being swept up. 87
Plasma Phys. Control. Fusion 53 (2011) 093001 Topical Review Figure 61. XUV images of the transition from the ablation phase to the implosion phase and stagnation in a 8 × 10 µm Cu wire array on MAGPIE [363, figure 53(a) only]. During this final implosion, the RT instability will continue to develop albeit at a greatly reduced rate. The r–z simulations, if they include precursor plasma ahead of the piston [377] are relevant here. Furthermore shock heating and reflection together with compression of the precursor column are now important additions. The skin depth of the current and magnetic field will increase with time due to both diffusion and cylindrical convergence [110]. The final pinch radius will depend on these two effects, the RT wavelength having now grown to typically 2 mm, i.e. approximately the effective thickness of the shell as discussed in [280] and section 4.7. Figure 61 shows three consecutive XUV images of an implosion in a 8 × 10 µm Cu wire array, the first at 185 ns is at the end of the ablation phase, showing the characteristic ∼0.5 mm wavelength of the modulation, with the emission concentrated near the wire cores. The precursor column on the axis is clearly seen, having formed by 130 ns, and has compressed 88
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A review of the dense Z-pinch

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