A review of the dense Z-pinch

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Plasma Phys. Control. Fusion 53 (2011) 093001 Topical Review Figure 62. Schematic of nested wire arrays with (a) low inductance and (b) high inductance connection of the inner array. Reprinted figure with permission from [325, figure 1]. Copyright 2000 by the American Physical Society. by radiative cooling coupled with the kinetic pressure ρVa 2 of the impinging precursor streams. At 215 ns, figure 61 shows the structure of the ‘magnetic piston’ half-way through the implosion phase, and consists of a large number of axisymmetric m = 0 magnetic bubbles moving towards the axis. To the extent that it is a snowplough mechanism which requires energy loss, inelastic collisions (excitation and ionization) will lead to XUV radiation, and this is stronger in front of the larger bubbles that move faster. By now the wavelength of the modulations has grown to ∼2 mm. Even with the small number of wires in this particular array the onset of global correlation is very evident, and represents the same phenomenon as observed in high wire number arrays. The RT structure is similar to that simulated by Peterson et al [233]. Note that in the laboratory frame as opposed to the accelerating frame represented in theories by gravity g, the bubbles are accelerating inward while the spike tips remain at the original wire-array radius. These spikes form the trailing mass, clearly obvious at 245 ns in figure 61, which will be considered in section 5.11. During the ablation and implosion phases, there appears to be no evidence of kink and azimuthal displacement instabilities as proposed by Felber and Rostoker [378], Marder et al [379] and Hammer and Ryutov [380] which would probably be only slowly growing anyway. Ivanov et al [381] imaged bubble formation in 8- and 4-wire cylindrical arrays, and employed Faraday rotation techniques to measure the magnetic field strength. However such fields are unlikely to be characteristic of high wire-number implosions. 5.6. Nested arrays The use of a nested, inner array has led to a significant improvement in the performance of the wire-array Z-pinch, and was used in high performance shots [1, 2] and in recent detailed studies [323]. It was proposed by Davis et al [60] so that, as the outer array plasma passed through the inner array, the current would switch to the inner array, because of the high conductivity of the inner wires and the inductive coupling between the two arrays. At this time the driving force behind the RT growth would also transfer to the inner array which would start to ablate and implode with initially no RT amplitude; thus at the final stagnation a much more symmetric plasma should result. Simulations by Chittenden et al [327] show three modes of operation as discussed in section 5.1 while experiments on MAGPIE [325] distinguished two modes, dependent on the fraction of total current induced in the inner array. Experiments were conducted with a 16 mm diameter outer array and an 8 mm diameter inner array each 16×15 µm aluminium. Figure 62 89
Plasma Phys. Control. Fusion 53 (2011) 093001 Topical Review shows (a) the (standard) low inductance scheme while (b) shows a novel high inductance inner array. The former had wires of 2.3 cm length while the inner array in (b) was 8.3 cm. Calculations by Chittenden et al [231] of magnetic diffusion in the r–θ plane indicated that the inner array in (a) carried 20% of the total current, while for case (b) measurements by the B-dot probe showed that the inner current was only ∼8 kA during the first 20 ns while the outer array was highly resistive, and it fell to lower values by the time of the collision of the two arrays. In case (a) at early times comparable wire-core expansion of both inner and outer arrays was measured by laser shadowgrams, while in case (b) very little expansion of the inner array wire cores was seen. The optical streak photographs and the plot of trajectories indicate two very different modes of operation. In figure 63 for the low inductance case shows the inner array accelerating inwards before the arrival of the outer array and both arrive on axis together. In contrast, for the high inductance case, a clear ‘transparent’ mode occurs with the outer array plasma proceeding between the wires of the inner array which then accelerate from rest with 100% transfer of the current. In both cases the streaked images show a precursor plasma on axis at ∼135 ns. Soft x-ray emission at early times is believed to be due to the impact of precursor streams from the outer array, as current alone does not lead to such emission. With more wires and higher current and rate of rise in current, the transparent mode appears to be dominant in nested W wire arrays on Z up to 19 MA [326]. This suggests that very little current flows at early times in the inner array, and after the outer passes through it, there is a rapid current transfer. After which, the inner behaves as a single array with its own precursor streams from each wire, axially non-uniform delayed implosion with trailing mass. This current transfer was first modelled by Terry et al [382], reasoning that it was caused by the higher radius path and lower inductance of the inner array after the outer passed through. Experimental confirmation of current transfer was shown by Bland et al [383] on MAGPIE while Sanford et al [384] demonstrated that the transparent mode applies to nested arrays as used for dynamic hohlraum studies at currents up to 20 MA. The normal mass ratio of the outer to inner is 2, but when reversed it was clear from the timings of the x-ray emission peaks that the transparent mode applied. Numerical simulations were complemented by analytic theory, which showed that the current switching was driven by the larger electric field ∼7×10 7 Vm −1 experienced by the stationary inner array, while the highly conducting moving outer array had a greatly reduced effective electric field, (E z +v r B ϑ ) ≈ 3×10 6 Vm −1 due to the large negative radial velocity v r . The current transfer can occur in a time
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A review of the dense Z-pinch

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