Effect of discrete wires on the implosion dynamics of wire array Z pinches

Abstract

A phenomenological model of wire array Z-pinch implosions, based on the analysis of experimental data obtained on the mega-ampere generator for plasma implosion experiments (MAGPIE) generator [I. H. Mitchell et al., Rev. Sci. Instrum. 67, 1533 (1996)], is described. The data show that during the first ∼80% of the implosion the wire cores remain stationary in their initial positions, while the coronal plasma is continuously jetting from the wire cores to the array axis. This phase ends by the formation of gaps in the wire cores, which occurs due to the nonuniformity of the ablation rate along the wires. The final phase of the implosion starting at this time occurs as a rapid snowplow-like implosion of the radially distributed precursor plasma, previously injected in the interior of the array. The density distribution of the precursor plasma, being peaked on the array axis, could be a key factor providing stability of the wire array implosions operating in the regime of discrete wires. The modified “initial” conditions for simulations of wire array Z-pinch implosions with one-dimension (1D) and two-dimensions (2D) in the r–z plane, radiation-magnetohydrodynamic (MHD) codes, and a possible scaling to a larger drive current are discussed.

Wire number dependence of the implosion dynamics, stagnation, and radiation output of tungsten wire arrays at Z driver

“…Nonethe-less, it is reassuring that the estimated velocities of $2 6 0.2 Â 10 7 cm=s (Fig.14(b)) are in reasonable agreement to those evaluated with optical techniques in Ref. 31. During the present investigation, optical diagnostics with the Z driver were not yet available.…”

“…We can only speculate the following plausible explanation which is also on line with Lebedev et al thinking. 31 When the wire number becomes larger than the optimum number ($375 6 25), the wire cores start merging very early during the prepulse stage of the load current pulse, the precursor plasma inside the array becomes negligible or non-existent, and the wire array pinches as a thin shell which is prone to instabilities. Applying this explanation to W and Al experimental results, we estimate wire core sizes and core expansion velocities close to those independently measured in Imperial College and Cornell University, 28,29,33,34 This finding further reinforces the plausibility of our speculations.…”

“…These estimates are in reasonably good agreement with the independently measured core sizes for both materials. 28,[31][32][33][34] The above discussion suggests that the optimum IWG op is the gap where the wire coronas merge very early during the prepulse stage of the load current pulse, the precursor plasma inside the array becomes negligible or non-existent, and the wire array pinches as a thin ($50l for W and $220l for Al) shell. Analytical calculations 35 and 2D model simulations 26 support this assumption and suggest that the plasma distribution inside the array, prior to the onset of the wire motion, enhances the pinch stability.…”

“…As the wire number increases, the ablated mass distribution and plasmas inside the array becomes more azimuthally uniform and lead to a more stable pinches. 30,31 However, when the IWG becomes smaller than the optimum, the global magnetic field dominates the private magnetic field and the flow of ablated mass and plasma inside the array quenches very early in the driving pulse current. This happens when the IWG is approximately equal to p times the wire core size.…”

Primary experimental results of wire-array Z-pinches on PTS

“…Both the implosion time and the trajectory have been normalized. Acceleration begins at ~0.67t imp , which is 0.44-0.74 on Z [8] and 0.78 on MAGPIE [9]. The array experienced a long ablation time during which the wires remain stationary at the initial positions.…”