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A one-dimensional radial magnetohydrodynamic model of the plasma ablated from a multi-MA wire-array Z pinch is developed. The model is used to compute the mass weighted-density width δ of the plasma at the end of the ablation phase. The wire-array cores are represented as a prescribed source of plasma injection. The plasma, beyond a thin boundary layer, is approximated as a perfect conductor experiencing only magnetic forces and negligible pressure gradients. Assuming that the current driving the Z-pinch implosion increases linearly with time t during the ablation phase, and that the mass-ablation rate varies as tν, it is shown that the density width δ is a function of the dimensionless parameter λ=ua(ta)ta/r0, where ua is the ablation velocity, ta is the total ablation time, and r0 is the initial wire-array radius. The velocity ua is defined such that its product with the mass-ablation rate equals the magnetic force at r0, which is assumed to be the mass injection point. A solution is obtained for the plasma flow in semianalytical form when the current is an exponential function of time, and ua is constant. The ablated plasma density width δ obtained under these two sets of conditions is compared. In addition, assuming that the plasma sheath at stagnation is proportional to the width δ, scaling relationships for the peak x-ray power radiated when the pinch stagnates on axis are suggested. [ABSTRACT FROM AUTHOR]

We report the results of a series of current scaling experiments with the Z accelerator for the compact, single, 20-mm diameter, 10-mm long, tungsten-wire arrays employed for the double-ended hohlraum ICF concept [M. E. Cuneo, Plasma Phys. Controlled Fusion 48, R1 (2006)]. We measured the z -pinch peak radiated x-ray power and total radiated x-ray energy as a function of the peak current, at a constant implosion time tau_{imp}=80ns . Previous x-ray emission current scaling for these compact arrays was obtained at tau_{imp}=95ns in the work of Stygar [Phys. Rev. E 69, 046403 (2004)]. In the present study we utilized lighter single-tungsten-wire arrays. For all the measurements, the load hardware dimensions, materials, and array wire number (N=300) were kept constant and were the same as the previous study. We also kept the normalized load current spatial and temporal profiles the same for all experiments reported in this work. Two different currents, 11.2+/-0.2MA and 17.0+/-0.3MA , were driven through the wire arrays. The average peak x-ray power for these compact wire arrays increased by 26%+/-7%to158+/-26TW at 17+/-0.3MA from the 125+/-24TW obtained at a peak current of 18.8+/-0.5MA with tau_{imp}=95ns . The higher peak power of the faster implosions may possibly be attributed to a higher implosion velocity, which in turn improves the implosion stability, and/or to shorter wire ablation times, which may lead to a decrease in trailing mass and trailing current. Our results show that the scaling of the radiated x-ray peak power and total radiated x-ray energy scaling with peak drive current to be closer to quadratic than the results of Stygar We find that the x-ray peak radiated power is P_{r} proportional, variantI;{1.57+/-0.20} and the total x-ray radiated energy E_{r} proportional, variantI;{1.9+/-0.24} . We also find that the current scaling exponent of the power is sensitive to the inclusion of a single data point with a peak power at least 1.9sigma below the average. If we eliminate this particular shot from our analysis (shot 1608), the power and energy scaling becomes closer to quadratic. Namely, we find that the dependence on the peak load current of the peak x-ray radiated power and the total x-ray radiated energy become P_{r} proportional, variantI;{1.71+/-0.10} and E_{r} proportional, variantI;{2.01+/-0.21} , respectively. In this case, the power scaling exponent is different by more than 2sigma from the previously published results of Stygar Larger data sets are likely required to resolve this uncertainty and eliminate the sensitivity to statistical fluctuations in any future studies of this type. Nevertheless, with or without the inclusion of shot 1608, our results with tau_{imp}=80ns fall short of an I2 scaling of the peak x-ray radiated power by at least 2sigma . In either case, the results of our study are consistent with the heuristic wire ablation model proposed by Stygar (P_{r} proportional, variantI;{1.5}) . We also derive an empirical predictive relation that connects the power scaling exponent with certain array parameters.