X-ray emission current scaling experiments for compact single-tungsten-wire arrays at 80-nanosecond implosion times

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)=80 ns. Previous x-ray emission current scaling for these compact arrays was obtained at tau(imp)=95 ns 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 +/- 0.2 MA and 17.0 +/- 0.3 MA, were driven through the wire arrays. The average peak x-ray power for these compact wire arrays increased by 26%+/- 7% to 158 +/- 26 TW at 17 +/- 0.3 MA from the 125 +/- 24 TW obtained at a peak current of 18.8 +/- 0.5 MA with tau(imp)=95 ns. 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 to I-1.57 +/- 0.20 and the total x-ray radiated energy E-r proportional to I-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 1.9 sigma 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 to I-1.71 +/- 0.10 and E-r proportional to I-2.01 +/- 0.21, respectively. In this case, the power scaling exponent is different by more than 2 sigma 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)=80 ns fall short of an I-2 scaling of the peak x-ray radiated power by at least 2 sigma. In either case, the results of our study are consistent with the heuristic wire ablation model proposed by Stygar (P-r proportional to I-1.5). We also derive an empirical predictive relation that connects the power scaling exponent with certain array parameters.