On the validation of a 3D inflow model for simulating wire array z-pinches, z-pinch energetics, and scaling of radiated power with current

Summary form only given. Development of a predictive computational model for wire array z-pinches has been inhibited by the 3D nature of the dynamics. We have developed a 3D computational model for simulating cylindrical wire array z-pinches. In lieu of trying to simulate individual wires in the array from the beginning of the initiation phase, which is computationally impractical, we have incorporated a steady state model of wire ablation physics into our 3D, radiation MHD code ALEGRA. Results are presented from a validation study using radiation pulses, currents, and density profiles from a variety of experiments with single wire arrays on the Z accelerator. The wire array is modeled using full length, periodic wedges with angles of 1 and 60 degrees, and 1 degree azimuthal cells. Radiation power pulses produced by arrays with different masses are matched by tuning the ablation rate. Results indicate that the mass ablation rate scales with wire diameter to the -0.49 power, slower than the -0.66 power deduced from experiments. While both wedge models produce power pulses in reasonable agreement with measurements, only the 60 degree wedge with uncorrelated perturbations in azimuth produces both the measured density profile and radiated power. The resulting web-like, azimuthal structure that develops in the z-pinch plasma has a significant influence on the current distribution, density profile and power pulse. Simulations show that shock heating and pdV work account for most of the energy radiated by the z-pinch at stagnation, through peak power. Results indicate that the sub quadratic scaling of peak power (P) with peak current (I) observed in experiments on Z
⁴
(P~I
^{1.24plusmn0.18}
) is correlated with significant precursor mass stagnating on axis before the main pinch. For 2.5 and 6.0 mg arrays, the simulated power scales as P~I
^1.35
with a stagnating precursor plasma, and P~I
^1.8
when stagnation of the precursor is precluded by decreasing the implosion time, which is consistent with P~I
²
based on energy conservation.