Three-dimensional electromagnetic model of the pulsed-power $Z$-pinch accelerator

A three-dimensional, fully electromagnetic model of the principal pulsed-power components of the 26-MA ZR accelerator [D. H. McDaniel et al., in Proceedings of the 5th International Conference on Dense $Z$-Pinches (AIP, New York, 2002), p. 23] has been developed. This large-scale simulation model tracks the evolution of electromagnetic waves through the accelerator’s intermediate-storage capacitors, laser-triggered gas switches, pulse-forming lines, water switches, triplate transmission lines, and water convolute to the vacuum insulator stack. The insulator-stack electrodes are coupled to a transmission-line circuit model of the four-level magnetically insulated vacuum-transmission-line section and double-post-hole convolute. The vacuum-section circuit model is terminated by a one-dimensional self-consistent dynamic model of an imploding $z$-pinch load. The simulation results are compared with electrical measurements made throughout the ZR accelerator, and are in good agreement with the data, especially for times until peak load power. This modeling effort demonstrates that 3D electromagnetic models of large-scale, multiple-module, pulsed-power accelerators are now computationally tractable. This, in turn, presents new opportunities for simulating the operation of existing pulsed-power systems used in a variety of high-energy-density-physics and radiographic applications, as well as even higher-power next-generation accelerators before they are constructed.

Figure 1

Cutaway view of the ZR accelerator at Sandia National Laboratories. Principal components of the accelerator are labeled.

Figure 2

Schematic of two pulse-forming sections of ZR with principal components labeled (dimensions in centimeters). Not shown here are the vacuum MITLs and load region.

Figure 3

Schematic of the transmission-line equivalent circuit model used in the Lsp simulation to model the ZR accelerator’s vacuum section and load. The starred elements indicate the measurement position for the MITL currents. Values for the various elements are given in Table .

Figure 4

Comparison of voltages between ZR-shot 1896 data, module 17 (black curves), and Lsp simulation (red curves) for the upper (a) IS, (b) PFL (c) OTL1, and (d) OTL2.

Figure 5

Individual switch-resistance time histories inferred from the simulation.

Figure 6

Comparison of measured and simulated electrical signals at (a), (b) the insulator stack, level A, (c) the current in the level A MITL, and (d) the load current.

Figure 7

Electric-field magnitude in the Lsp ZR simulation at times 1, 220, 300, and 400 ns in the $\theta =0$ plane.

Figure 8

Electric-field magnitude in the upper module laser-triggered gas switch in the $\theta =0$ plane at 1 and 100 ns. The arrows indicate the location of the conductivity channel in the switch.

Figure 9

Electric-field magnitude in the upper module water switches in the $\theta =0$ plane at 200 and 300 ns. The arrows indicate the location of the conductivity channel in the switch.

Figure 10

Electric-field magnitude in the upper model pulse-sharpening water switches in the $\theta =0$ plane at 250 and 350 ns. The arrows indicate the location of the conductivity channel in the switch.