Voltage measurements at the vacuum post-hole convolute of the $Z$ pulsed-power accelerator

Presented are voltage measurements taken near the load region on the $Z$ pulsed-power accelerator using an inductive voltage monitor (IVM). Specifically, the IVM was connected to, and thus monitored the voltage at, the bottom level of the accelerator’s vacuum double post-hole convolute. Additional voltage and current measurements were taken at the accelerator’s vacuum-insulator stack (at a radius of 1.6 m) by using standard $D$-dot and $B$-dot probes, respectively. During postprocessing, the measurements taken at the stack were translated to the location of the IVM measurements by using a lossless propagation model of the $Z$ accelerator’s magnetically insulated transmission lines (MITLs) and a lumped inductor model of the vacuum post-hole convolute. Across a wide variety of experiments conducted on the $Z$ accelerator, the voltage histories obtained from the IVM and the lossless propagation technique agree well in overall shape and magnitude. However, large-amplitude, high-frequency oscillations are more pronounced in the IVM records. It is unclear whether these larger oscillations represent true voltage oscillations at the convolute or if they are due to noise pickup and/or transit-time effects and other resonant modes in the IVM. Results using a transit-time-correction technique and Fourier analysis support the latter. Regardless of which interpretation is correct, both true voltage oscillations and the excitement of resonant modes could be the result of transient electrical breakdowns in the post-hole convolute, though more information is required to determine definitively if such breakdowns occurred. Despite the larger oscillations in the IVM records, the general agreement found between the lossless propagation results and the results of the IVM shows that large voltages are transmitted efficiently through the MITLs on $Z$. These results are complementary to previous studies [R. D. McBride et al., Phys. Rev. ST Accel. Beams 13, 120401 (2010)] that showed efficient transmission of large currents through the MITLs on $Z$. Taken together, the two studies demonstrate the overall efficient delivery of very large electrical powers through the MITLs on $Z$.

Figure 1

Cross-sectional drawing of one radial half of the refurbished $Z$ pulsed-power accelerator. The various components and stages are described in the text.

Figure 2

Cross-sectional drawing of one radial half of the refurbished $Z$ vacuum section.

Figure 3

(a) Cross-sectional illustration of the IVM installed in the lower volume of the $Z$ vacuum section, below the four MITLs, where only the left radial half of the $Z$ vacuum section is shown. (b) Zoomed-in cross-sectional illustration of the $Z$ accelerator’s double post-hole convolute region, highlighting the IVM’s upper connection point. (c) Zoomed-in cross-sectional illustration of the IVM’s lower connection point, highlighting the IVM’s $B$-dot probes, which are used to obtain the current carried by the IVM. (d),(e) Slightly rotated versions of that shown in (c), highlighting how the electrical and structural connections are made.

Figure 4

Schematic, not to scale, showing the load as thin orange lines, the anodes as thick black lines, and the cathodes as thick red lines. The IVM is represented by blue lines. All parts of the drawing depict axisymmetric structures, with the exception of the horizontal IVM rod, and the convolute posts and holes. The loop shown is to calculate the line integral of the electric field resulting in the voltage $V_{D,\text{conv}}$: the potential difference between the post-hole gap at the $D$ level of the vacuum convolute.

Figure 5

Plane of the IVM and, in red, the coordinate systems used to calculate its inductance. The voltage is applied at the gap shown in the figure. The gray thick line represents the lower anode (ground) of the accelerator.

Figure 6

Boundary element mesh used in the EIGER calculation of the IVM inductance. A high-density mesh is used along the angular dimension of the cavity surface in order to capture the modal variation excited at the junction of the horizontal wire section and the cavity wall.

Figure 7

Voltage comparisons at the $D$-level post-hole gap of the vacuum convolute for (a) shot 1177 ($Z$ prerefurbishment, IVM implementation I), (b) shot 2105 (IVM implementation II), and (c) shot 2172 (IVM implementation III). The red curves are the TLE-translated results (averaged over the four MITL-convolute levels), and the black curves are the IVM results obtained by using Eq. (1). The light blue and dark blue curves are upper and lower bounds, respectively, for the TLE translations, obtained as explained in the text. The orange curve is the inner MITL load current BIAVE, measured 6 cm from the machine axis of symmetry. Shot 2172 exhibits large errors after about 3030 ns and then again after 3090 ns in the translated voltage due to the flashing of the vacuum-insulator stack’s $B$ level; interestingly, the onset of large IVM voltage oscillations coincides with the first instance of flashing at 3030 ns.

Figure 8

Modulus of the ratio of the Fourier transforms of the TLE-translated voltage waveform and the time derivative of the IVM current waveform for shot 2105 for low frequencies. In particular, note that $\mathrm{Re}\delta (0)=2.82\mu \mathrm{H}$, is in good agreement with the calculated value of $L=2.76\mu \mathrm{H}$ in Table 1.

Figure 9

(a)–(e) Comparison of voltages at the $D$-level post-hole gap of the vacuum convolute for shots 2104, 2106, 2108, 2110, and 2120, respectively. The red curve is the TLE-translated voltage. The orange curve is obtained by using Eq. (1) with the IVM $B$-dot signals. The black curve is obtained as described in Sec. 4 by using the function $\delta (\omega )$ defined in that section, for shot 2105. The blue curve is the transit-time-corrected voltage of Eq. (4) assuming $\tau =6\mathrm{ns}$.

Figure 10

Load currents from the various experiments on the refurbished $Z$ machine discussed in this paper. As described in the text, different pulse shapes were obtained because different loads and accelerator configurations were used. The load current for 1177 is shown in Fig. 7.