Experimental study of current loss and plasma formation in the $Z$ machine post-hole convolute

The $Z$ pulsed-power generator at Sandia National Laboratories drives high energy density physics experiments with load currents of up to 26 MA. $Z$ utilizes a double post-hole convolute to combine the current from four parallel magnetically insulated transmission lines into a single transmission line just upstream of the load. Current loss is observed in most experiments and is traditionally attributed to inefficient convolute performance. The apparent loss current varies substantially for z-pinch loads with different inductance histories; however, a similar convolute impedance history is observed for all load types. This paper details direct spectroscopic measurements of plasma density, temperature, and apparent and actual plasma closure velocities within the convolute. Spectral measurements indicate a correlation between impedance collapse and plasma formation in the convolute. Absorption features in the spectra show the convolute plasma consists primarily of hydrogen, which likely forms from desorbed electrode contaminant species such as ${\mathrm{H}}_2\mathrm{O}$, ${\mathrm{H}}_2$, and hydrocarbons. Plasma densities increase from $1\times {10}^{16}{\mathrm{cm}}^{-3}$ (level of detectability) just before peak current to over $1\times {10}^{17}{\mathrm{cm}}^{-3}$ at stagnation (tens of ns later). The density seems to be highest near the cathode surface, with an apparent cathode to anode plasma velocity in the range of $35–50\mathrm{cm}/\mu \mathrm{s}$. Similar plasma conditions and convolute impedance histories are observed in experiments with high and low losses, suggesting that losses are driven largely by load dynamics, which determine the voltage on the convolute.

Figure 1

(a) An $R-Z$ cross section of the vacuum section and insulator stack of the $Z$ machine [1]. The vacuum section contains four outer-magnetically insulated transmission lines (MITLs) labeled A through D with anodes shown in blue and cathodes in red. Arrows indicate the radial location of the outer-MITL B-dot monitors (at $R=0.66\mathrm{m}$ on the A and D levels) and the stack B-dot and D-dot monitors (at $R=1.66\mathrm{m}$ on the A, B, C, and D levels). (b) An $R-Z$ cross section of the double post-hole convolute with the z-pinch dynamic-hohlraum [12, 13] load geometry. Anodes are shown in blue, convolute anode posts in cyan, cathodes in red, and holes in the cathode are represented by dashed red lines. An arrow indicates the radial location of the inner-MITL B-dot monitors (tan squares). The inner-MITL region ($R<58\mathrm{mm}$) varies with load type.

Figure 2

(a) An $R-\theta$ cross section of the upper post-hole convolute. Magnetic field lines are shown in black. Cartoon representations of plasma formation and the collection sites [22] on the downstream side of the convolute are shown in green. (b) An $R-Z$ cross section of the convolute showing the plasma collection site as predicted in simulations [22, 25].

Figure 3

(a)–(d) Plots of the losslessly propagated stack current (black), the inner-MITL current (cyan), and the difference between the two (red), called the convolute shunt current, for the four bolded load types from Table 1. A dot at the end of each trace represents the time of stagnation. The time at which the convolute shunt impedance drops below 2 ohms is defined as $t=0\mathrm{ns}$. Dashed lines indicate the uncertainty in each measurement [35].

Figure 4

(a)–(d) Plots of the stack voltage (black) and the convolute voltage (cyan) for the four bolded load types from Table 1. The convolute voltage was determined using a lossless translation of the stack voltage [38]. A dot at the end of each trace represents the time of stagnation. The time at which the convolute shunt impedance drops below 2 ohms is defined as $t=0\mathrm{ns}$. Dashed lines indicate the uncertainty in each measurement [35].

Figure 5

(a) A plot of the impedance collapse in the convolute for four nominally identical 70-mm-diameter stainless-steel wire-array experiments. Dashed lines indicate the uncertainty in the impedance for one experiment (other uncertainties are omitted for clarity). For a given load type, the impedance history was typically repeatable to within the uncertainty in the measurement. (b) A plot of the impedance collapse in the convolute for the four bolded load types from Table 1, assuming the standard B-dot calibrations. The general shape of the curves is similar; low-loss experiments appear to operate at slightly higher impedance, but the uncertainty in the measurement is much larger. A series of vertical lines indicates the uncertainty for each curve. (c) Same plot as (b) but assuming the systematic 0.956x correction to the inner-MITL B-dot calibrations detailed in Appendix A. Compared to (b), the impedance histories in (c) are more consistent with one another. A series of vertical lines indicates the uncertainty for each curve.

Figure 6

(a) A plot of the convolute voltage for the four bolded load types from Table 1. Dashed vertical lines indicate the time at which the electric field in the convolute exceeds the explosive-emission threshold of $240\mathrm{kV}/\mathrm{cm}$. The solid vertical line at $t=0\mathrm{ns}$ indicates the time the shunt impedance drops below 2 ohms in each experiment. Coincidentally, all of the voltages passed through roughly the same value shortly before $t=0\mathrm{ns}$. Since some of the voltages had already exceeded this value and were decreasing, while others were rising through the value, it does not appear that there is any significance to this observation. There does not appear to be a simple correlation between applied voltage and impedance collapse. (b) A plot of the electrical power in the convolute for the same four experiments showing no obvious simple correlation. (c) A plot of the integrated energy passing through the convolute. Once again, there does not appear to be a simple correlation.

Figure 7

(a) An $R-Z$ cross section of the convolute showing the field of view of the convolute-spectroscopy probe. The probe observed visible emission from the region downstream of the convolute post, where simulations indicated that plasma would collect. Dashed black lines indicate the field of view of the probe. The angle of the probe could be set to 0, 5, or 7.5 degrees relative to vertical (5 degrees shown). (b) An $R-Z$ cross section of the probe view in a null experiment. The probe could only see the inside of the aperture in the anode. No signal was observed in these measurements indicating minimal plasma formation at the probe. (c) An $R-Z$ cross section of a convolute-spectroscopy probe with a lithium fluoride (LiF) dopant on the bottom surface of the probe, shown in magenta. No lithium features were observed in this measurement, again indicating minimal plasma formation at the probe.

Figure 8

(a) Visible spectra from two experiments near stagnation are shown in black ($t=31\mathrm{ns}$) and blue ($t=24\mathrm{ns}$). Breaks in the signals at 4579, 5050, 5435, and 6328 Å are due to spectral and temporal calibration features. Vertical lines indicate the expected location of hydrogen and sodium spectral lines. There was a clear neutral hydrogen (H I) feature at 6563 Å and possible features associated with the neutral sodium (Na I) doublet at $5890/5896\AA$. There are no obvious spectral features at 4861, 4340, or 4102 Å. There are possible spectral features at 4831 and 4937 Å, which have not yet been identified. (b) A post-stagnation ($t=94\mathrm{ns}$), high-spectral-resolution plot of the H I (6563 Å) and singly ionized carbon (C II) lines at 6578 and 6583 Å. (c) A plot of a post-stagnation spectrum ($t=88\mathrm{ns}$) showing ${\mathrm{C}}_2$ absorption features (Swan bands) as well as the Na I doublet at $5890/5896\AA$. The magenta dots represent the most dominant spectral bands of the Swan system to aid in spectral identification (modified from Table I in Ref. [48]).

Figure 9

(a) An $R-Z$ cross section of the convolute-spectroscopy-probe field of view (black dashed lines) with a lithium fluoride (LiF) dopant (magenta band) located on the upper convolute post (anode). (b) A plot of the spectrum showing the neutral lithium (Li I) absorption line at 6708 Å. This demonstrated that a continuum source was located below the position of the Li dopant. The spectrum shown was averaged over $t=24$ to 104 ns in order to obtain a high signal to noise ratio. The Li I spectral feature was first clearly observed at $t=24\mathrm{ns}$.

Figure 10

(a) A plot of the propagated stack and inner-MITL currents with the convolute plasma emission intensity in the 6400 to 6450 Å spectral band as a function of time. Boxes over the emission signal indicate the times over which the spectral lineouts in (b) were taken. (b) Spectra showing the evolution of the neutral hydrogen feature at 6563 Å with time. The spectra have been normalized to unity and then offset by $+0.5$, $+0.25$, 0, and $-0.25$ for clarity.

Figure 11

A plot of the high-resolution spectrum shortly after stagnation ($t=67\mathrm{ns}$) showing continuum emission with neutral hydrogen (H I) and singly ionized carbon (C II) absorption features (black dots). A fit to the data is shown in red. The fit is a superposition of two Lorentzian profiles for the H I line at 6563 Å and two additional Lorentzian profiles for C II lines at 6578 and 6583 Å, which is convolved with a 2.7 Å FWHM Gaussian profile to account for instrumental broadening. The individual Lorentzians used in the fit are shown below.

Figure 12

(a) Plot of the convolute impedance (solid lines) and plasma electron density (squares) for a variety of load types. The dashed lines are exponential fits to the inferred densities. Vertical lines indicate the uncertainty in the density measurement. At early times the width of the absorption feature was dominated by instrumental broadening, which typically limited the measurement to densities above $1\times {10}^{16}{\mathrm{cm}}^{-3}$. Note that the SVS was slightly out of focus on the ZPDH experiment resulting in a measurement threshold of approximately $2\times {10}^{16}{\mathrm{cm}}^{-3}$. In all experiments, the electron density rose to a detectable level as impedance dropped, and typically exceeded $1\times {10}^{17}{\mathrm{cm}}^{-3}$ at or shortly after stagnation of the z-pinch load. In early-time measurements, where the spectral line shape was dominated by instrument broadening, the densities are represented by points at the measurement threshold. (b) The same plot shown in (a) including later times and higher densities. Note when a superposition of two Lorentzians was fit to the data, the larger FWHM was used to infer the density.

Figure 13

(a) A plot of the electron density at two different azimuthal locations (red circles and black squares) and exponential fits to the data for a shaped-pulse liner experiment. (b) A plot of the electron density at two different azimuthal locations (red circles and black squares) and exponential fits to the data for a different shaped-pulse liner experiment. The timing uncertainty between the two spectroscopy systems was approximately 1 ns, and each spectrum was integrated over $\pm 5\mathrm{ns}$ from the plotted point. These data sets indicate that the plasma density increased at a similar rate at each convolute post.

Figure 14

An $R-Z$ cross section showing the field of view of the two lines of sight in the dual-view probe. The cathode view is shown in black dashed lines and the anode view is shown in green dashed lines. The separation of the center of the two lines of sight is 4.5 mm.

Figure 15

(a) A plot of the convolute voltage (thin dashed) and impedance (thick solid) as a function of time for two different load configurations. (b)–(c) Plots of the electron density from the cathode view (black circles) and anode view (green squares) for the two experiments with Sigmoid curves fit to the data sets. The solid, vertical, cyan line indicates the time of stagnation. The delay between the fits to the cathode and anode view data sets was around 9–10 ns for the SS array and around 11–13 ns for the shaped-pulse liner for densities between $2\times {10}^{17}$ and $4\times {10}^{17}{\mathrm{cm}}^{-3}$. These delays correspond to closure velocities between 35 and $50\mathrm{cm}/\mu \mathrm{s}$. The timing uncertainty between the two systems was approximately 1 ns, and each spectrum was integrated over $\pm 5\mathrm{ns}$ from the plotted point.

Figure 16

An $R-Z$ cross section showing the radial view from post (anode) to cathode of the in-post convolute-spectroscopy probe. The surface shown in magenta was diamond turned to a mirror finish. The black dashed lines indicate the probe line of sight.

Figure 17

A plot of the convolute plasma spectrum (black dots) using the probe specified in Fig. 16 at approximately 10 ns prior to stagnation ($t=37\mathrm{ns}$). A fit to the data is shown in red. This fit indicates a 1.2 Å shift to lower wavelength, which is consistent with a $5.5\mathrm{cm}/\mu \mathrm{s}$ plasma moving towards the probe, assuming a stationary continuum source at the electrode surface. The accuracy of the wavelength scale is roughly $\pm 1\AA$. Dashed vertical lines indicate where the center of the neutral hydrogen line would be for 0, 5.5, 35, and $50\mathrm{cm}/\mu \mathrm{s}$, moving from right to left.

Figure 18

(a) Plots of the hydrogen, carbon, lithium, and sodium spectra generated with PrismSPECT with an ion density of $2\times {10}^{17}{\mathrm{cm}}^{-3}$ and an electron temperature of 1 eV. The experimentally observed singly ionized carbon lines at 6578 and 6583 Å are not observed in the simulated spectra. (b) Plots of the spectra at 2 eV. All experimentally observed features are also observed in the simulated spectra. (c) Plots of the spectra at 3 eV. All of the experimentally observed features are observed in the simulated spectra, but the neutral sodium and hydrogen lines are just below the assigned 5% limit of detectability. (d) Plots of the spectra at 4 eV. All of the spectral features are below the assigned 5% limit of detectability. Note that the H, Li, and Na plots were offset by $-0.1$, $+0.1$, and $+0.2$ for clarity.