Measuring the shock impedance mismatch between high-density carbon and deuterium at the National Ignition Facility

Fine-grained diamond, or high-density carbon (HDC), is being used as an ablator for inertial confinement fusion (ICF) research at the National Ignition Facility (NIF). Accurate equation of state (EOS) knowledge over a wide range of phase space is critical in the design and analysis of integrated ICF experiments. Here, we report shock and release measurements of the shock impedance mismatch between HDC and liquid deuterium conducted during shock-timing experiments having a first shock in the ablator ranging between 8 and 14 Mbar. Using ultrafast Doppler imaging velocimetry to track the leading shock front, we characterize the shock velocity discontinuity upon the arrival of the shock at the HDC/liquid deuterium interface. Comparing the experimental data with tabular EOS models used to simulate integrated ICF experiments indicates the need for an improved multiphase EOS model for HDC in order to achieve a significant increase in neutron yield in indirect-driven ICF implosions with HDC ablators.

Figure 1

Experimental concept. (a)–(c) Keyhole targets [22, 24, 25, 26] containing high-density carbon (HDC) capsules filled with liquid deuterium are indirectly driven using up to 192 beams at the National Ignition Facility (NIF) pointed at the top and bottom laser entrance holes. Most recent W-doped capsules have a multishell structure with the innermost $5\mu \text{m}$ made of undoped HDC with $\rho \sim 3.44\text{g}/{\text{cm}}^3$, a W-doped layer, an undoped HDC outer layer with $\rho \sim 3.48\text{g}/{\text{cm}}^3$, and a 3-$\mu \text{m}$-thick nanocrystalline undoped HDC topcoat with $\rho \sim 3.30\text{g}/{\text{cm}}^3$. The density of the W-doped layer depends on the doping level, from $3.56\text{g}/{\text{cm}}^3$ with 0.16 at. % W to 3.60 ${\mathrm{g}/\mathrm{cm}}^3$ with 0.25 at. % W and 3.64 ${\mathrm{g}/\mathrm{cm}}^3$ with 0.33 at. % W. An accurately shaped, 5–7 ns long pulse launches a series of strong shock waves into the capsule. Using a gold cone inserted in the capsule and sealed by a transparent window, the interferometric Doppler velocimeter VISAR instrument [27] tracks the shock velocity history inside the ablator and the deuterium. (d) Observing the shock velocity inside the HDC capsule is challenging because of scattering due to its microstructure, absorption due to photoionization, strong Fresnel reflection at the interface, and weak reflection at the shock front below 25 km/s. (e) Once the shock has reached the fluid ${\text{D}}_2$, it is easily tracked with VISAR to measure its shock velocity up to 150 km/s.

Figure 2

Experimental VISAR data and inferred shock velocity. Top: Example VISAR record for a two-axis keyhole experiment with an HDC ablator. Bottom: Corresponding shock velocity along the equator in the HDC ($t<3.1$ ns) and in the ${\text{D}}_2$ ($t>3.1$ ns) showing the sudden acceleration of the shock as it is transmitted into the deuterium (near 3.1 ns, vertical dotted line), including a weighted average of the velocity histories from VISAR channels leg A and leg B. Inset: Raw data for the equator region before and after ghost fringe subtraction [3].

Figure 3

Graphical construction of the impedance-matching procedure. Calculated Hugoniot curves are shown in $U_S\text{−}{u}_p$ and $P\text{−}{u}_p$ spaces (solid lines), together with calculated isentropic release curves (dotted lines). For a given incident velocity $U_S\left(\text{HDC}\right)$, one can determine, for a given HDC EOS, the incident particle velocity in HDC, $u_p\left(\text{HDC}\right)$, using the top panel, then follow a vertical line at constant $u_p$ to the lower panel to determine the incident shock pressure $P\left(\text{HDC}\right)$. Then, following a release curve until it crosses the ${\text{D}}_2$ Hugoniot, one determines the approximate transmitted shock pressure $P\left({\text{D}}_2\right)$ and particle velocity $u_p\left({\text{D}}_2\right)$. Following again a vertical, constant $u_p$ line back up into the upper panel until the intersection with the deuterium $U_S\text{−}{u}_p$ Hugoniot line, one obtains an approximate transmitted shock velocity $U_S\left({\text{D}}_2\right)$. Dashed-dotted and dashed lines show that for a given incident shock velocity $U_S\left(\text{HDC}\right)=25\mathrm{km}/\mathrm{s}$, LLNL 65 and 9061 models predict two very different transmitted shock velocities $U_S\left({\text{D}}_2\right)$ respectively near 28 and 31 km/s.

Figure 4

Diamond Hugoniot: Experimental data and tabular EOS models. The gray shaded area indicates the pressure range of the shock states explored in the present experiments. Data from Refs. [11, 12] measured relative to a quartz standard, and the data from Ref. [10] and Bradley et al. [12] using an Al standard were reanalyzed using updated quartz and Al Hugoniot models [31]. Reference [13] used a Cu standard. Data from Ref. [15] collected with a quartz standard are also included.

Figure 5

Shock velocity jump at the interface between the $\text{HDC}$ ablator and the liquid ${\text{D}}_2$ fuel surrogate. Experimental data (blue squares) assuming 2.40 as the refractive index of unshocked HDC. Calculated velocity jumps for various HDC EOS models assuming LLNL 1014 (based on Kerley's 2003 model [32], solid lines) or the DFT-MD based CEA table [33] (dashed lines) as the deuterium EOS with an initial density ${\rho }_0=168\text{mg}/{\text{cm}}^3$. Data from Ref. [15] are also included.

Figure 6

Influence of W doping on the shock impedance mismatch. Same data as reported in Fig. 5 with the level of W doping as a color code. One could expect that increasing the W-doping level should contribute to mitigating the photoionization and/or preheat effects. No clear correlation appears between the level of doping and the disagreement between the data and the 9061 model.

Figure 7

Shock velocity jump at the interface between a CVD diamond slab and a quartz plate. Experimental data and predictions using various models for HDC and a fit to experimental data for the quartz Hugoniot [31]. Data from Ref. [15] are also included.