Validation of implosion modeling through direct-drive shock timing experiments at the National Ignition Facility

Precise modeling of shocks in inertial confinement fusion implosions is critical for obtaining the desired compression in experiments. Shock velocities and postshock conditions are determined by laser-energy deposition, heat conduction, and equations of state. This paper describes experiments at the National Ignition Facility (NIF) [E. M. Campbell and W. J. Hogan, Plasma Phys. Control. Fusion 41, B39 (1999)] where multiple shocks are launched into a cone-in-shell target made of polystyrene, using laser-pulse shapes with two or three pickets and varying on-target intensities. Shocks are diagnosed using the velocity interferometric system for any reflector (VISAR) diagnostic [P. M. Celliers et al., Rev. Sci. Instrum. 75, 4916 (2004)]. Simulated and inferred shock velocities agree well for the range of intensities studied in this work. These directly-driven shock-timing experiments on the NIF provide a good measure of early-time laser-energy coupling. The validated models add to the credibility of direct-drive-ignition designs at the megajoule scale.

Figure 1

(a) A laser-pulse shape characterized by three pickets and a main pulse. (b) Target configuration driven by the triple-picket design includes an outer ablator made of a polymeric material comprising carbon and hydrogen, an inner cryogenic deuterium-tritium layer, and residual vapor. (c) At $\sim 6\mathrm{ns}$, several shocks traverse the ablator and ice. Each shock, characterized by a density jump (left axis) and pressure (right axis), is launched by the three pickets and the main pulse. The vertical dashed line shows the location of the interface between CH and DT.

Figure 2

(a) Schematic showing the experimental setup. The laser is incident on the target, excluding the region occupied by the cone (shown in green). The VISAR laser is incident from the right, probing the regions marked by the equator and the pole. Arrows indicate the beam repointing needed to improve on-target laser symmetry. Each on-target beam is characterized by a beam size that is approximately the size of the target. (b) Time-resolved raw VISAR data for shot N160705-001. The two-axis VISAR provides shock timing and velocity measurements at the pole (top) and equator (bottom) by spatially separating the two signals using a mirror.

Figure 3

Experimental pulse shapes from the four NIF shots considered in this work showing single-beam power from each cone vs time. (a) Shot N151025-003: low-intensity ($5\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$) double pickets, where the different cones have nominally the same picket energies. (b) Shot N151026-002: low-intensity double pickets, where the inner cones have lower picket intensities compared to the outer cones for the first picket. (c) Shot N160705-001: high-intensity double pickets ($1\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$), with nominally the same energies for all the cones. (d) Shot N161031-003: triple-picket pulse shapes, where the intensities are varied between $5\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ and $1\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$.

Figure 4

Sensitivity of shock velocities for low-intensity pickets. (a) Electron-temperature contours in the corona for flux-limited heat conduction. (b) Electron temperature in the corona for the nonlocal heat conduction. (c) Calculated shock velocity with the two heat-conduction models at the pole. (d) Calculated shock velocity with the two heat-conduction models at the equator.

Figure 5

Sensitivity of shock velocities for high-intensity pickets. (a) Electron-temperature contours in the corona for flux-limited heat conduction. (b) Electron temperature in the corona for nonlocal heat conduction. (c) Calculated shock velocity with the two heat-conduction models at the pole. (d) Calculated shock velocity with the two heat-conduction models at the equator.

Figure 6

Shock velocity for the low-intensity pickets for different equations of state; green is the FPEOS model, whereas blue is the SESAME model. (a) The pole and (b) the equator.

Figure 7

Contour plots showing mass density vs the radius ($y$ axis) and polar angle ($x$ axis) from simulations for shots corresponding to the lower-intensity double-picket pulse shapes at 3 ns [Figs. 3 and 3]. (a) The pole corresponds to $0{}^{\circ }$, the equator is at $90{}^{\circ }$. When the first-picket energies for the pole are decreased, the first shock slows advancing the catch-up time at the pole, while the equatorial shock positions remain unchanged.

Figure 8

Comparison of experimentally inferred shock velocities when only the inner-cone power is changed. (a) Polar shock velocities and (b) equatorial shock velocities. Shot N151025 has 20% higher inner-cone energy than N151026. The uncertainty in shock velocity is calculated to be $0.68\mu \mathrm{m}/\mathrm{ns}$ (within the thickness of the lines) and time is $\pm 80\mathrm{ps}$.

Figure 9

Shock velocity for the low-intensity pickets for shot N151025. Simulation in green and experiment in black for (a) the pole and (b) the equator.

Figure 10

Simulation (green) compared to experimental velocity (black) for N151026-002. (a) Polar shock velocity. (b) Equatorial shock velocity. The first discontinuity at $\sim 3.5\mathrm{ns}$ corresponds to the shock from the second picket catching up with the shock from the first picket.

Figure 11

Shock velocity for the high-intensity pickets for shot N160705 (with picket intensity of $1\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2)$. Simulation in green and experiment in black for (a) the pole and (b) the equator. The first discontinuity at $\sim 3.5\mathrm{ns}$ corresponds to the shock from the second picket catching up with the shock from the first picket.

Figure 12

Shock velocity for the low-intensity pickets for shot N161031. Simulation in green and experiment in black. (a) Shock velocity at the pole. (b) Shock velocity at the equator. The first discontinuity at $\sim 3.5\mathrm{ns}$ corresponds to the shock from the second picket catching up with the shock from the first picket, and the second discontinuity at $\sim 4.5\mathrm{ns}$ corresponds to the shock from the third picket catching up with the earlier shock.