Design of a High-Foot High-Adiabat ICF Capsule for the National Ignition Facility

The National Ignition Campaign’s [M. J. Edwards et al., Phys. Plasmas 20, 070501 (2013)] point design implosion has achieved DT neutron yields of $7.5\times 10^{14}$ neutrons, inferred stagnation pressures of 103 Gbar, and inferred areal densities ($\rho R$) of $0.90\mathrm{g}/\mathrm{cm}{}^2$ (shot N111215), values that are lower than 1D expectations by factors of $10\times$, $3.3\times$, and $1.5\times$, respectively. In this Letter, we present the design basis for an inertial confinement fusion capsule using an alternate indirect-drive pulse shape that is less sensitive to issues that may be responsible for this lower than expected performance. This new implosion features a higher radiation temperature in the “foot” of the pulse, three-shock pulse shape resulting in an implosion that has less sensitivity to the predicted ionization state of carbon, modestly lower convergence ratio, and significantly lower ablation Rayleigh-Taylor instability growth than that of the NIC point design capsule. The trade-off with this new design is a higher fuel adiabat that limits both fuel compression and theoretical capsule yield. The purpose of designing this capsule is to recover a more ideal one-dimensional implosion that is in closer agreement to simulation predictions. Early experimental results support our assertions since as of this Letter, a high-foot implosion has obtained a record DT yield of $2.4\times 10^{15}$ neutrons (within $\sim 70\%$ of 1D simulation) with fuel $\rho R=0.84\mathrm{g}/\mathrm{cm}{}^2$ and an estimated $\sim 1/3$ of the yield coming from $\alpha$-particle self-heating.

Figure 1

The T0 capsule (left) used in the high-foot implosions described here is identical to that used in the majority of the NIC implosions. The radiation temperature (right) driving the high-foot capsule (solid curve), however, is significantly different from that used by the low-foot NIC campaign (dashed curve).

Figure 2

The low-foot implosion shock structure (left) has four drive generated shocks and numerous shock reflection and rarefaction features that are not present in the three shock high-foot implosion design (right).

Figure 3

For the low-foot implosion (left), DCA modeling of the ablation process shows a distinct double-peak feature in the simulated ablation pressure profile (blue curve) correlated with the location of the carbon Li-like ionization state (black dotted curve). For the high-foot implosion (right), the double-peak feature in the ablation pressure profile is reduced significantly recovering a more ideal profile shape. In each case, the snapshot is taken just before the third drive-generated shock is launched.

Figure 4

The figure compares calculated growth factors (GFs) at the ablation front (left) and ice-ablator interface (right) for the low-foot implosion and high-foot implosion. These GFs are sampled at the time of peak implosion velocity. The primary comparison is between the black curve (low foot at a nominal drive and capsule thickness) and red curve (high foot at nominal drive and capsule thickness) for a $380\mathrm{km}/\mathrm{s}$ implosion and $290\mathrm{km}/\mathrm{s}$ implosion, respectively. The blue curve shows results for a high-foot, low-power implosion as in NIF shot N130501.

Figure 5

Density profiles at ignition time (defined as time when central fuel reaches 12 keV) for various adiabat capsules illustrate reduction in peak ablator density and increase in ablator width as adiabat increases. Values are normalized to the peak value of the $\alpha =1.5$ curve.

Figure 6

Two-dimensional multimode (up to mode 100) simulations with a spectrum of imposed surface roughness ($4\times$ nominal) show, in density, the expected instability growth on the capsule. From top to bottom, implosions with $\alpha =1.45$ (low foot), $\alpha =2.3$ (high foot), and $\alpha =2.8$ (high foot) are shown at $R\sim 200\mu \mathrm{m}$ (left column) and $R\sim 50\mu \mathrm{m}$ (right column).

Figure 7

Ratios of 2D multimode (up to mode 100) model yields over 1D model yields are plotted vs. a multiplier of the capsule surface roughness for implosions with $\alpha =1.45$ (low-foot, red), $\alpha =2.3$ (high-foot, blue), and $\alpha =2.8$ (high-foot, green) are shown. Even for a roughness multiplier of 4, which drops the simulated 2D yield to $0.1\times$ the 1D yield for the low-foot case, the high-foot implosions only drop to $0.6\times$ the 1D yield consistent with more resistance to ablation front RT instability.