Ion Thermal Decoupling and Species Separation in Shock-Driven Implosions

Anomalous reduction of the fusion yields by 50% and anomalous scaling of the burn-averaged ion temperatures with the ion-species fraction has been observed for the first time in $\mathrm{D}{}^3\mathrm{He}$-filled shock-driven inertial confinement fusion implosions. Two ion kinetic mechanisms are used to explain the anomalous observations: thermal decoupling of the D and ${}^3\mathrm{He}$ populations and diffusive species separation. The observed insensitivity of ion temperature to a varying deuterium fraction is shown to be a signature of ion thermal decoupling in shock-heated plasmas. The burn-averaged deuterium fraction calculated from the experimental data demonstrates a reduction in the average core deuterium density, as predicted by simulations that use a diffusion model. Accounting for each of these effects in simulations reproduces the observed yield trends.

Figure 1

Measured yields of (a) DD neutrons and (b) $\mathrm{D}{}^3\mathrm{He}$ protons from implosions with initial fuel density of ${\rho }_0=0.4$ (blue) and 3.3 (red) $\mathrm{mg}/\mathrm{cc}$. For each ${\rho }_0$, the deuterium fraction ($f_{\mathrm{D}}$) was varied. Points are artificially spread out in $f_{\mathrm{D}}$ for legibility. Hyades-simulated yield trends are shown for the low (dashed line) and high (dotted line) ${\rho }_0$.

Figure 2

Yields relative to clean 1D-Hyades simulations, for (a) DD neutrons and (b) $\mathrm{D}{}^3\mathrm{He}$ protons. Each dataset has been normalized to its value at $f_{\mathrm{D}}=0.5$. Modeled trends incorporating kinetic physics, such as decoupled ion temperatures (“2-Ti”, dashed lines; low-${\rho }_0$ only), and reduced ion kinetic models including ion diffusion (“RIK,” dotted lines) match the measurements better than clean simulations (solid lines).

Figure 3

Comparison of measured (points) and simulated (lines) burn-averaged ion temperatures $⟨T_i⟩$ for the (a) DD- and (b) $\mathrm{D}{}^3\mathrm{He}$-fusion reactions. The clean 1D simulations (solid lines) predict an increased $⟨T_i⟩$ with decreased $f_{\mathrm{D}}$, which is not observed in the low-${\rho }_0$ data. A model of decoupled D and ${}^3\mathrm{He}$ ion temperatures in 1D simulations (“2-Ti,” dashed lines) reproduces the low-${\rho }_0$ data. RIK simulations (dotted lines) model the absolute temperatures better than clean simulations.

Figure 4

“Burn-averaged deuterium fraction” $⟨f_{\mathrm{D}}⟩$ evaluated from the experiments for low-density (blue) and high-density (red) implosions, compared to 1D-clean simulations (lines). Simulated values for $⟨f_{\mathrm{D}}⟩$ differ slightly from the fuel $f_{\mathrm{D}}$ due to differences in the $\mathrm{D}{}^3\mathrm{He}$ and DD reactivity. Reduction of the deuterium in the core prior to burn is inferred for all implosions.

Figure 5

Density profiles near bang time for an equimolar $\mathrm{D}{}^3\mathrm{He}$ implosion with ${\rho }_0=3.3\mathrm{mg}/\mathrm{cc}$, comparing 1D-average-ion clean simulations (dotted lines) with simulations including reduced ion kinetic models of ion diffusion, ion thermal conduction, and tail-ion loss (solid lines). The deuterium (blue) diffuses to larger radii and ${}^3\mathrm{He}$ (red) is concentrated in the core, such that at peak burn $f_{\mathrm{D}}=0.33$. The RIK simulations reproduce the observed yields.