Neutron Time-of-Flight Measurements of Charged-Particle Energy Loss in Inertial Confinement Fusion Plasmas

Neutron spectra from secondary ${}^3\mathrm{H}(d,n)\alpha$ reactions produced by an implosion of a deuterium-gas capsule at the National Ignition Facility have been measured with order-of-magnitude improvements in statistics and resolution over past experiments. These new data and their sensitivity to the energy loss of fast tritons emitted from thermal ${}^2\mathrm{H}(d,p){}^3\mathrm{H}$ reactions enable the first statistically significant investigation of charged-particle stopping via the emitted neutron spectrum. Radiation-hydrodynamic simulations, constrained to match a number of observables from the implosion, were used to predict the neutron spectra while employing two different energy loss models. This analysis represents the first test of stopping models under inertial confinement fusion conditions, covering plasma temperatures of $k_{B}T\approx 1–4\mathrm{keV}$ and particle densities of $n\approx (12–2)\times {10}^{24}{\mathrm{cm}}^{-3}$. Under these conditions, we find significant deviations of our data from a theory employing classical collisions whereas the theory including quantum diffraction agrees with our data.

Figure 1

Results of two-dimensional hydra [29] simulations, symmetric about the $z$ axis (hohlraum axis) for (a) the electron density $n_e$, (b) the temperature $k_B{T}_e$, (c) the electron coupling ${\mathrm{\Gamma }}_e$, and (d) electron degeneracy ${\theta }_e$ at peak energy production in experiment No. N130813. The white curve defines the boundary between the fuel and surrounding carbon ablator. The observed ${}^3\mathrm{H}(d,n)\alpha$ neutron spectrum is sensitive only to the weakly coupled, nondegenerate plasma inside the white curve.

Figure 2

Map of the energy deposition of tritons in the plasma, summed over the burn duration and weighted by volume. The highest energy deposition occurs in the low-temperature, high-density regions surrounding the hot core. Tritons that escape the deuterium plasma are quickly stopped in the remaining carbon ablator (outside the white curve).

Figure 3

Energy distributions of reacting tritons (left panel) and their associated neutron spectra (right panel) as simulated using the plasma conditions shown in Fig. 1 and the default stopping model in hydra [31] for a set of radii spanning the deuterium plasma: 10–20 (black), 60–70 (blue), 70–80 (red), and from $80\mu \mathrm{m}$ to the carbon ablator (green). The mean triton energy decreases with radius, which reduces the Doppler shift and, thus, narrows the distribution of emitted neutrons. The energy loss also strongly increases the relative intensity of the neutron spectrum as the tritons approach the strong resonance in the ${}^3\mathrm{H}(d,n)\alpha$ cross section at a triton energy of 160 keV. An analogous behavior occurs in time: as the plasma cools and becomes more dense during the thermonuclear burn duration, the spectrum narrows and the ${}^3\mathrm{H}(d,n)\alpha$ yield per triton increases.

Figure 4

Spectra of ${}^2\mathrm{H}(d,n){}^3\mathrm{He}$ and ${}^3\mathrm{H}(d,n)\alpha$ reactions extracted from detectors (filled circle) along the lines of sight $(\theta ,\varphi )=(115°,316°)$ in panels (a) and (c), and (161°, 56°) in panels (b) and (d). The data points are spaced in increments of the full width at half maximum of each detector’s impulse response function, and contain statistical uncertainties (which are smaller than the marker size) from neutron interactions, photoelectrons, and digitizer noise. Simulated spectra (lines) are normalized to the measurements to emphasize differences in shapes. Results for the Maynard and Deutsch [15] (red) and Li and Petrasso [16] (blue) stopping power models are shown for ${}^3\mathrm{H}(d,n)\alpha$ spectra; only the Maynard and Deutsch model is shown for the ${}^2\mathrm{H}(d,n){}^3\mathrm{He}$ spectra as they are independent of the stopping model. Note that a higher degree of asymmetry in areal density and/or plasma conditions than was accounted for in the simulations is believed to be responsible for the worse agreement shown in panel (d) [40].