Inertial-confinement fusion-plasma-based cross-calibration of the deuterium-tritium γ-to-neutron branching ratio

The deuterium-tritium (D-T) $\gamma$-to-neutron branching ratio $\left[{}^3\mathrm{H}\right(d,\gamma ){}^5\mathrm{He}/{}^3\mathrm{H}(d,n\left){}^4\mathrm{He}\right]$ has been determined previously under inertial-confinement fusion (ICF) conditions and in beam-target based experiments. In the former case, neutron-induced backgrounds are mitigated compared to the latter due to the short pulse nature of ICF implosions and the use of gas Cherenkov $\gamma$-ray detectors. An added benefit of ICF based measurements is the ability to achieve lower center-of-mass energies as compared to accelerators. Previous ICF based experiments however report a large uncertainty in the D-T $\gamma$-to-neutron branching ratio of $\approx 48\%$, which arises from the necessity of an absolute detector calibration and/or a cross-calibration against the D-${}^3\mathrm{He} \gamma$-to-proton branching ratio. A more precise value for the branching ratio based on data taken at the OMEGA laser facility is reported here, which relies on a cross-calibration against the better known ${}^{12}\mathrm{C}$ neutron inelastic scattering cross section. A D-T branching ratio value of $\left(4.6\pm 0.6\right)\times {10}^{-5}$ is determined by this method.

Figure 1

An illustrated schematic of the GCD. D-T fusion $\gamma$'s Compton scatter in the $\gamma \text{−}e$ converter plate to produce relativistic electrons. The relativistic electrons generate Cherenkov radiation as they propagate through the gas medium inside the GCD. The resulting Cherenkov photons are reflected by a Cassegrainian mirror setup to a PMT for detection. Tungsten shielding is used to attenuate $\gamma$'s which can directly interact with the PMT to produce an extraneous signal. The distance between the pair of mirrors in the Cassegrainian setup provides a temporal delay between Cherenkov photon detection and direct $\gamma$ interactions in the PMT.

Figure 2

The ${}^{12}\mathrm{C}(n,n\text{'}\gamma ){}^{12}\mathrm{C}$ spectrum [36, 37] resulting from 14.1-MeV neutrons. The spectrum is approximately monoenergetic due to the intense line at 4.4 MeV which is orders of magnitude larger than other spectral features.

Figure 3

The GCD-3 and ${}^{12}\mathrm{C}$ puck experimental configuration [41]. The inner, front face of the beryllium puck holder is 6.26 cm from TCC. The front face of the GCD-3 is 20 cm from TCC. D-T fusion neutrons (solid, blue arrows) can inelastically scatter in the ${}^{12}\mathrm{C}$ puck to generate ${}^{12}\mathrm{C} \gamma$'s (dot-dashed, green arrows). The D-T fusion $\gamma$'s (dotted, purple arrows) are mostly unattenuated by the beryllium puck holder and ${}^{12}\mathrm{C}$ puck. The experimental layout allows the fusion $\gamma$'s to arrive at the GCD-3 $\approx 1$ ns before the arrival of neutron-induced $\gamma$'s.

Figure 4

Scope traces from four different shots. These traces are normalized to the product of the D-T neutron yield, photomultiplier tube gain, and mean quantum efficiency over the Cherenkov spectrum. Shots 77 361 and 77 374 (blue and orange, solid lines) are in the active configuration in which the beryllium puck holder is loaded with the ${}^{12}\mathrm{C}$ powder. Shots 77 365 and 77 367 (green and red, dashed lines) are in the background configuration in which the beryllium puck holder is empty. An excess signal can be seen from 0.8 to 1.6 ns in the active configuration which is due to ${}^{12}\mathrm{C}(n,n\text{'}\gamma ){}^{12}\mathrm{C}$ and subsequent ${}^{12}\mathrm{C} \gamma$ detection by the GCD-3.

Figure 5

The D-T fusion $\gamma$ signal. This signal is representative of the raw (non-normalized) signals shown in Fig. 4. The initial peak at $t=0$ is a result of peak emission of D-T fusion $\gamma$'s during the implosion. The second peak near 200 ps is due to ringing and is inherent to the instrument response function of the Photek PMT110.

Figure 6

The ${}^{12}\mathrm{C} \gamma$ signal. The signal results from the normalized traces shown in Fig. 4. The background configuration shot trace is subtracted from the active and the result is renormalized to the appropriate neutron yield, PMT gain, and quantum efficiency.

Figure 7

The GCD-3 responsivity, in productive particles per incident $\gamma$ for 400 psi (absolute) of ${\mathrm{CO}}_2$, is determined from Monte Carlo simulations conducted in GEANT4. The solid, red curve is representative of photons and the dotted, blue curve denotes electrons.

Figure 8

The ${\mathrm{SiO}}_2$ capsule spectra are shown for an areal density of $2.05\mathrm{mg}/\mathrm{c}{\mathrm{m}}^2$. The solid, blue curve represents the spectrum generated from MCNP simulations, and the dotted, red curve represents the spectrum generated from GEANT4 simulations.

Figure 9

The results of several experiments to measure the D-T ($\gamma /n$) branching ratio are shown. The branching ratio is plotted against the (effective) deuteron energy. The squares represent ICF based measurements which consider both the ${\gamma }_1$ and ${\gamma }_0$ components of the D-T $\gamma$ spectrum. The solid circles represent beam-target experiments which also consider both the ${\gamma }_1$ and ${\gamma }_0$ components. And the open circles represent beam-target experiments which only consider the ${\gamma }_0$ component of the D-T $\gamma$ spectrum.