Beta energy driven uniform deuterium–tritium ice layer in reactor-size cryogenic inertial fusion targets

Abstract

We have studied the effectiveness of beta heating on driving a deuterium–tritium (DT) ice layer toward uniformity within spherical inertial fusion targets. Beta heating results from the deposition of energy from the beta particles from the tritium decay in these targets. These targets are enclosed in a constant temperature environment. This study first considered a one-dimensional heat transfer model of an idealized target, geometry, and environment. We concluded that beta energy deposition can drive a nonuniform DT ice layer towards uniformity. The maximum rate at which this redistribution can occur is given by dδ/dt=δ̇=−δ/θTC, where δ=DT ice thickness in excess of that for a uniform layer and θTC=a time constant ≊1500 s. This translates to a factor of 10 reduction in nonuniformity every hour. We also evaluated, and continue to do so, the consequences of deviations from the idealized case assumptions and the selection of certain experimental parameters, on the actual behavior of DT ice in such cryogenic targets. The status of this work is such that we have confidence in the use of beta heating to drive the DT ice toward uniformity for reactor-size targets (∼1 mm and larger in diameter).

X-ray imaging of cryogenic deuterium-tritium layers in a beryllium shell

“…Solid D-T, by virtue of its relatively high vapor pressure and radioactive self-heating, forms an equilibrium surface that conforms to an isotherm. [19][20][21][22] Solid D-T layers grown in an environment with spherical isotherms will thus be spherical as well. Uniformly thick spherical D-T layers have been characterized inside of transparent plastic shells using visible light imaging.…”

“…This process, known as beta-layering, has been observed in numerous geometries and materials. [19][20][21][22]32] These observations determined that the redistribution rate is an exponential function of time and depends on the amount of 3 He in the sample. As 3 He accumulates from the beta-decay, the redistribution time constant increases.…”

“…4, give time constants of 27.0 and 29.7 minutes, in good agreement with previous measurements for D-T of 30 minutes. [19,20,32] The time constant is expected to change with the sample age, due to buildup of 3 He, and will be measured in the future.…”

National Ignition Facility target design and fabrication

“…Because of this higher temperature, the rate of sublimation is highest where the fuel layer is thickest, resulting in a redistribution of the D-T from the thickest parts of the layer to the thinnest. This natural process has become known as beta layering, and has a time constant for redistribution of about 30 min for a 50-50 deuterium-tritium mixture, with an additional dependence on ablator thermal conductivity and 3 He concentration (Martin et al, 1988;Bernat et al, 1991;Geidt et al, 2006 ). The beta-layering process works qualitatively very well, however the specification for the surface quality of the D-T solid-vapor interface is very stringent.…”

Increasing robustness of indirect drive capsule designs against short wavelength hydrodynamic instabilities

“…The x-rays filling the hohlraum ablate the outside of the spherical fuel capsule at its center, imploding and compressing deuterium-tritium (D-T) fuel. The fuel is initially in a spherical shell of solid D-T held at cryogenic temperature before the shot, self-smoothed by β-particle deposition from the T decay [3]. The laser pulse, Fig.…”