Radiation and electron thermal conduction damping of acoustic perturbations in igniting deuterium-tritium gas

We derive a dispersion relation for the damping of acoustic waves in equi-molar deuterium-tritium (DT) gas due to radiation coupling and electron thermal conduction and discuss its significance for inertial confinement fusion (ICF) targets with high-Z shells surrounding a central DT fuel region. As the shell implodes around DT fuel in such a target, shocks and waves are transmitted through the DT gas. If the shell is perturbed due to drive non-uniformity or manufacturing imperfection, these shocks and waves may be perturbed as well, and can potentially re-perturb the shell. This can complicate calculation of shell stability and implosion asymmetry and in general make the target less robust against implosion non-uniformity. Damping of perturbations in DT gas can alleviate these complications. Also, damping of low-order modes, which is primarily due to radiation coupling, can drive the DT gas to an isobaric and isothermal `equilibrium' configuration during ignition. We find that for the range of common ignition temperatures in targets with high-Z shells, 2.5 ≲ T_ig ≲ 3.5 keV, damping of low-order modes is significant for areal densities (ρr) in the broad range of 0.6 ≲ ρr ≲ 1.8 g cm^-2. This suggests it is advantageous to design these targets to achieve areal densities at ignition within this range. Furthermore, we derive a simple constraint between areal density and temperature, ρr = 0.34T₀ where T₀ is in keV, such that DT gas undergoing equilibrium ignition is optimally robust against non-uniformity.