Entropy generation from hydrodynamic mixing in inertial confinement fusion indirect-drive targets

The increase in entropy from the physical mixing of two adjacent materials in inertial confinement fusion (ICF) implosions and gas-filled hohlraums is analytically assessed. An idealized model of entropy generation from the mixing of identical ideal-gas particles across a material interface in the presence of pressure and temperature gradients is applied. Physically, mix-driven entropy generation refers to the work done by the gases in expanding into a larger common volume from atomic mixing under the condition of no internal energy change, or work needed to restore the initial unmixed state. The effect of a mix-generated entropy increase is analytically shown to lead to less compression of the composite ICF fluid under adiabatic conditions. The amount of entropy generation is estimated to be similar to 10 J for a Rayleigh-Taylor-induced micrometer-scale annular mixing layer between the solid deuterium-tritium fuel and (undoped) high-density carbon pusher of an imploding capsule at the National Ignition Facility (NIF). This level of entropy generation is consistent with lower-than-expected fuel compressions measured on the NIF [Hurricane et al., Phys. Plasmas 26, 052704 (2019)]. The degree of entropy increase from mixing of high-Z hohlraum wall material and low-Z, moderate- to high-density gas fills is estimated to lead to similar to 100 kJ of heat generation for NIF-scale experiments [Moody et al., Phys. Plasmas 21, 056317 (2014)]. This value represents a significant fraction of the inferred missing x-ray drive energy based on observed delays in capsule implosion times compared with mainline simulations [Jones et al., Phys. Plasmas 19, 056315 (2012)]. Published under an exclusive license by AIP Publishing.

Automated summary

The increase in entropy from the physical mixing of materials in inertial confinement fusion and gas-filled hohlraums is assessed. This mix-driven entropy generation leads to less compression of the composite ICF fluid under adiabatic conditions. The heat generation from the entropy increase can be significant in experiments conducted at the National Ignition Facility.