Analytic models of high-temperature hohlraums

A unified set of high-temperature-hohlraum models has been developed. For a simple hohlraum, PS=[AS+(1-αW)AW+AH]σTR⁴+(4Vσ/c)(dTR⁴/dt), where PS is the total power radiated by the source, AS is the source area, AW is the area of the cavity wall excluding the source and holes in the wall, AH is the area of the holes, {σ} is the Stefan-Boltzmann constant, TR is the radiation brightness temperature, V is the hohlraum volume, and c is the speed of light. The wall albedo αW≡(TW/TR)⁴ where TW is the brightness temperature of area AW. The net power radiated by the source PN=PS-ASσTR⁴, which suggests that for laser-driven hohlraums the conversion efficiency ηCE be defined as PN/PLaser. The characteristic time required to change TR⁴ in response to a change in PN is 4V/c[(1-αW)AW+AH]. Using this model, TR, αW, and ηCE can be expressed in terms of quantities directly measurable in a hohlraum experiment. For a steady-state hohlraum that encloses a convex capsule, ${P}N={(1{-}{{α}}W{)A}W{+A}H+[(1{-}{{α}}C{)A}C{(A}S+{{α}}W{A}W{)/A}T]}{σ}{T}RC⁴,$ where ${{α}}C$ is the capsule albedo, ${A}C$ is the capsule area, ${A}T{≡}{(A}S{+A}W{+A}H),$ and ${T}RC$ is the brightness temperature of the radiation that drives the capsule. According to this relation, the capsule-coupling efficiency of the baseline National Ignition Facility hohlraum is 15--23 % higher than predicted by previous analytic expressions. A model of a hohlraum that encloses a z pinch is also presented.