Progress toward a self-consistent set of 1D ignition capsule metrics in ICF

Abstract

One-dimensional metrics can be considered an upper bound on the performance that can be achieved given an implosion with an imploding mass Mimp and a given adiabat α, driven to an implosion velocity V by a specified ablation pressure Pa for single shell capsules with low-opacity ablators. The quantitative value of an ignition metric depends on the definition of ignition. We review the choices that have been made by various authors before settling on a definition based on yield amplification of 30 where yield amplification is the ratio of the yield from an implosion that includes the alpha particle and neutron deposition relative to the yield obtained from PdV work alone. We then derive improved 1D ignition metrics for radiation-driven inertial confinement fusion targets that span a wide range of drive pressures, adiabats, and scales. This includes emphasizing the importance of the total imploding mass and kinetic energy inside the ablation front, including the remaining ablator mass and kinetic energy, on the 1D ignition metrics. We have also explicitly included the sensitivity to ablation pressure driving the implosion, as well as the sensitivity to the coupling efficiency between the total incoming kinetic energy and the hot spot. For implosions in which the remaining ablator mass contributes to the total stagnated mass, we have developed an approach based on defining an effective implosion adiabat which incorporates the properties and the mass of the stagnated ablator as well as the cold DT fuel. We have added a dependence on total ρr to account for the fact that the time available for self-heating increases as the total ρr increases. This extends previous work in that the value of the product of stagnation pressure times burn width required for ignition depends on the total ρr as well as on the fuel ion temperature. Additionally, we show that ignition metrics derived from a requirement on the product of the hotspot ρr and the hot spot temperature are equivalent to ignition metrics derived from a requirement on the product of stagnation pressure and burn width. Further, we discuss those ignition metrics, developed as metrics for the underlying hydrodynamics in the absence of alpha heating, which can be used when alpha heating is present.