Assessment of Radiation Trapping in Inertial Confinement Fusion Implosion Experiments Based on Characteristic Quantities of Simple Models

The “volume-burn” approach to inertial confinement fusion utilizes a “pushered” shell to minimize the escape of thermal energy from the hot spot prior to ignition. Single-shell pushered implosions utilize an opaque high-Z inner shell lining to “trap” the radiation that would otherwise escape the core, cooling the fuel below the temperature required for ignition. We explore the physics of radiation trapping by means of existing analytic physical models and numerical radiation-hydrodynamic simulations, presenting simple metrics for the effectiveness of radiation trapping, not only in igniting implosions, but also in near-term experiments intended to demonstrate radiation-trapping effects. The Marshak wave model is extended to allow for converging geometry and simple hydrodynamic motion of the stagnating shell and is used to demonstrate relationships among the thermal energy of the fuel, the reduction of radiative flux escaping the fuel, and properties of the opaque shell surrounding the fuel that determine its effectiveness as a radiation trap. Implications of this model for future directions will also be presented. This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award Number DE-NA0003856.