On the gain scaling of ICF targets

A new gain model based on a adiabatic self-similar solution of the hydrodynamic equations is proposed for deuterium-tritium fusion capsules ignited by means of a thermonuclear spark at the fuel center. The model is applied to analyze gain curves that correspond to fixed values of the implosion velocity Uim. It is shown that the threshold energy investment into the fuel required for ignition scales as Ef,min α α3Uim−7 for capsules with initially thin shells, i.e. when the initial aspect ratio A0 ⪢ 1. In the opposite limit of initially thick capsule shells, the scaling of Ef,min with the entropy parameter a and the implosion velocity Uim, and that of the limiting fuel gain Gf∗ with Ef become ill defined; nevertheless, a fair agreement with the Livermore results is observed for α values between 1 and 2, and Uim ≈ 4 × 107 cm s−2.