On the gain scaling of ICF targets

Abstract

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 U im . It is shown that the threshold energy investment into the fuel required for ignition scales as E f,min α α 3 U im −7 for capsules with initially thin shells, i.e. when the initial aspect ratio A 0 ⪢ 1. In the opposite limit of initially thick capsule shells, the scaling of E f,min with the entropy parameter a and the implosion velocity U im, and that of the limiting fuel gain G f ∗ with E f become ill defined; nevertheless, a fair agreement with the Livermore results is observed for α values between 1 and 2, and U im ≈ 4 × 10 7 cm s −2.