On the scaling of the energy gain of ICF targets

摘要

A new gain model based on an adiabatic self-similar solution of the hydrodynamic equations is proposed for inertial confinement fusion (ICF) targets ignited by means of a thermonuclear spark at the fuel centre. The model is applied to analyse gain curves corresponding to fixed values of the implosion velocity Uim. It is shown that the adequate ignition criterion, allowing for the inertia of the cold fuel, implies ρsRsTs varies as Uim at the time of ignition, as contrasted to fixed values of the spark areal density, ρsRs, and the temperature, Ts, assumed in many of the earlier publications. The modified ignition condition leads to the scaling Emin varies as α3Uim-7 and Gf* varies as (E/α3)0.4 for the ignition energy threshold, Emin, and the limiting fuel gain, Gf*, of ICF capsules; α is the isentrope parameter of the cold fuel, E is the energy invested in the DT fuel. Stability and symmetry constraints do not affect this scaling when the initial aspect ratio of the fusion capsule A0 1; in the opposite case of initially thick capsule shells, the scaling of Emin and Gf* with Um, and α becomes ill defined.