ON THE SCALING OF THE ENERGY GAIN OF ICF TARGETS

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 U-im. It is shown that the adequate ignition criterion, allowing for the inertia of the cold fuel, implies p(s)R(s)T(s) proportional to U-im at the time of ignition, as contrasted to fixed values of the spark areal density, p(s)R(s), and the temperature, T-s, assumed in many of the earlier publications. The modified ignition condition leads to the scaling E(min) proportional to alpha(3)U(im)(-7) and G(f)* proportional to (E/alpha(3))(0.4) for the ignition energy threshold, E(min), and the limiting fuel gain, G(f)*, of ICF capsules; alpha 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 A(0) >> 1; in the opposite case of initially thick capsule shells, the scaling of E(min), and G(f)* with U-min and alpha becomes ill defined.