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 ρ s R s T s varies as U im at the time of ignition, as contrasted to fixed values of the spark areal density, ρ 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 varies as α 3 U im -7 and G f * varies as (E/α 3 ) 0.4 for the ignition energy threshold, E min , and the limiting fuel gain, G f *, 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 A 0 >> 1; in the opposite case of initially thick capsule shells, the scaling of E min and G f * with U m , and α becomes ill defined