Adiabat Shaping in Direct Drive Inertial Confinement Fusion Implosions through the Decaying Shock Approximation

We consider the implosions of a double-layer spherical target driven by a two-step pressure pulse. By employing the decaying shock approximation the adiabat of the entropy is shaped, following a simple power law in agreement with the established theoretical models. Then we directly calculate the optimum adiabat parameter for three different fuel density states and find that the higher the initial density is, the lower adiabat parameter. Although the calculated adiabat values are close to ones obtained in previous investigations, they are achieved for relatively fast irradiation times and low laser intensity.