  Improving the description of the equation of state (EoS) of deuterium-tritium
(DT) has recently been shown to change significantly the gain of an Inertial
Confinement Fusion (ICF) target (Hu et al., PRL 104, 235003 (2010)). We use
here an advanced multi-phase equation of state (EoS), based on ab initio
calculations, to perform a full optimization of the laser pulse shape with
hydrodynamic simulations starting from 19 K in DT ice. The thermonuclear gain
is shown to be a robust estimate over possible uncertainties of the EoS. Two
different target designs are discussed, for shock ignition and self-ignition.
In the first case, the areal density and thermonuclear energy can be recovered
by slightly increasing the laser energy. In the second case, a lower in-flight
adiabat is needed, leading to a significant delay (3ns) in the shock timing of
the implosion.
