A spherical target irradiated by laser beams located at 49o and 131° with respect to the polar axis has been considered. The illumination model has been used to evaluate the irradiation non-uniformity assuming circular and elliptical super-Gaussian laser intensity profiles and the irradiation scheme has been optimized by means of the polar direct drive technique. A parametric study has been performed providing the irradiation non-uniformity as a function of the polar direct drive displacement and of the laser intensity profile parameters. Moreover, two-dimensional axis-symmetric hydrodynamic simulations have been performed for a plastic sphere irradiated by laser beams characterized by a constant flat temporal power pulse. In these simulations, the front of the inward shock wave has been tracked providing the time-evolution of any non-uniformity. The results provided by the two methods — illumination model and hydrodynamic data — have been compared and it is found that the illumination model reproduces the main behavior exhibited by the hydrodynamic data. The two models provide compatible values for the optimum polar direct drive parameter and similar optimal super-Gaussian profiles.

We present a 2D analysis of direct-drive shock ignition for the laser Megajoule. First, a target design is chosen in the HiPER-like target family generated by scale up and down of the original HiPER target. A first analysis is done considering the 1D fuel assembly and 2D shock ignition by means of the ring at polar angle of 33°2. The intensity profile is top-hat and calculations are done for several different radii. It is shown that larger the radius, lower the minimum spike power is. In addition, the intensity in each quad can stay below 4 × 1014 W/cm2 and is considered non crucial for parametric instabilities such as two plasmons. A 2D analysis of the fuel assembly is done in a second step by considering the two rings located at 49° and 59°5 and their symmetric by the equatorial plane symmetry. It is shown that low mode asymmetries are important at the stagnation and can significantly affect the areal density obtained. Finally, full 2D calculations of shock ignition is done, using all the beams of the LMJ and show that the spike power needed for ignition and gain is increased by a factor greater than 3 regarding the power needed in perfectly isotropic fuel assembly. This increase is mainly due to high level low mode asymmetries generated during fuel assembly.