Fig. 1. Spherical target and main coordinate system []; vector direction of a generic surface element and versor of the th laser beam, ; coordinate system [, ] for the th laser intensity profile.

Fig. 2. Optimal laser intensity profiles (north hemisphere) for an axially symmetric beam configuration. The intensity profiles have been normalized to one () and the scale colour ranges from 0 to 1. Full dots correspond to the north pole and the grey curve is the equator projection on the focal planes.

Fig. 3. Polar coordinates of 40 quads of the LMJ facility. Quads for the configurations A and B; red quads of the north hemisphere (C) and blue quads of the south hemisphere (D).

Fig. 4. Optimal laser intensity profiles normalized to one (north hemisphere) for the LMJ configurations A–D. The power imbalance is given by the parameter and the laser intensity scale colour varies linearly from 0 to 1.