Previous experimental and numerical results have shown that in multi-MeV Bremsstrahlung x-ray sources created by picosecond laser pulses, the delivered on-axis dose increases if the laser interacts with under-critical plasmas. The effect of the laser-plasma interaction as a function of the plasma density gradient is thus first studied here, by focusing the short pulse of the Alisé laser on a solid tantalum target coated with plastic. Interaction conditions are modified by irradiating the target front side with a secondary nanosecond heating beam, prior to the main pulse. The length of the expanding plasma is modified by adjusting the delay between the interaction and heating beams. Various diagnostics give access to a whole set of consistent experimental results on the x-ray source properties which are compared successfully to self-consistent numerical simulations obtained with coupled PIC and Monte Carlo codes. All source parameters increase as the plasma length increases, in reason of the increasing number of high-energy electrons near the axis. In a second part of this talk, we use our simulation tools to predict the x-ray and neutron (produced by photonuclear interactions in the target) flash characteristics that can be expected on future PW lasers. Favourable scaling laws for the production of an intense, directional and short duration x-ray source versus intensity are observed. However, these findings also stress that radioprotection will become an important issue for future petawatt lasers operating at the kJ level.< Réduire