We address full particle-in-cell simulations of the next generation of Laser Wakefield Accelerators with energy gains > 10 GeV. The distances involved in these numerical experiments are very demanding in terms of computational resources and are not yet possible to (easily) accomplish. Following the work on simulations of particle beam-plasma interaction scenarios in optimized Lorentz frames by J.-L. Vay*, the Lorentz transformation for a boosted frame was implemented in OSIRIS**, leading to a dramatic change in the computational resources required to model LWFA. The critical implementation details will be presented, and the main difficulties discussed. Quantitative comparisons between lab/boost frame results with OSIRIS, QuickPIC***, and experiment will be given. Finally, the results of a three-dimensional PIC simulation of a > 10 GeV accelerator stage will be presented, including a discussion on radiation emission.

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