Efficient start-to-end 3D envelope modeling for two-stage laser wakefield acceleration experiments

Three dimensional Particle in Cell simulations of Laser Wakefield Acceleration require a considerable amount of resources but are necessary to have realistic predictions and to design future experiments. The planned experiments for the Apollon laser also include two stages of plasma acceleration, for a total plasma length of the order of tens of millimeters or centimeters. In this context, where traditional 3D numerical simulations would be unfeasible, we present the results of the application of a recently proposed envelope method, to describe the laser pulse ant its interaction with the plasma without the need to resolve its high frequency oscillations. The implementation of this model in the code Smilei is described, as well as the results of benchmark simulations against standard laser simulations and applications for the design of two stage Apollon experiments.