Characteristics of an envelope model for laser–plasma accelerator simulation

Simulation of laser–plasma accelerator (LPA) experiments is computationally intensive due to the disparate length scales involved. Current experiments extend hundreds of laser wavelengths transversely and many thousands in the propagation direction, making explicit PIC simulations enormously expensive and requiring massively parallel execution in 3D. Simulating the next generation of LPA experiments is expected to increase the computational requirements yet further, by a factor of 1000. We can substantially improve the performance of LPA simulations by modeling the envelope evolution of the laser field rather than the field itself. This allows for much coarser grids, since we need only resolve the plasma wavelength and not the laser wavelength, and therefore larger timesteps can be used. Thus an envelope model can result in savings of several orders of magnitude in computational resources. By propagating the laser envelope in a Galilean frame moving at the speed of light, dispersive errors can be avoided and simulations over long distances become possible. The primary limitation to this envelope model is when the laser pulse develops large frequency shifts, and thus the slowly-varying envelope assumption is no longer valid. Here we describe the model and its implementation, and show rigorous benchmarks for the algorithm, establishing second-order convergence and correct laser group velocity. We also demonstrate simulations of LPA phenomena such as self-focusing and meter-scale acceleration stages using the model.