Towards the petascale in electromagnetic modeling of plasma-based accelerators for high-energy physics

Plasma-based lepton acceleration concepts are a key element of the long-term R&D portfolio for the U.S. Office of High Energy Physics. There are many such concepts, but we consider only the laser (LWFA) and plasma (PWFA) wakefield accelerators. We present a summary of electromagnetic particle-in-cell (PIC) simulations for recent LWFA and PWFA experiments. These simulations, including both time explicit algorithms and reduced models, have effectively used terascale computing resources to support and guide experiments in this rapidly developing field. We briefly discuss the challenges and opportunities posed by the near-term availability of petascale computing hardware.