Plasma based laser Wakefield accelerators (LWFA) have been a subject of interest in the plasma community for many years. In LWFA schemes the laser pulse must propagate several centimeters and maintain its coherence over this distance, which corresponds to many Rayleigh lengths. These Wakefields and their effect on the laser can be simulated in the quasistatic approximation. The 2D, cylindrically symmetric, quasistatic simulation code, WAKE is an efficient tool for the modeling of short-pulse laser propagation in under dense plasmas [P. Mora & T.M. Antonsen Phys. Plasmas 4, 1997]. The quasistatic approximation, which assumes that the driver and its wakefields are undisturbed during the transit time of plasma electrons, through the pulse, cannot, however, treat electron trapping and beam loading.

Here we modify WAKE to include the effects of electron trapping and beam loading by introducing a population of beam electrons. Background plasma electrons that are beginning to start their oscillation around the radial axis and have energy above some threshold are removed from the background plasma and promoted to "beam" electrons. The population of beam electrons which are no longer subject to the quasistatic approximation, are treated without approximation and provide their own electromagnetic field that acts upon the background plasma. The algorithm is benchmarked to OSIRIS (a standard particle in cell code) simulations which makes no quasistatic approximation. We also have done simulation and comparison of results for centimeter scale GeV electron accelerator experiments from LBNL. These modifications to WAKE provide a tool for simulating GeV laser or plasma wakefield acceleration on desktop computers.