In the conventional inverse free electron laser (IFEL), electron acceleration is done via the interaction of an intense laser beam and a wiggler with a sinusoidal field variation.We have studied the effect on IFEL performance usins a wiggler that creates a nearly squarewave periodic field pattern [1.2]. A novel numerical technique is described which models this wiggler [I]. We find stable orbits and an improvement in IFEL acceleration -gradient, resulting in a gain in energy by as much as a factor of two (equivalent to four times the laser power), when compared with the conventional IFEL with a sinusoidal field wiggler [3]. In an experiment, the magnetic field can be synthesized by running a conventional ferromagnetic wiggler into saturation.