“…However, one need not limit the choice of undulator field profile to the sinusoid, providing other profiles result in significant advantages. In connection with the IFEL accelerator, in the past we have pointed out [1] that the use of an undulator profile that approximates a" square wave" will result in an enhanced acceleration gradient, by as much as a factor of two (equivalent in effect to an increase of laser drive intensity by a factor of four), similar to the helical undulator. This improvement (essentially at the fundamental FEL resonance) results largely from the fact that, for a given peak undulator field amplitude, the rms electron acceleration obtained from the square wave undulator is larger than that from the sinusoid; furthermore, the electron orbit is stable as well.…”