Quasi-analytical description of sideband generation in a FEL

The connection is established between the one-dimensional model and the sidebands in the square pulse two-dimensional problem. The features occurring in the square pulse problem are shown to be directly derived from the energy loss curve for the one-dimensional problem. Incidentally this work also provides a numerical check for two-dimensional (z,t) calculations. In any such calculation numerical diffusion and roundoff alter results. This quasi-analytical technique provides answers that are limited only by the ability to compute the much simpler one-dimensional problem