A method of varying the output of a free electron laser (FEL) on very short time scales to produce a slightly broader, but smooth, time-averaged wavelength spectrum. The method includes injecting into an accelerator a sequence of bunch trains at phase offsets from crest. Accelerating the particles to full energy to result in distinct and independently controlled, by the choice of phase offset, phase-energy correlations or chirps on each bunch train. The earlier trains will be more strongly chirped, the later trains less chirped. For an energy recovered linac (ERL), the beam may be recirculated using a transport system with linear and nonlinear momentum compactions M56, which are selected to compress all three bunch trains at the FEL with higher order terms managed.