High power self-similar radiation pulse in a free electron laser

Using 1D short wavelength (8 μm) Compton free electron laser (FEL) equations with slippage, we explore propagation of a high power pulse down a tapered undulator FEL travelling wave amplifier. For an appropriate taper, a short pulse (∼300 fs FWHM) with regular features will propagate self-similarly as it grows in power, slipping through a much longer electron pulse. The power spectrum of the pulse is nearly Gaussian with no sidebands. The electron energy is depressed by ∼33%, but slippage causes the peak pulse intensity to be about the same as the electron beam power density, ∼10 TW/cm2.