Transverse pulse shaping and optimization of a tapered hard X-ray free electron laser

Multidimensional optimization schemes for TW hard X-Ray free electron lasers are applied to the cases of transversely uniform and parabolic electron beam distributions and compared to examples of transversely Gaussian beams. The optimizations are performed for a $200$m undulator and a resonant wavelength of $\lambda_r=1.5\AA $ using the fully 3-dimensional FEL particle code GENESIS. Time dependent simulations showed that the maximum radiation power is larger for flatter transverse distributions due to enhanced optical guiding in the tapered section of the undulator. For a transversely Gaussian beam the maximum output power was found to be $\text{P}_{max}$=$1.56$ TW compared to $2.26$ TW for the parabolic case and $2.63$ TW for the uniform case. Spectral data also showed a 30-70$\%$ reduction in energy deposited in the sidebands for the uniform and parabolic beams compared with a Gaussian. An analysis of the maximum power as a function of detuning from resonance shows that redshifting the central wavelength by $\Delta \lambda / \lambda <\rho$ increases the power for all three transverse electron distributions.