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It is reported that [Z. Huang et al., Phys. Rev. Lett. 109, 204801 (2012)],high-gain free-electron laser (FEL) can be generated by transverse-dispersedelectron beams from laser-plasma accelerators (LPAs) using transverse-gradientundulator (TGU) assuming an ideal constant dispersion function without focusingoptics. The constant dispersion function keeps electrons beyond the resonantenergy bandwidth still being on resonant with the FEL radiation. Instead, inthis paper, the case with focusing optics in an LPA-driven FEL using TGU isnumerically studied, in which the dispersion function should be monotonouslydecreasing along the undulator. Even though the FEL resonance is not alwayssatisfied for off-energy electrons in this case, through subtly optimizing theinitial dispersion and focusing parameters, it is feasible to achieve a similarradiation power to the case assuming an ideal constant dispersion functionwithout focusing optics, and meanwhile, to attain a good transverse coherence.Moreover, higher radiation power could be expected if longitudinally tapering,transverse-gradient variation in different sections are systematicallyconducted, which is demonstrated with intense global multiparametersoptimizations based on GENESIS simulation.

Improving the energy-extraction efficiency of laser-plasma accelerator  driven free-electron laser using transverse-gradient undulator with focusing  optics and longitudinal tapering