Frequency redshift of seeded FEL radiation generated with a low-energy chirped electron beam

One method to achieve coherent radiation in a free-electron laser (FEL) driven by a laser-plasma accelerator is to reduce the electron beam slice energy spread by stretching the beam in a chicane, producing a linear energy chirp. Seed radiation at the resonant wavelength propagating in an undulator with the energy-chirped beam may be coherently amplified. With such a linear-energy-chirped beam, it is observed in simulations using Genesis 1.3 that the peak frequency of the seeded FEL radiation redshifts linearly with the amount of electron beam chirp and the undulator propagation distance, and inversely with the undulator wavelength and electron energy. This observed FEL radiation redshifting is explained by the dispersion of the microbunching structures during propagation due to the energy chirp of the electron beam, and analysed using the coupled Maxwell-Vlasov equations. Implications for planned laser-plasma accelerator driven FEL experiments at the BELLA Center are discussed.