Beam lines using echo-enabled harmonic generation can be designed to have extremely low sensitivity to energy chirps in the electron beam, as shown through theory and detailed simulations. These designs would allow stable and coherent radiation to be produced even when using electron beams with a large amount of shot-to-shot jitter in the longitudinal profile. DOI: 10.1103/PhysRevSTAB.17.110707 PACS numbers: 41.60.Cr, 42.65.Ky
I. MOTIVATIONA major motivation for seeding a free-electron laser (FEL) with external lasers is to achieve stable output with coherent pulses having a time-bandwidth product close to the transform limit. While the quality of the seed laser itself is important, any nonuniformity in the electron bunch can also lead to variations in both the power and phase of the output pulse. Gradients in the local average (slice) electron energy are particularly deleterious to output mode quality, especially when a high harmonic of the initial seed laser is desired. Harmonic generation typically requires a dispersive element such as a chicane which shifts different parts of the beam by a distance proportional to the local energy offset. An initially coherent signal can become highly degraded in quality after a combination of longitudinal dispersion and harmonic upshifting.Echo-enabled harmonic generation (EEHG) [1] uses phase mixing to combine the energy modulations from two input lasers with wavelengths λ 1 and λ 2 , producing bunching at a wavelength λ X . The corresponding wave numbers k ≡ 2π=λ are related by k X ¼ pk 2 − mk 1 , where p and m are integers. Sign conventions are chosen so p and m are typically positive. A chicane is placed after each modulating undulator with dispersion R 1 and R 2 . The convention used here is that drifts and simple chicanes have dispersion R 56 > 0.The EEHG scheme is inherently less sensitive than high gain harmonic generation (HGHG) [2] to energy chirps in the electron beam [3,4]. Through careful adjustment of the parameters for EEHG, this sensitivity will be further reduced to the point where slice energy variations comparable to the FEL bandwidth itself introduce only modest phase errors. Following this prescription allows even an electron beam with large energy chirps that fluctuate from shot to shot to generate stable and coherent radiation. The technique of coupling multiple inputs through phase mixing is used in other fields such as magnetic resonance and plasma physics. The added flexibility from allowing for reduced coupling could be useful in a wide range of systems to enhance stability or coherence.
II. ANALYSISIn the HGHG scheme, microbunches experience a longitudinal displacement of roughly Δz ≃ R 56η as they pass through a chicane, whereη is the relative offset of the average electron energy in the microbunch from the nominal energy. These displacements change the phase of the complex bunching parameter, defined asb ≡ hexpð−ihk 1 zÞi at the harmonic h of an input laser with wavelength λ 1 . The resulting phase shift is given byThe quantity ΔΨ will also b...