Strong wiggler field assisted amplification in a second-harmonic waveguide free electron laser

As a technique to reduce the size of compact waveguide free electron lasers (FELs) operated from microwave to the far infrared, a longitudinal interaction mechanism was recently proposed to operate waveguide FELs at the second harmonic. With a gain formulation based on Madey’s theorem in the limit of small wiggler field, it was shown analytically that second harmonic waveguide FELs can reduce significantly the electron energy required for radiation at a given frequency. As it is advantageous to operate second harmonic waveguide FELs with strong wiggler field, Madey’s theorem is used here to reformulate their interaction gain for strong wiggler fields up to [....] with the axial electron velocity Taylor expanded to the eighth order of the wiggler field. Given that Madey’s theorem has not been established for second harmonic waveguide FELs, their interaction gain is also formulated independently by solving their pendulum equation without recourse to Madey’s theorem. These two gain formulas are not analytically identical, but numerically they lead to an excellent agreement over a wide range of system parameters, thus confirming the applicability of Madey’s theorem. The interaction analyses presented form a thorough and detailed description of second harmonic waveguide FELs in the small-signal regime and for wiggler field that is both practical and beneficial

Nonlinear amplification in a second-harmonic waveguide free-electron laser

This paper describes the results of numerical simulation of second-harmonic waveguide free-electron lasers (FELs) from the small-signal regime to the large-signal regime. Aimed at reducing the size and hence the cost of compact waveguide FELs operated from the microwave to the far infrared, these unconventional waveguide FELs can substantially decrease the minimum electron energy required for strong FEL radiation at a given frequency while increasing the small-signal gain. This contribution focuses on their saturation behaviors, taking into consideration variation in wiggler field and electron-energy spread. Depending on the roundtrip power loss within the FEL cavity and the initial electron-energy spread, the computed relationship between interaction gain and in-cavity power can be used to maximize the output power at a given electron current. Furthermore, it is found that gain degradation due to electron-energy spread remains relatively unchanged regardless of radiation power and wiggler field