Energy spread effects in second harmonic waveguide FELs

It has been recently established that second harmonic waveguide free electron lasers (FELs) can significantly reduce electron energy required for strong laser amplification at a given frequency. Compared to conventional waveguide FELs, their interaction gain has a stronger dependence upon the wiggler field and as such it is preferable to operate them with large wiggler field to achieve high interaction gain. Given that the energy dependence of the electron velocity and hence the phase of the ponderomotive potential is likely to be amplified at large wiggler field, it is possible that the high gain anticipated with large wiggler field may be compromised with more severe energy spread effects. To this end, we use a recently developed numerical code for waveguide FELs to study energy spread effects in second harmonic waveguide FELs. Numerical examples are used to assess both the small and large wiggler cases. It is shown that the energy spread induced gain degradation remains relatively unchanged as the wiggler field increases. Instead the bandwidth of positive interaction is found as a dominant factor to control the gain degradation. Comparison with conventional waveguide FELs is also presented to reinforce the above finding. Therefore the wiggler field strength can be treated as a free design parameter and used to achieve large interaction gain without contributing to the energy spread induced gain degradation.