| Summary: | We analytically estimated the three-dimensional free electron laser (FEL) power gain length’s increase due to the collective effects of an ultrarelativistic electron beam, namely, geometric transverse wakefield, coherent synchrotron radiation, and microbunching instability. We showed that the gain length is affected by an increase of the electron beam projected emittance, even though the slice (local) emittance is preserved. We also proved that the minimum gain length and the maximum of output power may notably differ from the ones derived when collective effects are neglected. Finally, we demonstrated that our model may be handy for a parametric study of electron beam six-dimensional brightness and FEL performance as a function, e.g., of the bunch length compression factor, the accelerator alignment tolerances, and the optics design.
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