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A novel definition for the three-dimensional free electron laser gain length is proposed [1], which takes into account the increase of electron beam projected emittance as due, for example, to geometric transverse wakefield and coherent synchrotron radiation developing in linear accelerators. The analysis shows that the gain length is affected by an increase of the electron beam projected emittance, even though the slice (local) emittance is preserved, and found to be in agreement with Genesis code simulation results. It is then shown that the minimum gain length and the maximum of output power may notably differ from the ones derived when collective effects are neglected. The proposed model turns out to be handy for a parametric study of electron beam sixdimensional brightness and FEL performance as function, e.g., of bunch length compression factor, accelerator alignment tolerances and optics design.

Estimate of free electron laser gain length in the presence of electron beam collective effects