Di Mitri, S. MOP079 FEL electron emittance undulator brightness 2015 2015-12 Linear accelerators delivering high brightness electron beams are essential for driving short wavelength, high gain free-electron lasers (FELs). The FEL radiation output efficiency is often parametrized through the power gain length that relates FEL performance to the electron beam quality at the undulator. Experimental data and simulation results of existing and planned FEL facilities are used to explicit the relationship between the FEL output wavelength and the electron beam six-dimensional brightness*. Practical formulas are provided that show the dependence of the exponential gain length on the beam brightness**.