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In order to ensure proper SASE lasing of a fourth Generation light source,one of the goal is to produce an electron beam of small emittance and toconserve it until its used in the machine undulator. One of the non recoverableemittance increase is the collision of the electron beam during its transportwith the residual gas. Based on previous work by others, we have derived auseful expression of emittance increase for electrons of any energy and crosscheck its validity for energies above 100 MeV with an analytical formula.

Emittance Growth by Beam-Gas Scattering in Single Pass Accelerator