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 to conserve it until its used in the machine undulator. One of the non recoverable emittance increase is the collision of the electron beam during its transport with the residual gas. Based on previous work by others, we have derived a useful expression of emittance increase for electrons of any energy and cross check its validity for energies above 100 MeV with an analytical formula.
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