For compact short-Rayleigh length free electron lasers(FELs), the area of the optical beam can be thousands oftimes greater at the mirrors than at the beam waist. A fixednumerical grid of sufficient resolution to represent the narrowmode at the waist and the broad mode at the mirrorswould be prohibitively large. To accommodate this extremechange of scale with no loss of information, we employ acoordinate system that expands with the diffracting opticalmode. The simulation using the new expanding coordinateshas been validated by comparison to analytical cold-cavitytheory, and is now used to simulate short-Rayleigh lengthFELs.
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