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Modern x-ray free-electron lasers (XFELs) produce x-ray pulses of exceptionaltransverse coherence. This is due largely to the process of optical guiding bywhich the radiation is both refractively guided by the bunched electron beamand gain guided by the preferential amplification of on-axis radiation. Theseeffects may be summarized by an effective index of refraction, which has beenused in the past to study the transverse dynamics of the FEL process withsignificant simplifications and approximations, but never fullyself-consistently. We present here a self-consistent method for studying highgain FELs in the linear regime by approximating the FEL equations tosecond-order in the lateral displacement from the nominal electron beam axis.This is made possible by casting the FEL equations in the language of opticalfibers with an appropriately chosen refractive index. We demonstrate that thisapproach is both fast and highly accurate, indicating that the most importantFEL dynamics are inherently second-order. In its full form our method cancapture the effects of transverse offsets in both the x-ray beam and theelectron beam, making it a versatile tool for studying non-ideal effects inseeded FELs, regenerative amplifier XFELs, and even self-amplified spontaneousemission (SASE) FELs.

A self-consistent refractive index model for fast simulation of free-electron lasers