Phase-matching segmented wigglers in free-electron lasers

Since many free-electron lasers use a segmented undulator, it is important to understand the requirements on phase matching between the undulators. A simulation that self-consistently determines the phase slippage between the light and the electrons is used to study these effects, The simulation is found to be in agreement with an analytic formulation of the phase slippage. A seeded x-ray free-electron laser is studied which makes use of a segmented undulator with quadrupoles in the gaps to provide strong focusing. Optimal performance is found for gap lengths corresponding to a phase slippage within about 20% of a wavelength through a unit cell consisting of an undulator and gap.