Off-axis electron orbits in free-electron-laser beams of finite thickness, subjected to combined helical wiggler and axial guide fields, have been studied analytically. A semiempirical equation for the electron velocity components, averaged over the electron’s oscillatory (betatron) motion, has been derived as a function of the radial displacement of the electron guiding center. The predictions from the equation are compared with single-particle numerical simulations, and with free-electron-laser experiments. Good agreement is found.

• Received 5 August 1985

DOI:https://doi.org/10.1103/PhysRevA.32.3448