Off-axis electron orbits in realistic helical wigglers for free-electron-laser applications

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.