The effects of wiggler taper rate and signal field gain rate in free-electron lasers

A dimensionless formulation of the motion of electrons in free-electron lasers (FEL) with tapered wigglers is derived that takes into account the cumulative effects of tapering and signal field gain. The mathematical problem involves three small parameters: epsilon , measuring the slowness of spatial variations of the wiggler field; mu , the ratio of signal wavelength to wiggler period, and kappa , the square of the ratio of the plasma frequency to signal frequency. Two limits governing the relation between mu and epsilon and three limits governing the relation between kappa and epsilon are identified. The mathematical problems which result consist of the solution of strictly nonlinear oscillators with slowly varying parameters and small perturbation terms. Techniques from the asymptotic theory of nonlinear oscillations are used to derive results pertinent for FEL problems.<>