Effects of Wiggler Taper Rate and Signal Field Gain Rate in Free-Electron Lasers

摘要

Derived is a dimensionless formulation of the motion of electrons in free electron lasers with tapered wigglers and systematically account for 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 wave length to wiggler period, and kappa, the square of the ratio of the plasma frequency to signal frequency. We identify two distinguished limits governing the relation between mu and epsilon, and three distinguished limits governing the relation between kappa and epsilon. 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. (ERA citation 12:041619)