UP-FREQUENCY CONVERSION IN A 2-RESONANT-WAVE HIGH-GAIN FREE-ELECTRON-LASER AMPLIFIER

A free-electron laser is able to resonate at two different frequencies , both in free space an in a waveguide. The two waves have positive an d negative slippage. We describe the nonlinear interaction between the two waves by a set of partial differential equations which in free sp ace do not require the slowly varying envelope approximation (SVEA). I n a waveguide a less restrictive SVEA is applied to each wave. By inje cting a small signal at the low frequency, a strong signal and bunchin g are produced at the high frequency. This effect suggests a new metho d of generating short wavelength radiation.