Harmonic operation of a free-electron laser.

Harmonic operation of a free-electron-laser amplifier is studied. The key issue investigated here is suppression of the fundamental. For a tapered amplifier with the right choice of parameters, it is found that the presence of the harmonic mode greatly reduces the growth rate of the fundamental. A limit on the reAection coefficient of the fundamental mode that will ensure stable operation is derived. The relative merits of tripling the frequency by operating at the third harmonic versus decreasing the wiggler period by a factor of 3 are discussed. A free-electron laser (FEL) produces coherent radiation when an electron beam passes through a spatially periodic magnetic field (called a wiggler). The frequency of the amplified radiation is determined by the condition that the Doppler-shifted frequency of the radiation, viewed in the beam frame, coincides with a harmonic of the Doppler-shifted frequency of the wiggler. As a result , the frequency scales as the harmonic number times the square of the beam voltage divided by the wiggler period. ' Because of the favorable scaling with voltage, FELs show promise for operating at high frequencies. However, there are technological limits on attainable voltages, and the gain falls off rapidly with decreasing wiggler period (we give explicit scaling of gain versus frequency below). Thus, to reach ultrahigh frequencies it may be advantageous to operate at a harmonic of the fundamental frequency. The existence of higher harmonics in the emission spectrum of a FEL was predicted in a number of theoretical publications, ' and has been measured in several experiments. However, these experiments were designed to operate in the fundamental mode; harmonic generation , which was weak, was merely a by-product associated with bunching of the electron beam in a linearly polarized wiggler. It would be desirable to construct a FEL in which the harmonic mode, rather than the fundamental , dominated. The primary difficulty with such an approach is that the fundamental mode has a larger growth rate than the harmonic, and tends to dominate in the nonlinear regime. This is an especially serious problem in an oscillator as experiments run for many growth times. In an amplifier with an injected signal, on the other hand, it is only necessary to reduce the growth rate of the fundamental enough so that its amplitude is still small at the end of the device. For this reason we investigate an amplifier in which a signal is …