Coherent Harmonic Radiation

Abstract

In this chapter, we discuss harmonic generation in free-electron lasers. Harmonic generation in free-electron lasers occurs by both linear and nonlinear mechanisms. The principal difficulty with linear harmonic generation, however, is that the beam quality requirement associated with the growth rate of the linear instability increases with the harmonic number. Nonlinear harmonic generation is driven parasitically off of a high-power fundamental and is less sensitive to the electron beam quality than the linear instability. Harmonics are not commonly seeded in free-electron lasers. The growth of harmonic radiation starts by a combination of shot noise on the electron beam and the initiation of harmonic bunching due to the growth of power at the fundamental. This gives rise to a rapid initial growth of the harmonic power which quickly rolls over to the slower growth associated with the linear instability. The linear instability drives harmonic growth until the fundamental reaches a power level necessary for the nonlinear mechanism to take over, after which the harmonic power grows exponentially with a growth rate that scales as the product of the harmonic number and the growth rate of the fundamental. In this regime, the harmonic grows substantially faster than the fundamental until the harmonic saturates. Saturation of the harmonic typically occurs slightly prior to that of the fundamental due to over-bunching of the electrons at the harmonic wavelengths.