Spontaneous emission of an electron beam in a quasiperiodic Wiggler magnet configuration

Summary form only given. In a recent paper, we have studied an unusual FEL interaction mechanism in which the electron beam is premodulated at two different frequencies (Kong et al., 1997). We have shown that if the the two modulation frequencies are not integrally but irrationally related then considerable radiation is generated at frequencies that are irrational multiples of the fundamental FEL radiation frequency. The generation of these irrationally related harmonics modifies the basic FEL mechanism and as such they may be utilized to manipulate the FEL spectrum. In this contribution, we extend our previous results and consider the realization of electron beam modulation at two irrationally related frequencies by means of a quasiperiodic wiggler configuration consisting of two conventional periodic wigglers. In order to understand the characteristics of this quasiperiodic wiggler configuration, spontaneous emission of a general dual-wiggler structure is formulated. Number theory arguments are then used to derive the resonant condition for an FEL interaction in an infinitely long quasiperiodic wiggler. Subsequently numerical examples are used to demonstrate that significant radiations can be generated simultaneously at both the usual FEL harmonics, which are integer multiples of the fundamental FEL radiation frequency, and the irrationally related harmonics. When the interference between the two constituent wigglers of the quasiperiodic wiggler configuration is appropriately adjusted and enhanced, the integrally related harmonics are suppressed considerably. This may be used to relieve the problem of mirror degradation for some FEL´s operated at ultraviolet and X-ray wavelengths.