Study of electron beam with modulated energy distribution for optical klystron FELs

The development of an intense and coherent light source is expected in the X-ray region, because of its many applications in this region. But it is difficult to obtain such a short wavelength with ordinary FEL using the resonator and conventional laser. SASE FEL without the resonator is a promising scheme due to the improvement of accelerator technology. The high power FEL in the 2—4 nm range has already been proposed at SLAC [1,2]. The quasi-stable optical klystron [3,4] can reduce the wiggler length significantly for a soft x-ray SASE FEL. According to the numerical study the gain curve of the quasi-stable optical klystron has multiple gain peaks with narrow width and high gain. Fig. 1a shows the gain curve of the quasi-stable operation of the optical klystron and modulated energy distribution of the electron beam coupling to the positive gain peaks. Fig. 1b represents the gain curve of the uniform wiggler. When the energy spread of an electron beam is larger than a gain peak, the FEL gain becomes very low due to the negative gain of the gain function. But if the distribution of electron energy is modulated and its modulation peaks couple to the positive peaks of the optical klystron gain function, we can obtain the high FEL gain although the total energy spread of the electron beam is large. With the latest technology of laser pulse shaping, it is possible to produce femtosecond pulses [5,6]. This pulse shaping apparatus called liquid crystal spatial light modulator (LC SLM). Two LC SLMs are combined between a pair of polarizes. When the LC modulator is operated by applying a voltage, the liquid crystals rotate towards the direction of propagation of light and produce the modified pulses. With this apparatus, the user can specify the waveform with arbitrary profiles. When the modulated laser that is obtained in this way irradiates the photocathode, the modulated electrons are extracted with the same temporal profile, because the response time of metal photocathode is of femtosecond order. This is a very important property of our concept. This is the advanced operation of quasi-stable optical klystron with energymodulated electron beam. The electrons extracted with temporal modulation are accelerated with an RF gun. Then these electrons are accelerated in different RF phases.