A simple method for the determination of the structure of ultrashort   relativistic electron bunches
  In this paper we propose a new method for measurements of the longitudinal profile of 100 femtosecond electron bunches for X-ray Free Electron Lasers (XFELs). The method is simply the combination of two well-known techniques, which where not previously combined to our knowledge. We use seed 10-ps 1047 nm quantum laser to produce exact optical replica of ultrafast electron bunches. The replica is generated in apparatus which consists of an input undulator (energy modulator), and the short output undulator (radiator) separated by a dispersion section. The radiation in the output undulator is excited by the electron bunch modulated at the optical wavelength and rapidly reaches 100 MW-level peak power. We then use the now-standard method of ultrashort laser pulse-shape measurement, a tandem combination of autocorrelator and spectrum (FROG -- frequency resolved optical gating). The FROG trace of the optical replica of electron bunch gives accurate and rapid electron bunch shape measurements in a way similar to a femtosecond oscilloscope. Real-time single-shot measurements of the electron bunch structure could provide significant information about physical mechanisms responsible for generation ultrashort electron bunches in bunch compressors. The big advantage of proposed technique is that it can be used to determine the slice energy spread and emittance in multishot measurements. It is possible to measure bunch structure completely, that is to measure peak current, energy spread and transverse emittance as a function of time. We illustrate with numerical examples the potential of the proposed method for electron beam diagnostics at the European X-ray FEL. 
E.L. Saldin, E.A. Schneidmiller, and M.V. Yurkov