vertical direction, inducing a correlation between the temporal distribution and the vertical displacement. The bending magnet chromatically disperses the electrons in the horizontal plane, making the information about the beam energy profile available along that direction. The beam longitudinal phase space can then be visualized on a fluorescent YAG crystal + CCD camera system placed downstream, as shown in Fig. \[Figure\_ebeam\_measurement\]. This particular $E(t)$ distribution corresponds to the configuration in which most of the results presented in this paper have been obtained. The energy profile is very close to a parabola with a quite small linear component (i.e., ) and a much more significant quadratic component with . In Section \[simulations\] we consider the impact of this quadratic component upon double peak formation.

As shown in the right panel of Fig. \[Figure\_ebeam\_measurement\], the current profile is almost flat in the middle of the bunch, even if a slow ramp towards the tail can be noticed. Experimentally, there is a typical shot-to-shot jitter of $\approx 50\,$fs of the relative electron beam-seed timing. This jitter in conjunction with current inhomogeneities results in a fluctuation of the FEL power, as the seed “explores” different temporal portions of the beam. This effect may be 