## 3 FEL Performances
### Energy Per Pulse & Temporal Jitter  
This dramatic increase of the longitudinal coherence with respect to a SASE source is only the first evident advantage of starting the amplification process from an external seed. The seed introduces indeed a number of additional handles to control amplification and the resulting output pulse properties. The central emission frequency at the lowest order of approximation is determined by the harmonic of the seed laser. The central emission frequency jitter is therefore normally lower than the linewidth by up to an order of magnitude. A SASE source is characterized by an intrinsic pulse energy fluctuation associated with the startup from the electron shot noise. From this point of view a seeded FEL is, conversely, a completely deterministic system. The fluctuations of the pulse energy are determined by fluctuations of the external parameters driving the amplifier, as the energy of the electron beam, the timing between electrons and seed, and the intensity of the seed itself. The energy jitter may be lower than 5%, as in the example shown in Figure 5, where the histogram of the energy per pulse from FEL-1 in optimized conditions at 51 nm is displayed. This value may be compared to the typical energy jitter of the input seed laser in the UV, which is about 1%. A typical figure for the energy jitter is 10-15% for FEL-1 and 25-35% for FEL-2 with the double cascade. In terms of temporal synchronization, the seed timing largely determines the arrival time of the FEL photon pulse. At FERMI the optical synchronization between the seed and the lasers used in pump an probe experiments, which originates from the same oscillator, is associated to a jitter between the FEL light and the other sources of about 5 fs [25]. Recent measurements have shown even lower values, below 3 fs [22]. Figure 4: Spectrum of FERMI FEL-2 at harmonic 65 of the input seed. As in Figure 3, wavelengths are dispersed along the horizontal axis. As in Figure 3 the vertical axis represents the vertical position at the spectrometer detector. Figure 5: Histogram of the energy per pulse measured from FEL-1 at harmonic 5 (51 nm). Acquisition of 220 consecutive shots, average 131 \(\upmu\)J, standard deviation 4.8 \(\upmu\)J. The typical energy per pulse depends on the wavelength of operation and in the requirements on the spectral linewidth. Highest energy per pulse may be achieved in saturated conditions, where the pulse shape may be affected by non-linear processes in the longitudinal electron dynamics. On FEL-1 an energy per pulse larger than 100 u\(\upmu\)J is available in the entire range of operation (20-100 nm), in conditions of single mode, narrow linewidth spectral line. On FEL-2 this is possible in the low end of the spectral energy range, at wavelengths above 8-10 nm. The average energy per pulse decreases while increasing the photon energy, down to about 10 uJ at 4 nm. The energy per pulse may be lower than the one achievable in an optimized equivalent SASE FEL where most of the charge in the bunch participates to the FEL action. The seeded portion of the electron beam is typically of the order of 100 fs, which can be 10-20% or less of the entire bunch. Compressing the entire electron bunch down to the seed duration in an ultrashort multi-kA spike of current would ensure a higher efficiency, but would also introduce a much higher sensitivity to longitudinal jitter between the seed pulse and the current, and the compression process would be strongly affected by self-field effects, such as space charge, coherent synchrotron radiation and space charge fields [26], which alter the smooth distribution of the electron longitudinal phase space necessary to preserve the quality of the pulse during amplification. Moreover, an excess of peak current would increase the gain to a value leading the electron shot noise background to compete with the seed at saturation, and this would remove most of the advantages of seeding the amplifier.