# FEL Pulse Duration Evolution along Undulators at FLASH
## 3 FEL Measurements  
In order to measure the pulse duration of the XUV FLASH pulses, we used the terahertz streaking technique [26; 27; 28]. In short, this method is based on the photoionization of noble gas atoms in the presence of a strong terahertz (THz) field. If the generated electron wave packet is shorter than half the streaking field period, the temporal structure of the wave packet will be mapped onto the kinetic energy distribution of the emitted electrons and can thus be used to determine the XUV pulse duration. The measurements were performed at the dedicated photon diagnostic beamline FL21 in the FLASH2 branch, which is equipped with a permanently installed THz streaking setup [29]. The setup consisted of the interaction chamber containing a time-of-flight spectrometer, a dedicated laser system delivering about 1 ps long pulses at 1030 nm with pulse energy of 3.5 mJ at a repetition rate 10 Hz, and a THz generation setup based on optical rectification using a nonlinear crystal LiNbO\({}_{3}\)) (for details, see, e.g., [30; 31]). In Ref. [31], it was discussed that there is an optimum number of photoelectrons created in the ionization process by the FEL pulse. One needs sufficiently many electrons to record a single-shot photoelectron spectrum while limiting the number of electrons so that the resulting space charge effects are negligible. For our setup, this leads to an optimum XUV pulse energy in the range of several hundred nJ to few \(\mu\)J, depending on the wavelength for neon as the target gas (\(P_{n}\)_on_\(\sim\)\(5\times 10^{-7}\) mbar). To ensure the same experimental conditions for all measurements, the streaking setup was left unchanged during the gain curve measurements, while the transmission of a variable XUV attenuator [32] was adapted such that the average number of created photoelectrons was constant for each measured setting. The FEL was operating in the burst mode delivering three pulses (with 1 \(\mu\)s spacing), while the first pulse was streaked by the terahertz field and the second pulse was used as the reference photoelectron spectrum. The actual pulse duration was derived according to the methods described in [31]. FLASH2 is equipped with 12 variable-gap undulator segments, each of 2.5 m length and 31.4 mm period [11]. The pulse duration was measured with the streaking setup while varying the number of undulators contributing to the lasing. The shown data result from 3 different measurement campaigns. In the first one, FLASH2 was set to 3 different wavelengths: 8, 12, and 16 nm with a constant electron bunch energy of 1.00 GeV and an electron bunch charge of 0.19 nC, leading to XUV pulse durations on the order of 100 fs FWHM. For the second campaign, the FLASH2 electron bunch energy was 875 MeV with a bunch charge of 0.2 nC, and the wavelength was set to 10 and 20 nm, leading to XUV pulse durations ranging from 50 to 160 fs FWHM. Besides these two campaigns, the third campaign was performed with a significantly lower electron bunch energy of 434 MeV and an electron bunch charge of 0.2 nC, leading to a wavelength of 34 nm. The experimental results are summarized in Table 1. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Wavelength**} & **Electron Bunch** & \multirow{2}{*}{\(z_{sat}\)} & \multirow{2}{*}{\(\tau_{ph}^{min}(FWHM)\)} & \multirow{2}{*}{\(E_{sat}\)} & \multirow{2}{*}{\(\tau_{e}^{sat}(FWHM)\)} & \multirow{2}{*}{\(\tau_{el}|M\)} \\  & **Energy** & & & & & \\ \hline
8 nm & 1008 MeV & 9.4 & 75 fs & 60 \(\mu\)J & 7 fs & 22 \\
10 nm & 875 MeV & 8.9 & 50 fs & 39 \(\mu\)J & 8 fs & 13 \\
12 nm & 1008 MeV & 7.7 & 88 fs & 88 \(\mu\)J & 9 fs & 16 \\
16 nm & 1008 MeV & 7.0 & 105 fs & 130 \(\mu\)J & 12 fs & 16 \\
20 nm & 875 MeV & 6.1 & 95 fs & 50 \(\mu\)J & 15 fs & 13 \\
34 nm & 434 MeV & 8.3 & 77 fs & 26 \(\mu\)J & 20 fs & 8 \\ \hline \hline \end{tabular}
\end{table}