## 3 Linear Streaking Measurements at Free-Electron Lasers
### Experimental implementation
Different arrival times of the XFEL pulse relative to the streaking laser lead to an overall shift of the whole spectrum as depicted in Figure 11c,d, where the XFEL pulse overlaps with the negative or positive part of the vector potential and the resulting spectrum is shifted accordingly. An individual peak followed by a tail (c) can be distinguished from a pulse containing two well-separated spikes (d) or even three individual spikes as shown in Figure 11e. If one repeats this analysis for each single shot and plots the number of shots versus the corresponding pulse durations, an estimation of the average FWHM X-ray duration can be built up as a histogram (Figure 12). The average pulse duration of the XFEL is best fitted by a Gaussian distribution with a mean value of \(\sim\)4.5 fs and a standard deviation of 1.7 fs. Clearly, this is a very  
Figure 11: Streaking of few-femtosecond X-ray pulses. The top panel (**a**) shows the principle of the X-ray pulse duration evaluation: the maximal shifted peak of the measured PE spectrum is associated with an overlap of the X-ray pulse with a local maximum of the streaking field (blue pulse on the left). This energy shift \(\Delta\varepsilon\) defines the gradient of the energy-to-time conversion and the overall width \(\delta_{\mathrm{s}}\) of the streaked spectrum is used for the determination of the XFEL pulse duration. The green X-ray pulse, twice as long and depicted in the middle, gives rise to a very similar PE spectrum, leading to a residual ambiguity of the XFEL pulse length measurement. Panels (**b–e**) show four different streaked photoelectron spectra as measured in the experiment (solid blue lines) at different values of the NIR vector potential and the respective linear streaking ramp (dashed orange lines) derived from the maximum shifted peak of the spectrum. Corresponding pulse duration upper limits are given and shown on the right vertical axes (red bars) (reproduced with permission from [69], Copyright Nature Publishing Group, 2014). conservative upper limit and the actual pulse duration is likely to be considerably shorter for the vast majority of LCLS pulses in this mode of operation. **Measurement of sub-femtosecond X-ray pulses**  
Due to pulse-to-pulse fluctuations there are some pulses that are considerably shorter than the average duration. XFEL theory predicts a temporal pulse substructure composed of a train of ultrashort spikes [100] with a typical width corresponding to the coherence time, characterized by the X-ray photon energy bandwidth and machine specific parameters. For the parameter range during the measurements at the LCLS, spike durations of about one femtosecond and even below are expected to occur (compare for example Ref. [48]). The average number of spikes per XFEL pulse can be estimated, but it will also be subject to shot-to-shot variations. Occasionally, an X-ray pulse consisting of just one single isolated spike will occur. A closer analysis of the data confirms the existence of such ultrashort'single-spike' pulses, constituting about 5% of the total number of shots. By sorting and collating the streaked spectra with just one peak and determining their centers, one can identify the energy shift \(\Delta\varepsilon\) and the spectral width \(\delta_{\mathrm{s}}\) for each of these shots. Figure 13 shows the measurement principle for attosecond X-ray pulses: For the evaluation of these single-spike pulses one assumes that due to simple statistical considerations the predominant number of XFEL shots overlaps with a part of the ramp of the vector potential and hence again Equation (2) is valid in most cases. Then one can employ a reasoning similar to that described above to assess an upper limit for the pulse duration.