# Toward the Generation of an Isolated TW-Attosecond X-ray Pulse in XFEL
## 4 Summary and Discussion  
All the results reviewed in this article are summarized in Table 1. Most schemes produced radiation power larger than 1 TW. However, with respect to the pulse duration, the current modulation methods result in a pulse shorter than 100 as in the hard X-ray region. For [PERSON] et al. [38], the pulse duration was larger than 100 as due to the width of the good emittance region. This width was determined by the width of the slots in the foil in the bunch compressor section. For [PERSON] et al. [39], the intersection area between the tilted electron beam and the radiation determined the pulse duration. This intersection area cannot be smaller than the transverse width of the electron beam itself. The last row in Table 1 shows which method provides inherent synchronization between an attosecond pulse and an optical pulse. Unfortunately, the methods used by [PERSON] et al. [38,39] did not provide the inherent synchronization. From this point of view, other methods are preferable. However, this inherent synchronization is not sufficient to ensure successful pump-probe experiments due to the timing jitter introduced by mechanical vibration. It has recently been demonstrated that at FEL experimental stations, the timing jitter generated due to the free space propagation of \(\sim\)100 m and folding mirrors can be controlled with 5 fs accuracy via currently available technology [48,49]. Using a feedback loop [50] for all the mirrors (i.e., both optical and X-ray mirrors), this mechanical vibration can be suppressed and the time delay between pump (optical laser) and probe pulse (X-ray) can be controlled within 20 attoseconds RMS. An XFEL pulse might even be synchronized with current spike and with optical laser on an attosecond time-scale with the help of rapidly developing technologies in the near future. For the realization of a TW-as XFEL with existing FEL specifications, a new undulator line needs to be constructed with delay units between the undulator sections for most proposals, except for the scheme in [PERSON] et al. [44]. The existing undulator line may be modified so that the delay units are inserted between the undulator sections. However, there is a possibility of FEL power degradation \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Reference**} \\ \hline
**Parameter** & [38] & [39] & [37] & [40] & [42] & [44] \\ \hline Photon energy (keV) & 12.4 & 12.4 & 10 & 7.7 & 12.4 & 12.4 \\ FEL power (TW) & 0.95 & 2.38 & 6.6 & 1.8 & 1.2 & 1.5 \\ Pulse duration (as) & 142 & 363 & 53 & 62 & 100 & 36 \\ Beam energy (GeV) & 5.8 & 5.8 & 8 & 7 & 10 & 10 \\ Peak current (kA) & NA & NA & 12–18 & 5 & 33 & 35 \\ Inherent synchronization & No & No & Yes & Yes & Yes \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison between the main parameters of the methods reviewed. Figure 9: Simulation results with single current-spike method-single pass in Figure 8. (**a**) FEL power growth in the undulator line; (**b**) Temporal profile for five different seeds in the simulation. Blue line represents a specific case among the five different cases. Reproduced from [PERSON] et al. [44] with permission. when the undulator line is operated in normal SASE mode to generate femtosecond FEL pulses, because the delay unit will play the role of drift section between the undulator sections. A long drift section is harmful for the FEL process due to the bunching factor degradation, which is caused by the space charge force and speed difference between the electrons smearing out the microbunching in a long drift section. There is still a technical issue that all the schemes mentioned above have not discussed seriously. When the beam is bunched at a bunch compressor in an XFEL machine, microbunching instability will occur due to the space charge effect [51] or coherent synchrotron radiation [52]. The microbunching effect on the generation of the current spikes as in Zholents [20] has to be addressed.