# Opportunities for Two-Color Experiments in the Soft X-ray Regime at the European XFEL
## 4 Numerical Simulations for Two-Color Generation and Transport
### Generation and Transport of fs-Long Two-Color Pulses in the Low-Charge Mode of Operation  
The SASE3 undulator consists of 21 undulator segments each providing 5 m magnetic length (corresponding to a total length of about 6 m each) with a period of 68 mm. A magnetic chicane splits the SASE3 undulator into 11 cells for U1 and 10 cells for U2; we assume that all cells are closed except for the first 2 and the last 4 cells in U1 as well as the first 3 cells in U2. Therefore, 5 cells of U1 and 7 cells of U2 are closed and contribute to lasing. In order to be delivered to the SASE3 undulator, the electron beam must pass through the SASE1 line [25]. It was shown [26] that lasing in the SASE1 undulator can be inhibited, but due to quantum fluctuations [27; 28] and synchrotron radiation, the electron parameters deter  
Figure 5: Nominal 20 pC electron beam at the entrance to the SASE3 undulator. (**a**) current profile (red) and resistive wakefields in the undulator (green); (**b**) energy (red) and energy spread (green) profiles of the electron bunch; (**c**) horizontal (red) and vertical (green) normalized emittance as a function of the position inside the bunch; (**d**) horizontal (red) and vertical (green) betatron function inside the bunch. The head of the bunch is on the right. of resistive wakes in the SASE1 undulator affects the electron beam energy distribution. Therefore, the electron beam propagation through the SASE1 undulator, accounting for these effects, was included in the simulations. Figure 5 shows the results of start-to-end simulations of the electron beam passing through the European XFEL linac [29] and SASE1 undulator up to the entrance of the SASE3 undulator. It refers to a low-charge 20 pC mode of operation, not yet enabled at the time of writing, but foreseen at the European XFEL. The electron beam obtained in this way is sent through the first part of the SASE3 undulator U1, with 5 active segments tuned at 630 eV. The results of a statistical simulation run calculated by Genesis [30], which has been used for all simulations in this paper, are shown in Figure 6.  
After lasing in U1, the electron beam goes through the magnetic chicane, while the photon beam passes through the optical delay line. Under the assumption that X-ray diffraction effects in the optical delay line are negligible and that its mirrors do not sensibly modify the wavefront, the 630 eV radiation pulse, generated in the U1 undulator, is just delayed with respect to the electron beam at the U2 undulator entrance. In our simulations the electron beam propagating through the chicane maintains all its parameters, except for the electron density modulation (micro-bunching), which is washed out during the passage through the chicane. We therefore take the numerically simulated electron beam distribution at the end of undulator U1 and use it for the FEL simulations in U2. The proper shot noise is automatically introduced into the electron beam by the Genesis simulation code. The results from the lasing of the seven active segments at the end of U2, tuned at 250 eV are presented in Figure 7, where a statistical run is shown. Both pulses are characterized by pulse durations much shorter than the 10 fs and pulse energies of several 10 micro) are reached. As discussed already above, the pulse generated in U2 has a slightly longer pulse duration (about 3.3 fs FWHM) that the one generated in U1 (about 1.5 fs FWHM). The second radiation pulse has larger variance in spectral position, power profile and intensity, compared to the first pulse. In fact, assuming a perfectly reproducible electron beam, shot-to-shot variations of the first radiation properties originate from the stochastic nature of the SASE process; in the second undulator, radiation is emitted by a stochastically spoiled electron beam, therefore the properties of the second pulse are not only driven driven by the stochastic SASE process, but also by shot-to-shot differences in electron beam.