# Opportunities for Two-Color Experiments in the Soft X-ray Regime at the European XFEL
## 4 Numerical Simulations for Two-Color Generation and Transport
### Performance of the Fresh-Slice Upgrade Option  
As discussed above, the SASE3 two-color setup can potentially benefit from an adaptation of the fresh slice technique proposed and tested at the LCLS [17] exploiting a wakefield structure, where the generation of 10-fs-long radiation pulses was reported. A similar wakefield structure is considered for installation at the European XFEL [33]. The fresh slice technique is based on exploiting two different lasing windows within the electron beam at different parts of the undulator, both up to the saturation level. Aside from a magnetic chicane, the only crucial component for the realization of this scheme is a wakefield structure to transversely deflect the tail of the electron beam. If the electron beam orbit is  
Figure 10: False color representation of radiation intensity distribution of both radiation pulses with different photon energies at various image planes from Figure 9. Peak photon density is provided above the plots. The method of an intermediate source re-imaging would allow one to obtain comparable radiation distribution size as well as the photon flux.  
Figure 9: Schematic representation of the focusing conditions for two-color lasing at SASE3. If both KB mirrors are tuned in order to minimize the astigmatism for imaging the virtual source \(S\), located between sources \(S1\) and \(S2\), then the images at planes \(I1\) and \(I2\), separated by 1.3 mm, suffer from aberration. However this solution allows one to obtain good radiation quality and comparable photon densities at the \(\tilde{I}\) image plane (see lower figure and Figure 10).  
tuned in a way that the tail of the electron beam radiates in the first undulator part and the head in the second, it is possible to obtain a negative delay between the two FEL pulses, provided that the distance between the lasing windows exceeds the electron beam retardation responsible for radiation slippage in the undulator.  
The lengths of the head and the tail lasing windows depend on the amplitude of the transverse kick induced by the wakefield structure onto the electron beam; in particular, the head window is longer than the tail one, and their length also decreases with the wavelength. Therefore, in case of large photon energy separation, it may be beneficial to emit the pulse with lower photon energy with the tail of the beam in U1, followed by emission of the pulse with larger photon energy with the head of the beam in U2. This sequence should yield pulses with similar durations and minimize the radiation slippage in U2.  
We performed numerical simulations for the two-color SASE3 scheme based on the setup in Figure 2b. In our particular case study we consider a 500 pC electron beam with 8 kA compression and 15 m average beta function. One 2m-long corrugated wakefield structure module is assumed to be installed upstream the SASE3 undulator to deflect the tail of the electron bunch vertically. Two SASE pulses of about 2 keV photon energy reach saturation, as illustrated in Figure 11. No electron beam delay is introduced by the magnetic chicane in this case, and the temporal separation of the two pulses is roughly \(-10\) fs (\(-3\)\(\upmu\)m of spatial separation). With the magnetic chicane turned on, the second radiation pulse can be delayed up to +1 ps level; hence, zero delay between the radiation pulses is possible. Photon energy separation of the two pulses is chosen to be small only for illustration purposes and can be adjusted freely over the full range of photon energies available at the specific setting of the electron beam energy (see Table 1).