# Opportunities for Two-Color Experiments in the Soft X-ray Regime at the European XFEL
## 2 Project Scope  
The simplest way currently available to enable the generation of two temporally separated pulses of different wavelengths at X-ray Free-Electron lasers (XFELs) consists of inserting a magnetic chicane between two undulator sections as suggested in [15] and experimentally proven in [11; 16]. The scheme is illustrated in Figure 1. The two sections act as independent undulators, which will be referred to as U1 and U2. We briefly remind that the fundamental wavelength in an undulator is calculated as  
\[\lambda=\frac{\lambda_{u}(1+K^{2})}{2\gamma^{2}}, \tag{1}\]  
where \(\lambda\) is the radiation wavelength, \(\lambda_{u}\) is the undulator period, \(K\) is the root mean square (rms) undulator parameter, and \(\gamma\) is the relativistic Lorenz factor of electrons. The undulator parameters in U1 and U2 are independently tunable, and will be indicated with \(K_{1}\) and \(K_{2}\), respectively, leading to two independent resonant wavelengths \(\lambda_{1}\) and \(\lambda_{2}\) in U1 and U2. The electron beam enters the first undulator U1, tuned to the resonant wavelength \(\lambda_{1}\). After passing through U1, both the electron beam and the emitted Self-Amplifie  
Figure 1: Simplest two-color scheme relying on a single magnetic chicane. (SASE) radiation enter the magnetic chicane. The chicane introduces a delay \(\Delta t\) to the electron beam, while the radiation propagates unperturbed. When the delayed electron beam enters the second undulator U2, the SASE process starts from shot-noise again. Therefore, if U2 is tuned to the resonant wavelength \(\lambda_{2}\), then at the undulator exit, one obtains a first radiation pulse at wavelength \(\lambda_{1}\), followed by a second one with wavelength \(\lambda_{2}\) delayed by an interval \(\Delta t\) that can be varied by changing the strength of the chicane magnets. The energy of the electron beam remains practically unchanged while passing through U1 and U2. Therefore, the accessible photon energies for different electron beam energies are defined by the tunability range of the undulator parameter \(K\) as presented on Table 1.  
The FEL amplification process causes deterioration of the quality of the electron beam, as the slice energy spread grows together with radiation power. To ensure lasing at two wavelengths, the electron beam quality at the entrance of the second undulator U2 has to be still good enough to sustain the FEL process. The longer the target SASE wavelength \(\lambda_{2}\) is, the more relaxed the electron beam quality requirements are, therefore, the more radiation power can be extracted in U1. As a result, in order to maximize the combined extracted radiation power at large wavelength separations, it is preferable to operate under the condition \(\lambda_{1}<\lambda_{2}\). In addition, due to deterioration of the electron beam quality, the lasing window--and hence the emitted pulse duration--in U2 is expected to be longer than in U1. In an undulator, the electron beam is delayed by one resonance wavelength per one undulator period. Therefore, the radiation emitted in U1 will slip ahead of the electron beam in U2. The actual delay depends on the wavelength of the second color, and can be estimated to be about several femtoseconds. Ramping up the magnetic field in the chicane can only increase this delay and, depending on the electron beam energy, delays of up to 3 ps can be achieved (see Table 1). Therefore, even when the chicane is switched off, one cannot expect to achieve full temporal overlap of the two colors, and in particular zero-crossing is not possible. However, as discussed above, the duration of the second pulse is generally longer, so the arrival times of the two pulses can be comparable. We consider two methods to deliver soft X-ray pulses from U1 and U2 with tunability through zero delay. The first method is to introduce a compact optical delay line into the magnetic chicane. This will lead to a full control of the relative temporal separation between the two pulses as shown in Figure 2a.