# Synchronised TeraHertz Radiation and Soft X-rays Produced in a FEL Oscillator
## 1 Introduction
It can therefore be developed in medium size laboratories, big hospitals or university campuses and represents an elementary upgrade of a basic THz FEL oscillator. Section 2 describes the generalities of the double source constituted by a THz free-electron laser oscillator and by a X-ray Thomson/Compton source driven by the same electron beam. Section 3 presents the THz free-electron laser oscillator, focusing the attention on geometry and working points suitable for this particular operation. Section 4 gives the details of the THz optical cavity. Section 5 provides an overview of the X-ray production by means of Thomson/Compton scattering. Finally, we conclude presenting considerations about the optimal layout, characterisation and performances of the dual source providing simultaneous THz and Soft X-ray radiation and discussing the possibility of developing such a device. Double Source Constituted by a THz FEL Oscillator and a Thomson/Compton Source Driven by the Same Electron Beam: Generalities  
In this section, we will determine the parameters of a THz FEL oscillator alimented by an electron beam accelerated by a Super Conducting (SC) Energy Recovery Linac (ERL) [18; 19]. An SC accelerator is required because the FEL oscillator is based on the passage of successive electron beams at a large repetition rate inside the undulator. Moreover, the energy recovery option allows for a sustainable approach to the radiation generation. We based our study on an ERL similar to those described in [13; 14; 20]. A DC gun, JLab-like, equipped with solenoid and bunchers, guarantees low-emittance and a large repetition rate. The average current was maintained below 7-8 mA. The instabilities connected to the high-order modes are taken under control by a suitable design of the cavities [21; 22], together with the insertion of dumpers. Table 1 presents values of the electron beam parameters given by start-to-end simulations, generated by Superconducting Linacs operating at the aforementioned energies (see also [5; 8; 14; 21]). The table reports the slice emittance and energy spread values, since, in the FEL process, only the characteristics of the core of the electron beam are significant. The electron beam provides THz radiation with interesting properties and, at the same time, suitable for driving Thomson back-scattering. Even if the interaction is in the classical range (Thomson regime), following the usual lexicon in the field, we will also refer to the process as inverse Compton (or simply Compton) scattering. The accelerated electron bunches, travelling through the undulator, produce THz FEL radiation that is then reflected backward by the front mirror. The total distance travelled by the radiation \(L_{rt}\) back and forth in the cavity and the repetition rate of the electron bunch train \(f\) must be connected in such a way that the radiation arrives exactly synchronised to a successive electron beam at the entrance of the undulator after a round trip: \(L_{rt}\) should therefore be a multiple of the distance between two successive bunches \(L_{rt}=v_{e}\)_/_f_, \(v_{e}\) being the electron bunch velocity. Figure 1 shows an option based on a four-mirror cavity of the radiation source layout. The THz radiation produced by the FEL undulator propagates freely up to the tilted front mirror. Here, it is reflected off-axis and then obliquely sent to the Compton interaction point (IP) by a second mirror. The interaction therefore takes place at a small angle. The THz radiation is then shifted laterally by a few centimetres, thus circumventing the undulator. The focusing needed for increasing the luminosity of the process is provided by the mirrors surrounding the IP. This configuration is quite usual in Thomson/Compton sources based on lasers in Fabry-Perot cavities [20; 23; 24]. In addition, \(L_{rt}=n\Delta l\) (\(n\) integer), \(\Delta l\) being the electron bunch-to bunch inter-distance. If n > 1, more than one electron beam is simultaneously present inside the cavity.