# State of the Art of High-Flux Compton/Thomson X-rays Sources
## 3 Discussion of Different Paradigms: Low Energy Sources Operating in Classical Regime
### (iii) Superconducting Linac + Laser in Cavity
The superconducting cavities can be operated in the two-pass two-way conditions, either for doubling the energy or for energy recovery. Contained dimensions and expenses and the energy recovery operation make minimum the cost per photon and maximum the sustainability of this device option. Present state of the art of the average current in ERL photo-injectors is about 10 mA [88], but several projects world-wide aim at 100 mA and above [89]. Table 3 summarizes typical parameters of these sources. For this last paradigm, the X-ray flux achievable can be also expressed approximately in terms of the average electron beam current \(I_{e}\), laser power \(P_{FP}\) stored in the Fabry-Perot cavity and effective repetition rate of collisions \(f_{FP}\) as :  
\[N_{X,hw}\approx 1.4\times 10^{17}P_{FP}(MeV)I_{e}(mA)f_{FP}(MHz)\frac{Q(nC)}{ \sigma_{x}^{2}(\mu m^{2})}\gamma^{2}\theta_{acc}^{2}. \tag{5}\]  
This formula shows that only the projects BriXS and UHFLUX could reach and even overcome the flux of synchrotrons, this occurring when the average current achieves 100 mA, and the laser power stored in the Fabry-Perot optical cavity exceeds 1 MW. Figure 3: BriXSinO as an example of Paradigm (iii) with energy recovery (average electron beam current up to 8 mA). In all the three paradigms introduced above, the sources deliver sequences of picosecond long X-ray radiation bursts (shorter than the ones produced by synchrotrons) with polarization completely controlled from linear to circular or elliptical. Moreover, the small dimension and the round shape of the emitting source, with radii in the range of 10-80 \(\upmu\)m, increasing the local transverse coherence of the radiation beam, makes possible to exploit the effect edge enhancement needed in phase contrast techniques. The coherence areas, moreover, expand as \(\lambda L/\sigma^{2}\) after propagating a significant length \(L\) from the source to the end user, with \(L\) typically of the order of few tens of meters. This is a key issue for advanced radiological imaging applications. The advantages of paradimg (i) derives from the low value of beam emittance that can be achieved thanks to the high gradient of the radiofrequency field maintained in the cavities of the accelerator and to the fact that the electron beam is dumped and restored after each collision. This permits to converge the electron beam at IP to foci of sizes of the order of 10-20 \(\upmu\)m and to exploit also the focusing possible for a single pulse laser. Main drawback of this paradigm is the intrinsic limitation of the repetition rate achievable, about 100 Hz in the present state of the art. Same considerations hold for the laser pulse, except for the possible option of a laser recirculator (a device experimentally implemented, but not yet tested on ICS facilities) that multiplies at each RF pulse the collision number by a significant factor. The repetition rate of the source could raise from 100 Hz to a few kHz, enhancing, in turn, the effective X-ray flux to the end user. The machine could also be easily upgraded in energy by adding more RF accelerating modules so that nuclear photon energies larger than 20 MeV can be achieved by ICS based on this paradigm with GeV-class warm Linacs, like the one described in the EuroGammas proposal. Sophisticated techniques, like laser chirping, tilting or modulation could be tested for incrementing the spectral flux. Paradigm (ii) presents the advantage of the high repetition rate associated to the storage of the electrons in a ring. The beam instabilities in this configuration at low energies (50 MeV) impede, however, to focus tightly the beam at IP. The laser is necessarily a system in Fabry-Perot cavity, characterized by low single-passage energy and transverse sizes of order of 50-100 \(\upmu\)m. The use of a double cavity could permit a double color operation. On the other hand, the implementation of pulsed operations is hard. The upgrade in energy is also an issue, since it entails to re-design the whole machine.