# Conceptual and Technical Design Aspects of Accelerators for External Injection in LWFA
## 4 SINBAD-ARES Accelerator Design
### Working Points  
At ARES it will be possible to work with three different compression techniques: pure velocity bunching, pure magnetic compression with longitudinal collimation, and hybrid combination of the two. As already mentioned in the introduction, the main advantage of the velocity bunching technique is the absence of CSR, which allows for obtaining very high brightness at low energies. In contrast to this, the main advantages of pure magnetic compression combined with the slit are the very high current that can be achieved and the more distributed RF phase tolerances, as explained further in the next section. The charge loss at the slit location constitutes the main disadvantage of the latter technique, potentially limiting the scheme feasibility to low repetition rate accelerators, due to the radiation level increase in the chicane. Moreover, since the beam can not be directly focused to a few micrometers while traveling in the magnetic compressor, a focusing lattice has to be foreseen to inject the beam in to the experimental area.  
An hybrid approach allows for combining the advantages of both techniques and it is has been identified as very promising also in other facilities [74].  
Beam dynamics simulations for studying the production of fs bunches using the longitudinal collimation in the chicane are not trivial because of the high transverse-longitudinal bunch size aspect ratio. The 1D CSR model indeed is only valid when the dimension of the bunch meets the Derbenev criterion:  
\[\sigma_{x,y}\sigma_{z}^{-2/3}\rho^{-1/3}<<1 \tag{16}\]  
where \(\sigma_{x,y}\) is the beam RMS transverse size, \(\sigma_{z}\) is the RMS bunch length and \(\rho\) is the curvature radius in the dipole. This condition fails for our parameter range, thus implying that a 3D CSR model is necessary. Figure 12 illustrates qualitatively the differences in the phase space distribution obtained at the chicane exit using different models for the space charge and the CSR calculation. A detailed study and comparison between the results obtained by the different codes can be found in [66].  
Table 5 presents three working points which are suitable for the LWFA experiment. Those working points have been discussed in detail also in [77]. They are given at the entrance of the plasma chamber, i.e., after the twiss parameters of the compressed beam have been matched with the typical ones required at the plasma chamber entrance [78].  
WP1 and WP2 are obtained by using the pure magnetic compression scheme, while WP4 uses an hybrid compression scheme.  
As already outlined in the introduction, the possibility of tuning the properties of the externally injected beam is very important for the optimization of the acceleration in LWFA with external injection. Simulations of WP1, WP2 and WP4 show that a wide range of input beam parameters suitable for external injection could be produced at ARES.  
Figure 12: Qualitative comparison of beam phase spaces at the exit of the bunch compressor using different physical models for space charge and CSR calculation in the bunch compressor [66]. For the simulations the particle codes IMPACT-T [75] and CSRTrack [76] have been used. In the figure the following abbreviations are used: SC = space charge, CSR = coherent synchrotron radiation.