## 3 Elements of the Beam Line Prototype
### The Energy Selector System Prototype  
A prototype of an energy selector system (ESS), designed and developed at the INFN-LNS a few years go [25], is based on four permanent magnet dipoles with alternating fields, similar to a bunch compressor chicane [26]. Each dipole is 88 mm long; the drift space between the central and peripheral dipoles is 85 mm whereas a 10 mm drift distance separates the central dipoles. In such drift space, the particles with different energies are dispersed along the radial plane and a moving slit is used to select ions within a certain energy range. Figure 6 shows a scheme of the ESS prototype together with the parameters for the calculation of the path length of a proton inside the magnetic chicane, for the calibration equation and for the acceptance of the system. \begin{table}
\begin{tabular}{c c c c} \hline \(n^{\circ}\) **of PMQ** & **Geometric length** & **Field gradient** & **Bore diameter** \\ \hline
1 & 160 mm & 101 T/m & 30 mm \\
2 & 120 mm & 99 T/m & 30 mm \\
2 & 80 mm & 94 T/m & 30 mm \\ \hline \end{tabular}
\end{table} 
Table 1: The ELIMED PMQs system features. Figure 5: ELIMED PMQs layout. The ESS prototype has been successfully calibrated using accelerator-driven proton beams with FWHM energy spread of 0.5% in the energy range between 2.5 and 5 MeV at the Laboratori Nazionali di Legnaro (LNL) in Padova and between 4.5 and 12 MeV at the LNS in Catania. Figure 7 shows an example of the experimental results of the slit positions as a function of the energy measured in the energy range available at the LNL, along with a comparison with theoretical predictions. Based on the parameters shown in Figure 6, the equation describing the slit position as a function of the energy can be derived:  
\[T=\sqrt{\left(\frac{qx(\Delta x-tan\alpha_{2}}{B_{1}})+\frac{(1-cos\alpha_{2} }{B_{2}}\right)^{2}+{M_{0}}^{2}c^{4}-E_{0}} \tag{1}\]  
where \(q\), \(M_{0}\) and \(E_{0}\) are charge, mass and rest energy of the ion beam, respectively, \(\Delta x\) is the slit position, \(\alpha_{i}\) and \(B_{i}\) are the bending radius and the magnetic field of the first and the second dipoles, respectively. As shown in Figure 7 (lower panel) the Equation (1) can evaluate the ion energy in a very good agreement with the experimental measurements (upper panel). The energy resolution of the system can be estimated from the derivative of Equation (1) as shown in Equation (2). \[E_{res}=\left(\frac{dT}{dx}\right)\times\Delta x=\frac{\left(\frac{qc}{\frac{1 -cos\alpha_{1}}{B_{1}}+\frac{1-cos\alpha_{2}}{B_{2}}}\right)\times\sqrt{(E_{ 0}+T)^{2}-{M_{0}}^{2}c^{4}}}{E_{0}+T}\times\Delta x \tag{2}\]  
According to the scaling factor, the experimental results indicate that the system can select protons with an energy resolution of about 30% at 30 MeV ensuring a better resolution for lower energies. The experimental results have also been compared with the GEANT4 predictions showing a rather good agreement and allowing a fine-tuning of the simulation parameters. The ESS prototype has been also characterized with laser-driven proton beams at the TARANIS laser facility (Queen's University, Belfast, UK). During the test experiment two energies, 4.5 and 7 MeV, have been selected using the selection system. Energy spreads, fluence, angular divergence, spot sizes of the proton beam coming out from the energy selection system have been measured for both energies  
Figure 6: Scheme of the ELIMED ESS prototype. selected. Preliminary results show energy spreads of about \(\pm\)7% and \(\pm\)8% for 4.5 and 7 MeV, respectively. The measured average fluence is \(5\times 10^{6}\) p/cm\({}^{2}\) when a 4.5 MeV proton beam is selected and about \(10^{6}\) p/cm\({}^{2}\) in the case of 7 MeV protons. The results of this experiment will be published elsewhere. The predicted transmission efficiency of the ESS prototype is quite low (few particles out of ten thousands).