## 3 Elements of the Beam Line Prototype  
### The Focusing System Prototype  
The permanent magnet quadrupoles (PMQs) prototype, designed and realized at the INFN-LNSS, consists of two PMQs of 80 mm length and two PMQs of 40 mm length with an active bore of 20 mm and 1 mm thick shielding pipe, placed inside the bore for the protection of the magnets. The magnetic field gradient is about 100 T/m [17]. The system has been designed to improve the transmission and the selection efficiencies of a magnetic energy selector prototype based on four permanent magnet dipoles with alternating field gradient (see section 3.2 for a detailed description). The PMQs are based on a hybrid Halbach cylindrical array with eight sectors, as shown in Figure 1. The poles are set at 45\({}^{\circ}\) with respect to the horizontal axis and are attached to four iron sections, almost saturated, used as supporting structure as well as magnetic flux guides. The poles have a rectangular main body (13 \(\times\) 14 mm\({}^{2}\)) with two smaller pieces close to the bore, which allow increases of the field and, hence, the gradient inside the bore itself. The T-like magnets between two poles are modeled as three independent squared pieces (10 \(\times\) 10 mm\({}^{2}\)). The magnetic features of each section of the quadrupole have been evaluated from the BH curve of the materials, NdFeB N50 for the magnets and iron XC10 for the other four parts. Each magnet has its own direction for the permanent magnetization (see red arrows in Figure 2). Design based on hybrid Halbach design with standard rectangular magnetic blocks. Field maps are simulated with 0.5 mm step and scaled according to the measurements provided by the SigmaPhi Company (Vannes, France) during the manufacturing process [17]. The system can be used for focusing and collecting protons up to 30 MeV, although, according to the simulation results, the best performances can be achieved for energies lower than 20 MeV. An example of particle tracing performed using the code for optics calculation TraceWin[24], in the PMQs system optimized for the 5 MeV proton injections in the energy selector prototype is shown in Figure 3. The ESS is simulated as a three collimator system in line: collimator 1 and 2, with a 10-mm diameter aperture, are used to remove from the beam particles with large divergence, the slit is a rectangular aperture of 1 \(\times\) 10 mm and is responsible for the energy selection and the selected energy resolution. The focusing system ensures a transmission efficiency of about 1%-2% for the whole beam line. Figure 2: The layout of the PMQs system prototype based on hybrid Halbach design. The PMQs prototype has been tested with 10 MeV proton beam delivered by the Tandem accelerator at the LNS. Figure 4 shows the comparison between the 10 MeV proton beam spot distribution predicted by the beam optics simulations and the experimental data taken using Gafchromic film, EBT3 type. As one can see from the comparison, a good agreement between the simulation and the measured spot size has been obtained. A new system, characterized by higher field uniformity and capable of focusing ions with energies up to 60 MeV/n, has been recently designed for the ELIMED section of the ELIMAIA beam line. It will consist of 5 PMQs with the characteristics described in the Table 1. This is the lowest proton energy of interest for medical applications, for instance, eye melanoma are treated worldwide with 60 MeV proton beams. This is the reason why transport and selection of 60 MeV/n ions represents our first goal in the feasibility studies related to the applications of laser driven ion beams for therapeutic purposes. Figure 4: Comparison between the simulation results and the experimental measurements (inset) for the 10 MeV proton beam spot along the PMQs system. Figure 3: Horizontal envelop **(upper panel)** and vertical envelop **(lower panel)** of the beam line for a monochromatic beam (5 MeV) with a spot size of 100 \(\upmu\)m and 170 mrad half angle divergence.