# Design and Diagnostics of High-Precision Accelerator Neutrino Beams
## 4 Target  
Secondary particle productions hold the key for neutrino experiments, as the neutrino energy spectrum, flux, and kinematic distributions are strictly related to the secondaries emitted at the target. Therefore, it is fundamental for future experiments to have a precise knowledge of the interactions of the primary beam with the secondary target. As discussed in the previous sections, conventional neutrino beams are obtained from the decays of charged mesons (\(\pi\), K) produced by protons impinging on a target. High-intensity neutrino beams-often called _Superbeams_-produced by multi-MW proton accelerators rely extensively on low-Z targets [82]. The higher beam power on the target compensates for the reduced yield compared to high-Z metallic compounds. Specifically, beryllium, graphite, or other carbon-based compounds, nickel-chromium superalloys, and mercury are the most common choices, given their robustness to radiation damage [83]. Granular or fragmented metallic targets have been also considered given their ability to absorb higher beam power, with promising results [84; 85]. Neutrino experiments need to extrapolate and determine the flux of neutrinos from the yield of secondary hadrons produced by the target. This is often the most important source of systematic uncertainties. While it is possible to derive models for secondary production by fitting experimental data [86], the uncertainties remain high (>10%), especially for the low energy region, as reported in several surveys [87; 88; 89]. The number of \(\pi^{+}\) produced per POT grows linearly with the primary proton momenta [90], which determines the accessible momenta for the secondaries and, hence, the neutrinos. The neutrino beam energy range is set by focusing only pions and kaons around a given central momentum. While lower energy proton machines such as J-PARC MR [91] can be operated at a higher repetition rate, the secondary yield is suppressed linearly with the proton energy compared, for instance, to the CERN SPS that can run with \(4\times 10^{13}\) 400 GeV/c protons extracted in 4.8 s (lower energy favouring longer spill). Therefore, neutrino beam designers tune several parameters of the primary proton source, e.g., the primary proton momentum, extracted intensity, and repetition rate, to reach the sought-for intensity of the facility. The target optimization plays the most important role in the optimization of secondary yields. Besides the choice of target materials, the target geometry determines the re-interaction probability and absorption of the secondary particles coming out of the target after the collision with the primaries. The optimisation of the target geometry, however, is not only driven by the produced yields, but also by mechanical constraints and cooling requirements, especially in the cases of high-intensity beams [92]. In CNGS, for instance, the target was an assembly of air-cooled, thin graphite rods, acting as multiple targets that could be hit separately. In this way, the spare targets were already located on-site. Heat management is another parameter that needs consideration, especially in Superbeams. The energy deposited in the target material by the primary beam results in tensile stresses radiating out from the central beam spot [93]. The main parameters that determine the heat endurance are the specific heat and the tensile properties of the medium. These properties drive the choice of the heat dissipation system. Heat dissipation may occur through the container that holds the target and the heat transfer from the target material can be either conductive or radiant in solid targets. Conductive internal heat transfer is very effective in metal targets, while radiant heat transfer is better suited for high-emissivity refractory materials and inserts, such as graphite [94]. The target's overall size plays a central role in the cooling design. An increased surface implies a larger radiative heat transfer and the change of the size of a target is driven by the absorption/emission parameters of the material.