# Design and Diagnostics of High-Precision Accelerator Neutrino Beams
## 9 Hadron Dump Diagnostics
Particle rates range, at NuMI, from about \(7\times 10^{8}/\)cm\({}^{2}\) for \(10^{13}\) protons-per-pulse at the hadron monitor to a few \(10^{6}/\)cm\({}^{2}\) at the muon monitors. At the higher energies of CNGS, about \(10^{8}\) muons/cm\({}^{2}\) are observed during the 10.5 us fast extraction. In narrow-band beams, the possibility to monitor muons fluxes and their spectra downstream of the hadron dump is particularly interesting to access to the bulk of the low-energy muon neutrinos produced from two-body decays of pions. In ENUBET, those are located in the \(E_{\
u}<4\) GeV region of Figure 2. Unlike kaons, in \(\pi^{+}\rightarrow\mu^{+}\
u_{\mu}\) the small pion-muon mass difference results in forward-emitted muons that reach the hadron dump before crossing the wall of the decay volume. This flux component is particularly interesting since it lies at lower energies with respect to kaon-generated \(\
u_{\mu}\). The ENUBET Collaboration is studying a muon monitoring system composed of 8 stations with iron absorbers ranging from 2 m (upstream) to 0.5 m (downstream). The transverse distribution of muons is limited to about 30 cm FWHM and the highest muon fluence is about \(2\times 10^{6}\) muons/cm\({}^{2}\). The total neutron rates integrated over the experiment lifetime at the most upstream station are \(\sim\)8 \(\times\)\(10^{11}\) decreasing to \(6\times 10^{6}\) n-1 MeV-eq/cm\({}^{2}\) in the most downstream station (The neutron flux is expressed in non-ionizing-dose units, i.e., in 1 MeV equivalent  
Figure 13: Muon monitoring detectors employed for the CNGS neutrino beam (**left**) and the J-PARC beam (**right**). The CNGS chambers consisted of 42 muon detectors separated by 11.25 cm and spanning a length of 2.7 m. The J-PARC system (MUMON) is composed of \(7\times 7\) ionization chambers (left side of the picture) and \(7\times 7\), 1 cm\({}^{2}\), PIN photodiodes (right side). The beam enters from the right side. Reproduced under CCA4.0-I license with permission from Sissa-Medialab [28]. neutron fluence (n-1 MeV-eq) and provides the radiation-hardness requirements of the detectors). In monitored neutrino beams and all narrow-band beams, radiation damage is much smaller than wide-band beams, where the hadron dump collects the non-interacting primary protons, too. The designers of monitored neutrino beams envisage the use of fast detectors to reconstruct muons on an event-by-event basis and measure their momentum individually from their range with the detector stations. The energy and position measurement at the single particle level is a novel tool to separate signal muons from pions and halo muons. The distributions of the two components are well separated in momentum (Figure 14) and, to a lesser extent, in the position of the impact point and the reconstructed angle. The energies of muon neutrinos corresponding to bins of muon momentum-reconstructed by range--show a clear anti-correlation in energy due to the kinematics of 2-body decays. The shape and normalization of the corresponding \(\
u_{\mu}\) are thus precisely constrained by the muon distributions. Muon diagnostics provide the \(\
u_{\mu}\) flux from pions with a precision of \(\sim\)20% in wide band beams [62]. In monitored neutrino beams [146; 147], it reaches a per-cent level precision and allows for the implementation of the NBOA technique described in Section 10.6.