# Design and Diagnostics of High-Precision Accelerator Neutrino Beams
## 3 Extraction and Monitoring of Primary Protons  
Since their early developments, neutrino beams have mostly relied on synchrotrons as the source of primary protons. For instance, the J-PARC Main Ring has been employed for T2K [26], the CERN Super Proton Synchrotron (SPS) for the West Area Neutrino Facility [27] and CNGS [28], the Fermilab (FNAL) Main Injector and Booster for the NuMI beamline [29] and MiniBooNE [30], respectively. Differently from linear accelerators, synchrotrons can reach high energies (\(\mathcal{O}\)(10-100) GeV), and offer different proton extraction schemes that suit the maximum rates sustainable by the detectors and the diagnostics, and the features of the neutrino beamline. The proton extraction methods employed for neutrino beamlines are based on two main schemes: fast and slow extraction. * In the _fast extraction_, a kicker magnet is used to extract all protons stored in the machine in a time shorter than a machine revolution period. Such time is typically in the \(\mathcal{O}\)(1-10 \(\upmu\)s) range. According to the experimental requirements, the protons can be shared into several macro-pulses. These pulses always have a fine structure that corresponds to the proton bunches produced by the Radio Frequency (RF) cavities of the machine. * The _slow extraction_ is driven by an unstable resonant motion of the particles in the transverse phase space, which is used to continuously spill the beam out of the machine over a long time (up to several seconds). This instability is controlled by acting on the machine optics (e.g., \"tune\") and non-linear elements (e.g., sextupoles and/or octupoles). The fast extraction is the method used by all neutrino beams currently in data taking: this scheme is driven by the use of magnetic horns (see Section 6.1) as focusing devices for the secondaries, which result in high-intensity wide band beams. The flux of the secondary particles and, hence, of neutrinos, is enhanced by the large angular and momentum acceptance of the horns. Neutrino beams at the GeV scale, equipped by horns, benefit by an increase of acceptance of about one order of magnitude than a bare target experiment or a static beamline, i.e., a beamline where the focusing is performed only with static magnetic elements (dipoles and quadrupoles). Among the drawbacks of a fast extraction, the first one is target fatigue, which is worsened by the fast and large instantaneous rate of the energy deposition (Section 4). The fast extraction also impacts the diagnostics and the instrumentation along the beamline, which has to cope with particle rates of tens of GHz per detector channel. Finally, it challenges the Near Detectors of long-baseline experiments, like DUNE, due to the pile-up of neutrino interactions. A fast extraction scheme is not viable in a monitored neutrino beam, where the leptons in the beamline have to be identified at a single-particle level. The low particle rate resulting from the long spills of the slow extraction can be compatible with an event-by-event detection process and extend the lifetime of the target (Section 4). The main limitation of the slow extraction is the difficulty of using a magnetic horn, as the Joule heating from the long current pulses in the horn conductor can compromise the device beyond repair. A remarkable example is the ESS\(\
u\)SB project [31, 32], discussed in Section 6.1. Examples of fast and slow extraction implementations used for different types of neutrino beams, as well as the latest developments, can be drawn for instance from the CERN-SPS-a machine that gave substantial contributions to neutrino physics since its early days. The SPS can extract an intensity up to about \(4.5\times 10^{13}\) protons, with a particle momentum up to 450 GeV/c. Recently, it was used to drive the CNGS neutrino beam, with a fast extraction cycle providing two proton pulses 10.5 \(\upmu\)s long of \(\sim\)2.4 \(\times\)\(10^{13}\) protons each, separated by a 50 ms time interval and with a 5 ns RF bunching structure [33, 34, 35].