# Design and Diagnostics of High-Precision Accelerator Neutrino Beams
## 6 Focusing of Secondary Mesons
### Horns  
Magnetic horns were first proposed by [PERSON] in 1961 [107] and, since then, have been employed by all wide-band neutrino beams at the GeV scale. A horn is composed of conductor sheets on which a current flows in the longitudinal direction during the proton extraction, producing a strong magnetic field. A schematic representation of the device is reported in Figure 6.  
The toroidal magnetic field of a horn provides a two-plane strong focusing for particles of a given sign and defocuses particles of opposite sign. Therefore, the focusing is accompanied by the suppression of the background from wrong-sign hadrons. Reverting the direction of flow of the current is equivalent to enriching the beam of anti-neutrinos instead of neutrinos (or vice-versa). This is an essential requirement for long-baseline experiments, like DUNE or HK, where CP violation is established by the comparison of \(v_{\mu}\to v_{e}\) and \(\overline{v}_{\mu}\to\overline{v}_{e}\) transitions. Figure 6: Schematic view of a magnetic horn: the device is axially symmetric and focuses particles of a given sign in both the transverse dimensions. The symmetry axis is also the target and beam axis. Various types of horns (e.g., conical, parabolic, ellipsoidal, plugged) have been developed and employed over the years, and a comprehensive discussion can be found in [14]. All the future wide-band neutrino beams will rely on multiple consecutive horns (e.g., two in HK, three in DUNE) to further increase the flux by re-capturing right-sign pions or kaons at the border of the acceptance of the previous horn and further charge-select and focus the secondary beam. Multi-horn systems have been also constructed and implemented at the CERN PS neutrino beam [108; 109], CERN SPS West Area Neutrino Facility (WANF), BNL neutrino program [110], CNGS, and in the current generation of long-baseline experiments (T2K and NO\(\
u\)A ). The magnetic field of a horn is proportional to the injected current and inversely proportional to the transverse radius; this is why very high currents (>100 kA) are typically used, placing the target in the proximity of the horn inner conductor and, often, integrated inside the neck. The horn conductors undergo extremely large thermo-mechanical stresses. The pulsed currents of hundreds of kA induce a strong Joule heating on the device, which sums up to the thermal load coming from the energy deposited by the secondary particles crossing the conductor sheets. Besides, the very high magnetic fields generate strong forces, which might distort the horn shape. The increase of temperature also reduces the tensile strength, further weakening the horn structural stability. For this reason, a horn is always coupled to a complex cooling system, usually made by an extensive network of pipes and nozzles that spray water on the conductors. The power supply and the radiation damage of the connection cables are sources of potential failures, too, and a careful study of every part of the horn infrastructure is mandatory for stable operation [111]. On top of this, extended running can make the horn components extremely radioactive, imposing further limits on repairs and interventions. As a matter of fact, horns are among the most delicate parts of any beamline, and failures are fairly common [112]. The length, intensity, and repetition rate of the proton extraction are the most critical parameters for a horn design, operation, and lifetime, together with the value of the horn current. Typical configurations used for several years in various neutrino beamlines are reported in Table 1, where a correlation between these parameters is quite evident. The lower the horn peak current, pulse length, proton intensity and energy, the higher the repetition rate achievable for stable operation. Hence, a horn operated with a slow extraction like the one of the WANF (6 ms proton pulses) required a low current and repetition rate for a stable operation.