= Solution
Use a high-energy <proton> beam on a target to produce secondary <pions>, then select and focus the negative ones. A <magnetic horn> and a charge-selecting dipole system remove positive pions, limiting wrong-sign $\nu_\mu$ contamination. Select a narrow range of <magnetic rigidity>; if additional species rejection is available, velocity or mass discrimination reduces negative <kaon> contamination at the same momentum.
\Image[/past-exam-of-the-particle-and-nuclear-physics-course-of-the-university-of-cambridge/2021-antineutrino-beam.png]
{title=A focused negative-pion decay beam producing muon antineutrinos}
The selected $\pi^-$ travel through an evacuated <decay tunnel> and undergo $\pi^-\to\mu^-\bar\nu_\mu$. Their forward <Lorentz boost> concentrates the <antineutrinos> within an angle of order $1/\gamma_\pi$. Choose a tunnel long enough for substantial pion decay but short compared with the boosted <muon> decay length. Since $\tau_\mu\simeq2.2\,\mu\mathrm s$ is much longer than $\tau_\pi\simeq26\,\mathrm{ns}$, this reduces secondary $\mu^-\to e^-\bar\nu_e\nu_\mu$ contamination.
Downstream magnets sweep the remaining charged particles into absorbers, and shielding stops residual hadrons and <muons>. The <antineutrino> beam continues straight through. Parent-particle collimation, charge selection, and a forward detector improve purity; neutral-kaon decays, remaining wrong-sign parents, and muon decays prevent perfect purity. <Neutrinos> themselves cannot be focused or charge-selected by these magnets. Neutrinos produced after stopped-muon decay or capture are much less forward and can be reduced by directional and energy selection.
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