Impact of instrumental effects and target thickness on the SPARC magnetic proton recoil spectrometer response function

The SPARC tokamak aims to demonstrate net fusion power gain in tokamaks (Q-fus > 1). To measure neutron emission, a neutron spectrometer based on the magnetic proton recoil technique is being developed. This diagnostic operates by converting collimated neutrons into recoil protons through elastic scattering on a polyethylene target. The recoiled protons are then separated based on their momentum by a magnetic field and subsequently detected by a hodoscope composed of plastic scintillation detectors coupled to photomultiplier tubes. This allows neutron energies in the 2–20 MeV range to be discriminated, though only neutrons in a narrower energy window (±25% around the selected central energy) can be measured. The instrument will contribute to the determination of the total fusion power and provide information on plasma parameters such as ion temperature and the presence of non-thermal fuel ions. In this study, the design rationale of the hodoscope is presented and the main instrumental effects that govern proton collection are characterized. The hodoscope is divided into three regions with different channel widths, depths, and lengths, jointly optimized to satisfy three coupled physical requirements: sufficient energy resolution at the 14.1 MeV DT peak, full proton containment up to 18.75 MeV, and limitation of the background through minimization of the detector volume. Three correction factors are evaluated through dedicated simulations: the vertical signal loss due to protons falling outside the scintillator rod length, the cross-talk between adjacent channels, and the background contribution per channel. A correction scheme combining all three factors is presented.