NuMI: Neutrinos at the Main Injector

• NuMI is a neutrino beam facility that uses 120 GeV protons striking a segmented graphite target and pulsed focusing horns to produce controlled muon-neutrino streams.
• The system employs comprehensive real-time diagnostics and beam monitoring tools, achieving sub-percent control of flux characteristics and systematic uncertainties.
• Ongoing upgrades and modular design enhancements have increased beam power from 0.7 MW to over 1 MW, setting the foundation for next-generation LBNF/DUNE experiments.

Neutrinos at the Main Injector (NuMI) denotes the Fermilab facility providing high-intensity muon-neutrino beams for long- and short-baseline oscillation and cross-section experiments, primarily via interactions of 120 GeV protons from the Main Injector with a segmented graphite target, pion focusing via high-current magnetic horns, and decay in a long, shielded tunnel. NuMI is the reference for U.S. accelerator-based neutrino physics, delivering controllable, well-characterized fluxes to a suite of experiments (NOvA, MINOS, MINERvA, MicroBooNE, ICARUS), and its design and operational experience shape the architecture of the next-generation Long-Baseline Neutrino Facility (LBNF). The facility has evolved from initial operation at 700 kW to demonstrated 1 MW performance. Detailed modeling, real-time diagnostics, and systematic optimization of beamline elements underlie the sub-percent control of flux characteristics and systematic uncertainties.

1. Accelerator Complex and Beam Delivery

The NuMI beamline is fed by the Main Injector, which receives protons accelerated to 120 GeV and extracts them in fast, single-turn extraction, resulting in a 10 μs spill. Advances such as slip-stacking in the Recycler ring combine multiple Booster batches, increasing the protons per pulse delivered to NuMI. With six on-center and six momentum-offset batches merged, the number of protons per MI pulse reached up to $5\times10^{13}$, and, combined with cycle-time reduction to 1.067 s, yields ≳1 MW beam power (Schreckenberger, 2023). The resulting power is given by

$$P_{\text{beam}} = \frac{E_p \cdot N_p \cdot e}{T_{\text{cycle}}}$$

where $E_p$ is the proton energy (120 GeV), $N_p$ the protons per cycle, $e$ the elementary charge, and $T_{\text{cycle}}$ the MI cycle time. Table 1 summarizes parameter evolution (Schreckenberger, 2023):

Era	Cycle Time (s)	Protons/Cycle ($10^{13}$)	Beam Power (MW)
Initial (2005)	1.33	3.6	0.5–0.7
Megawatt Era	1.067	5.0	1.02

Anticipated upgrades (PIP-II, ACE) will see further increases: $N_p$ up to $8.5\times10^{13}$, and cycle time reduced to 0.65 s for >2 MW.

2. Target, Focusing Horns, and Secondary Beamline

The proton pulse impinges on a segmented graphite target (POCO ZXF-5Q, 95–125 cm length, water-cooled, beryllium end windows) (Adamson et al., 2015, Wickremasinghe et al., 16 Dec 2024). Dynamic heat loads per pulse approach 30 kW; FEA shows safety factors >7 under 1.2 MW conditions (Papadimitriou et al., 2015).

Secondary mesons (mainly π^+, K^+) are focused by two pulsed aluminum horns (parabolic double-conductor geometry) carrying up to 200 kA current, producing an azimuthal magnetic field $B_\phi(r) = \mu_0 I / (2\pi r)$ (Yonehara et al., 2023, Adamson et al., 2015). The parabolic profile yields a net angular deflection via integrated dipole and quadrupole field components, with optics well-approximated by linear thin-lens formalism and multipole expansion

$$\Delta\theta(r) = -\frac{q\mu_0 I}{2\pi p_z}[a_1 + a_2 r + a_3 r^2+\cdots]$$

with dipole and quadrupole ($a_1\simeq6\times10^{-3}\,\text{m}^{-1}$, $a_2\simeq0.07\,\text{m}^{-2}$) terms dominant (Yonehara et al., 2023). Charge/polarity selection is achieved by horn-current direction, allowing neutrino ($\nu$) or antineutrino ($\bar\nu$) operation.

Downstream, focused mesons enter a 675 m helium-filled decay pipe (NuMI) where $\sim$80% of ∼3 GeV pions decay within the pipe (Adamson et al., 2015). Surviving hadrons are absorbed in a composite Al/steel/concrete absorber; un-decayed μ produce a tertiary muon beam for monitoring.

3. Beam Diagnostics, Monitoring, and Stability

Real-time and periodic monitoring is essential for flux normalization and beam stability. The suite includes:

• Beam Position Monitors (BPMs): resonant-cavity monitors upstream of target, ±50 μm resolution, supporting auto-tuning within ±200 μm (Wickremasinghe et al., 16 Dec 2024).
• Profile Monitors (SEMs, multiwires): mm-scale spot-size measurement.
• Hadron Monitors: ion-chamber arrays after absorber, sensitive to high-energy protons/pions.
• Muon Monitors: three He-gas ion-chamber arrays (downstream alcoves), providing a proxy for parent pion spectrum and horn focusing performance (Yonehara et al., 2023, Wickremasinghe et al., 16 Dec 2024). Hoch-precision current inference (≤0.05%) is realized through beam profile analysis using machine learning.
• Cross-checks: hadron monitor and muon monitor data drive daily horn-current scans, beam alignment, and drift compensation.

Beam-based alignment, including Budal monitors (upstream isolated-fins), maintains sub-mm registration of target and horn axes. The "Autotune" feedback system applies BPM data to trim-magnet, ensuring per-pulse steering corrections.

4. Neutrino Flux Prediction and Systematics

Flux modeling involves a full chain simulation, constrained by hadron-production (NA49, MIPP) near-target data (Collaboration et al., 2016):

• Thin/replica target yields: π^±, K^± production data parameterize $$d^2N/(dp\,d\theta) \approx A\,p^{\alpha}\exp(-Bp_T^2)$$, scaled from NA49 158 GeV to 120 GeV (Collaboration et al., 2016).
• Beamline geometry and focusing: alignment, horn current, and target-horn spacing induce correlated shifts (∼1–3%) in the 4–6 GeV flux region.
• Monte Carlo Integration: the GEANT4-based model propagates all particles, applies data-driven reweighting, and accumulates $E_\nu$ spectra at each detector.
• Total uncertainties: 7.8% (thin-target constraint) and 5.4% (thick-target), with systematic breakdown (hadronic, focusing, geometry).
• In situ confirmation: neutrino-electron elastic and low-ν charged-current scattering in MINERvA validate thin-target predictions to within experimental uncertainty.

The resulting flux for LE-ν NuMI mode at MINERvA: 287 νμ/m²/10⁶ POT, with $\langle E_\nu\rangle\approx3.5$ GeV, ν̅μ/νμ ≈6%, intrinsic (νe+ν̅e)/νμ ≈1% (Collaboration et al., 2016).

5. Timing, Baseline, and Velocity Measurements

NuMI’s fine temporal substructure allows precision velocity and time-of-flight (TOF) measurements. The 10 μs spill comprises six 1.6 μs batches, each with 81 RF bunches separated by 18.83 ns, individual bunches with σ_b ≈1 ns (Adamson et al., 2014).

Key features for TOF and velocity extraction (MINOS):

• Detector timing: both Near (1.04 km) and Far (735 km) detectors use HP5071A Cs clocks, GPS PPP with 0.5 ns repeatability.
• Latency calibration: identical auxiliary scintillator detectors measure electronic latencies, achieving ΔL_rel =24 ± 1 ns between near and far (Adamson et al., 2014).
• TOF extraction: joint-likelihood constructed from the measured proton waveform convoluted with detector resolution. Baseline survey distance $L=734\,291.9\pm2.3$ m (Sagnac-corrected).
• MINOS result: $(v/c-1) = (1.0\pm1.1)\times10^{-6}$, total systematic 2.6 ns (dominated by baseline survey), consistent with light-speed propagation. Planned improvements (precise shaft survey, latency loop closure, GPS characterization) aim for <1 ns systematics and precision of few × 10⁻⁷ on $v/c-1$ (Adamson et al., 2014).

6. Optimization, Upgrades, and Operational Experience

Major upgrades and operational strategies are outcomes of a multi-year program of optimization (Wickremasinghe et al., 16 Dec 2024):

• Target evolution: initial 700 kW design advanced to 1 MW (2019) with thicker, wider graphite fins, upstream shock-absorber fins, and long-term plan for higher-density fins (anticipated 5–10% pion-yield increase).
• Horn alignment and current optimization: periodic horn current scans (±10 kA), GEANT4-based simulations on target-horn spacing (Horn 1 positioned 30 cm upstream).
• Cooling: addition of air diverters (Horn 1) dropped stripline temperatures by 50 °C; baffle ID increase reduced oxidation.
• Operational resilience: repeated failures (stripline fatigue, copper corrosion, BPM digitizer damage) led to FEA-driven mechanical re-engineering, switch to stainless steel, redundant diagnostics, rad-tolerant electronics relocation.
• Modular design: targets and horns built as modular, hot-swappable units (6-week turnover), supporting sustained 1 MW output.
• Integrated online simulation: Optuna-based hyper-parameter optimization deployed for automated tuning, reducing beam loss by 30%.

NuMI's stable operation increased delivered integrated POT by 25% (over three years post 1 MW upgrade), reduced horn failures by 90%, and improved near/far flux characterization (Wickremasinghe et al., 16 Dec 2024).

7. Legacy and Future Integration with LBNF/DUNE

NuMI operational experience is foundational for the Long Baseline Neutrino Facility beamline (Papadimitriou et al., 2015, Papadimitriou et al., 2017). Directly inherited elements include single-turn fast extraction, segmented graphite targets, double-parabolic horn geometry (230 kA, 0.8 ms), and shielded decay pipes (194–250 m, 4 m diameter). Radiological protection is elevated: a geomembrane barrier and multi-ply geosynthetics, 5.6 m-thick concrete around decay pipe, and engineered drainage systems. Design for immediate upgradeability to 2.3–2.4 MW is implemented for all non-replaceable components. Modular, redundant diagnostics and hot-swappable critical systems are mandated from "Day 1" (Wickremasinghe et al., 16 Dec 2024, Papadimitriou et al., 2017). The NuMI model guides future facility design and best practices: robust cooling, automated alignment, real-time modeling, continuous "lessons learned" reviews, and maintenance-driven risk reduction.

• "Measurement of the Velocity of the Neutrino with MINOS" (Adamson et al., 2014)
• "Fermilab Main Injector and Recycler Operations in the Megawatt Era" (Schreckenberger, 2023)
• "The NuMI Neutrino Beam" (Adamson et al., 2015)
• "Neutrino Flux Predictions for the NuMI Beam" (Collaboration et al., 2016)
• "Exploring the Focusing Mechanism of the NuMI Horn Magnets" (Yonehara et al., 2023)
• "Updates and Lessons Learned from NuMI Beamline at Fermilab" (Wickremasinghe et al., 16 Dec 2024)
• "Design of the LBNE Beamline" (Papadimitriou et al., 2015)
• "Design Of The LBNF Beamline" (Papadimitriou et al., 2017)