NuMI: Neutrinos from the Main Injector

• NuMI is a high-power accelerator facility at Fermilab that produces tunable neutrino beams for precision long-baseline neutrino oscillation experiments.
• It employs advanced beamline components, including high-current magnetic horns and graphite targets, along with innovative slip-stacking and monitoring techniques to achieve >1 MW beam power.
• Operational insights from NuMI have informed designs for future experiments like DUNE by addressing challenges in thermal management, mechanical fatigue, and systematic uncertainties.

The Neutrinos at the Main Injector (NuMI) facility at Fermilab is a high-power accelerator complex dedicated to the production of intense, tunable neutrino beams for long-baseline experiments. Designed to support precision measurements in neutrino oscillation physics, NuMI has continuously evolved with substantial upgrades to its primary beamline, meson production targets, magnetic horn focusing systems, decay volumes, and comprehensive monitoring infrastructure. The operational experience, performance, and challenges encountered in NuMI beam delivery provide critical benchmarks for the design and operation of future facilities such as the Long-Baseline Neutrino Facility (LBNF) and the Deep Underground Neutrino Experiment (DUNE).

1. System Architecture and Beamline Components

NuMI utilizes 120 GeV protons from Fermilab’s Main Injector, extracted via a single-turn kicker, to deliver intensities up to (and above) 1 MW to a graphite target (Adamson et al., 2015, Wickremasinghe et al., 16 Dec 2024). The beam transport line consists of a 350 m lattice of dipoles and quadrupoles with trim correctors and beam position/intensity/shape monitors (BPMs, SEMs, toroids), maintaining beam spot sizes of 1.1–1.5 mm (σ) at the target and sub-100 μm positioning repeatability. The target, constructed of POCO graphite fins (20 mm deep, 15 mm high, 6.4–9 mm wide per segment for >1 MW operation), is water cooled and remotely adjustable in both longitudinal and transverse dimensions to accommodate energy spectrum retuning and to mitigate alignment drifts (Adamson et al., 2015, Wickremasinghe et al., 16 Dec 2024).

Immediately upstream of the target, a graphite baffle with an enlarged inner diameter for the 1.5 mm beam spot and augmented by upstream cylindrical fins, serves to intercept mis-steered protons, limit damage to the horns, and accommodate thermally induced misalignments. Downstream, two high-current (>200 kA) aluminum magnetic horns generate predominantly toroidal fields, modeled as (Yonehara et al., 2023):

$b_\phi = \frac{\mu_0 I}{2\pi r}$

with field multipole expansion terms introducing dipole and quadrupole optics that focus secondary pions into the decay volume:

$$\theta(p_z, r, \theta_0) = \theta_0 - \frac{q\mu_0 I}{2\pi p_z} (a_1 + a_2 r + a_3 r^2)$$

Transition and weld locations, current pulse widths (2.3 ms historically, reduced to 0.8 ms for >1 MW), air diverter stripline cooling, and robust load-balancing are engineered to address metal fatigue and high-current pulse-induced failures (Wickremasinghe et al., 16 Dec 2024).

Mesons thus focused are injected into a 675 m-long decay pipe (2 m diameter, steel-walled, surrounded by concrete with integrated copper cooling), where they decay mostly into muons and neutrinos. The pipe is helium-filled under current operations for radioprotection and cooling optimization. The decay volume is terminated by a hadron absorber (aluminum, steel, and concrete layers), followed by 240 m of dolomite rock acting as a muon shield.

2. Accelerator Operations and Upgrades

NuMI’s high-power regime is enabled by the interplay of several Main Injector (MI) and Recycler innovations (Schreckenberger, 2023). The slip-stacking technique in the Recycler affords the injection and phase-space merger of twelve 84-bucket Booster batches, achieved via off-center RF frequency offsets to minimize direct-current beam issues. Recent transition from “Radial On-Center” to “Radial Off-Center” slip-stacking reduced the required frequency separation (from 2520 to 1680 Hz at 20 Hz Booster rate) and halved loss rates in the MI. Alongside, shortening the MI ramp time (from 1.2 s to 1.067 s and targeted further to 0.65 s) directly increases beam power per

$P = |e| E \ \frac{N}{T}$

resulting in NuMI operation at >1 MW, with further increases planned under the Accelerator Complex Evolution (ACE) project (Schreckenberger, 2023).

These innovations ensure that high average intensity (up to 4 × 10¹³ proton pulses every 1.33 s) is delivered to the NuMI production target with minimal beam loss (<10⁻⁵ in the transport line), as verified by beam permit systems checking hundreds of hardware and monitoring interlocks (Adamson et al., 2015).

3. Beam Monitoring, Alignment, and Control

NuMI employs an extensive suite of diagnostics throughout the beamline (Adamson et al., 2015, Yonehara et al., 2023, Wickremasinghe et al., 16 Dec 2024):

• Primary Beamline: Multiple BPMs, SEMs, toroids, and resistive-wall monitors continuously provide spatial and intensity profiles at sub‑micron/milliradian granularity. The integrated Autotune system employs this feedback to pulse-to-pulse steer the beam.
• Target Hall & Carrier: Budal monitors (wire loops) detect the passage of the beam via induced voltage, facilitating offline beam-based alignment scans to sub‑millimeter precision.
• Post-Target: The hadron monitor immediately downstream of the absorber samples remnant protons/mesons, with ionization chamber arrays providing beam centroid, width, and flux measurements.
• Muon Monitors: Three alcoves containing ionization chambers measure muons of threshold energies ~4, 10, and 20 GeV, respectively. The muon profile is a highly sensitive proxy for horn focusing and proton beam intensity. Analytical expansion of the focusing field as dipole/quadrupole components enables using the centroid motion in muon monitors as a diagnostic for horn current; ML-based algorithms have improved the accuracy of horn current determination to ±0.05% (Yonehara et al., 2023).

Beam-based alignment is performed during commissioning and after significant hardware interventions by rastering a reduced-intensity beam across physical references (e.g., baffle, horns), precisely locating mechanical axes and refining operational settings to minimize spectrum distortions at downstream detectors.

4. Beamline Performance, Upgrades, and Lessons Learned

Substantial hardware upgrades have been required to reach and sustain 1 MW operation (Wickremasinghe et al., 16 Dec 2024). Notable updates include:

• 1 MW Target and Horns: New graphite targets with increased width and height, augmented by additional upstream fins to mitigate window thermal shocks. Enhanced horn stripline cooling (air diverters) and stripline redesign to accommodate >200 kA pulses have addressed recurrent failures from thermal cycling, electrical imbalance, and material fatigue.
• Baffle and Beam Optics: Enlargement of the baffle aperture and optimization of quadrupole lattice parameters allowed for a higher-intensity, larger-spot (>1.5 mm) proton beam while managing thermal loads (<50°C baffle rise in normal operation).
• Systematic Ramp-Up: Beam power increases have been executed in staged fashion, with operational experience indicating that precise beam centering, chromaticity optimization, and careful tuning are required to avoid excessive baffle heating, horn stripline failure, and thermal excursions.
• Reliability Improvements: Key lessons involve (i) rigorous thermal and mechanical analysis of beam-exposed components; (ii) systematic implementation of redundant or easily replaceable systems (e.g., spare horns); (iii) adoption of robust, high-conductivity graphite for next-generation targets; and (iv) advanced real-time data acquisition and monitoring (Badgett et al., 2015).

A documented practice is to conduct comprehensive simulation-guided thermal studies before any major hardware change, use instrumented surveillance for early detection of component stress or failure, and include deliberate redundancy and maintenance access in future LBNF/LBNE beamline design (Wickremasinghe et al., 16 Dec 2024, Papadimitriou, 2011, Papadimitriou et al., 2015).

5. Neutrino Flux Tuning, Uncertainties, and Experimental Implications

Producing a well-characterized and tunable neutrino spectrum underpins the NuMI facility’s physics program. The horn current, target position, and horn separation can be systematically varied to shift the peak neutrino energy (∼3–4 GeV for νμ, with longer tails for ν̄μ) (Adamson et al., 2015). This tunability, combined with in situ beam instrumentation and off-axis configurations (as exploited by NOvA), allow tailored fluxes for specific oscillation channel sensitivities.

Neutrino flux estimation has evolved from purely Monte Carlo predictions (using Geant or FLUKA hadron production models) to hybrid models that incorporate external thin-target data (e.g., NA49), thick-target replica measurements (MIPP), pion/kaon yields, and “low-ν” and νe⁻ scattering in situ normalization (Collaboration et al., 2016). A typical weighting formula for correcting simulated pion yields is

$$w(x_F, p_T, p) = \frac{f_\text{Data}(x_F, p_T, p_0)}{f_\text{MC}(x_F, p_T, p_0)} \cdot s(x_F, p_T, p)$$

where $x_F$ is the Feynman x, $p_T$ the transverse momentum, and $s$ a scaling factor.

Propagated uncertainties in beam optics, alignment, and hadron production are quantified using multi-universe random sampling, resulting in flux predictions constrained to 5–8% across 0–20 GeV (Collaboration et al., 2016). This precision is essential for systematics budgets in cross-section and oscillation analyses in MINOS, MINOS+, MINERvA, NOvA, and MicroBooNE.

6. Cross Sections, Oscillations, and Physics Reach

NuMI’s performance enables a diverse range of high-precision physics measurements:

• Inclusive CC Cross Sections: High-statistics samples yield νμ/ν̄μ–Fe cross sections measured to 2–8% (νμ, 3–9% ν̄μ) in the 3–50 GeV range. Analysis using the “low-ν method” for flux normalization extracts the flux and systematics-independent cross section shape and normalization (0910.2201). The cross-section ratio

$r = \frac{\sigma(\bar{\nu}N)}{\sigma(\nu N)}$

approaches the QPM asymptote as predicted, with strong constraints on nucleon anti-quark content.

• Oscillation Measurements: The 735 km baseline (Fermilab–Soudan) and tunable energy spectrum yield $\nu_\mu$ (and $\bar{\nu}_\mu$) disappearance measurements sensitive to atmospheric $\Delta m^2$ at few-percent precision, and direct limits on $\sin^2(2\theta_{23})$ ($>0.75$ at 90% CL) (Adamson et al., 2012). MINOS also constrains electron-neutrino appearance, θ₁₃, and sets null results in sterile neutrino searches (Orchanian, 2011, Timmons, 2015).
• Systematics Mitigation: The use of near and far detectors with functionally identical technology, comprehensive beam monitoring, and analysis techniques exploiting low-ν, CCQE, and energy-reconstructed spectra reduce correlated systematics from flux, cross-sections, and detector response.

7. Outlook and Implications for Future Facilities

NuMI’s experience is foundational for the design, construction, and commissioning of subsequent long-baseline beamlines such as LBNE/LBNF/DUNE (Papadimitriou, 2011, Papadimitriou et al., 2015, Papadimitriou et al., 2017, Wickremasinghe et al., 16 Dec 2024). Key aspects directly carried forward include:

• Modular hardware engineered for high-reliability and easy maintenance under high activation.
• Target and horn systems retrievable via rail or articulated manipulators; use of segmented or beryllium targets considered for enhanced thermal performance.
• Beamline and decay pipe shielding designed for >2.3 MW operation (thicknesses of 5.5–5.6 m concrete), with engineered geomembranes and controlled drainage to protect groundwater.
• Integrated, simulation-validated radiological and environmental mitigation strategies.
• Advanced data acquisition and monitoring infrastructure, leveraging high-bandwidth, scalable, partitionable networks (Badgett et al., 2015).
• Institutionalization of thorough thermal and mechanical simulation, regular monitoring, and staged power ramp-up as operational doctrine.
• Value engineering and staged build-out strategies to optimize cost, schedule, and flexibility (Moore et al., 2015).

NuMI demonstrates that systematic analysis of operational failures—such as horn stripline fatigue, baffle overheating, and digitizer/beam monitor replacements—combined with ongoing hardware R&D, simulation-driven design revision, and continuous monitoring, are prerequisites for reliable high-intensity accelerator neutrino beam operation (Wickremasinghe et al., 16 Dec 2024). The facility’s legacy is a blueprint for achieving the intensity, stability, and reliability required by the next generation of oscillation experiments probing CP violation, mass hierarchy, and beyond-standard-model physics.