Transverse emittance reduction in muon beams by ionization cooling

The study addresses whether ionization cooling can reduce the transverse emittance of muon beams sufficiently and reliably to enable future muon-based facilities (muon colliders and neutrino factories). Muon beams, produced as tertiary beams from pion/kaon decays, occupy large phase-space volumes and must be cooled rapidly within the muon lifetime (2.2 μs at rest). Conventional cooling methods (stochastic, electron, synchrotron radiation cooling) are too slow for muons, motivating ionization cooling: passing muons through low-Z absorbers to lose momentum via ionization energy loss, with longitudinal momentum restored by RF cavities. The Muon Ionization Cooling Experiment (MICE) was designed to demonstrate and quantify transverse emittance reduction from ionization cooling and to compare measurements with theory and simulation, thereby establishing the viability of this technique for future facilities.

Prior work established the principles of ionization cooling and its potential for muon facilities, with theoretical formulations of normalized transverse rms emittance evolution under energy loss and multiple scattering. Alternative approaches under development include phase-space compression in cryogenic helium gas with strong E and B fields (PSI), and production of ultracold muons via resonant laser ionization of muonium atoms. A prior MICE analysis (Nature 2020) reported an unambiguous cooling signature via increased core phase-space density after an absorber. Studies of multiple Coulomb scattering in LiH by MICE found good agreement with GEANT4 models, supporting reliable modelling of the heating term. Electron-positron collider proposals (FCC-ee, CEPC, ILC, CLIC) and alternative muon sources (positron-driven) provide broader context for the importance of compact, precise muon colliders and neutrino factories requiring intense, low-emittance muon beams.

Experimental apparatus: The MICE cooling channel comprised a magnetic lattice of 12 superconducting solenoid coils arranged as two spectrometer solenoids (upstream TKU and downstream TKD) surrounding a central focus-coil module that housed the absorber (LiH or liquid hydrogen, LH2). Each spectrometer solenoid provided up to 4 T uniform field in the tracker region and contained additional matching coils. The focus-coil pair tightly focused the beam at the absorber to minimize β⊥ and reduce multiple scattering-induced heating. Coils were powered with opposite polarities to flip field polarity at the absorber center, suppressing canonical angular momentum growth. A partial return yoke contained stray fields. A downstream matching coil was inoperable due to a power lead failure; lattice settings were optimized to retain clear cooling sensitivity.

Beam production and selection: Muons were produced by ISIS synchrotron protons on a titanium target, with a transfer line delivering beams tunable to 140–240 MeV/c. A brass/tungsten diffuser at channel entrance tuned input emittance (3–10 mm). For this study, beams at ~140 MeV/c and nominal input emittances of 4, 6, 10 mm were used. Particle identification upstream used two TOF detectors (TOF0, TOF1) and two threshold Cherenkov counters; downstream, TOF2, a pre-shower calorimeter (KL), and the electron-muon ranger (EMR) identified decay electrons and validated muon tracks. Two identical scintillating-fiber trackers (TKU, TKD), each with five stations of triple-layered 350 μm fibers in 3 T fields, measured position and momentum by helical track fits including scattering and energy loss. For low-transverse-momentum tracks, momentum resolution was improved by combining tracker fits with TOF velocity.

Absorbers and materials: LiH absorber was a 65.37 ± 0.02 mm-thick disc at ρ = 0.6957 ± 0.0006 g/cm³, with 95.52% 7Li and 4.48% 6Li. The LH2 absorber was a 22 L vessel (300 mm diameter cylinder) with dome-shaped Al windows; on-axis LH2 thickness 349.6 ± 0.2 mm at ρ = 0.07053 ± 0.00008 g/cm³ (20.51 K). Total on-axis Al window thickness for the LH2 module was 0.79 ± 0.01 mm; additional Al 6061-T651 windows were located near TKU and TKD. Material parameters (ρ, Z/A, I, X0) used in modelling are documented.

Optics and beam sampling: Due to under-focusing in the transfer line, TKU optics were mismatched, yielding oscillatory β and increased β at the absorber, degrading cooling. A rejection-sampling algorithm (KDE-based accept-reject) was devised to carve matched subsamples from the measured parent beams, targeting Gaussian beams with βx = 311 mm and dβx/dz = 0 at TKU, and specified transverse emittances. KDE estimated Parent(u) in 4D transverse phase space; a Gaussian Target(u) defined the desired covariance. Particles were accepted with probability e × Target/Parent, with e chosen to bound probabilities by 1. This procedure reduced β at the absorber by ~28% vs parent. For each absorber configuration, six independent matched subsamples at TKU with εt = 1.5, 2.5, 3.5, 4.5, 5.5, 6.5 mm were produced, enabling emittance-scan studies; sample sizes are reported in Extended Data.

Event selection: Criteria required exactly one space point in TOF0 and TOF1, one valid track in TKU and TKD; TOF0–TOF1 timing and TKU momentum consistent with a muon; tracks within a 150 mm-radius fiducial and χ²/dof < 8; TKU momentum in 135–145 MeV/c; TKD momentum in 120–170 MeV/c (empty) or 90–170 MeV/c (with absorber); and diffuser radial excursion within aperture by at least 10 mm. The same criteria were applied to simulation.

Measurement and model: The emittance change was defined as Δεx = εx,down − εx,up between TKD and TKU reference stations. The theoretical dependence on input emittance was derived from the ionization cooling equation, yielding Δεe(z) = εi − εe[1 − exp(−∫0^z (dE/dz)/εe dz)], where εe is the equilibrium emittance and dE/dz follows Bethe–Bloch. The expected Δε includes all traversed materials (absorber plus Al windows, including spectrometer-solenoid windows and LH2-vessel windows when present). A full GEANT4-based simulation (MAUS) of the apparatus was used both to predict cooling performance and to estimate detector-related corrections.

Systematic uncertainties: Systematics were assessed by parameter scans in simulation, assigning the induced Δε shift as uncertainty for each source: tracker misalignments (±3 mm translations, ±3 mrad rotations); magnetic field uncertainties (±1% in Center coils, ±5% in End coils in each spectrometer); tracker material (±50% glue density); TOF01 timing uncertainty (±60 ps). Uncertainties were combined in quadrature per εi bin; totals grow with emittance (e.g., ~0.026 mm at 1.5 mm to ~0.084 mm at 6.5 mm).

• Ionization cooling was directly quantified as a reduction in normalized transverse emittance after traversing absorbers.
• Empty-channel controls (No absorber and Empty LH2) showed no cooling; slight heating was observed due to optical aberrations and scattering in Al windows (additional heating in Empty LH2 due to vessel windows).
• Both LiH and full LH2 absorbers produced emittance reductions for input emittances ≳2.5 mm at ~140 MeV/c, consistent with ionization cooling expectations and model predictions including window effects.
• Linear fits to Δε versus input ε at TKU yielded:
  • No absorber: intercept 0.102 ± 0.007 mm, slope −0.011 ± 0.012
  • LiH: intercept 0.297 ± 0.006 mm, slope −0.115 ± 0.013
  • Empty LH2: intercept 0.150 ± 0.005 mm, slope −0.006 ± 0.013
  • Full LH2: intercept 0.279 ± 0.007 mm, slope −0.118 ± 0.013
• Effective equilibrium emittances (from linear trends) were 2.6 ± 0.4 mm (LiH) and 2.4 ± 0.4 mm (full LH2) for β* ≈ 450 mm and p ≈ 140 MeV/c, in agreement with theoretical expectations (~2.5 mm including window contributions).
• Statistical tests rejected the null hypothesis that slopes in absorber and empty cases are compatible: p < 10^-5 for both LiH vs No absorber and Full LH2 vs Empty LH2.
• No significant performance difference between LH2 and LiH was observed in this setup, due to scattering in absorber windows degrading LH2 performance to be similar to LiH.
• Reconstructed data agreed well with simulation across configurations; detector and transmission corrections were applied.

The results directly address the central question of whether ionization cooling can reduce muon-beam transverse emittance within realistic accelerator components. By observing emittance reduction only when absorber material is present and quantifying its dependence on input emittance, the study validates the ionization cooling mechanism and its theoretical description, including multiple-scattering heating and material effects (e.g., Al windows). The measured equilibrium emittances near 2.5 mm at 140 MeV/c match expectations for the given optics (β* ≈ 450 mm) and materials, demonstrating predictive control.

This establishes ionization cooling as a practical means to generate lower-emittance muon beams, a prerequisite for muon colliders and neutrino factories. While ultimate collider targets require orders-of-magnitude further reduction (transverse and longitudinal emittances O(10^-2 mm)), this experiment confirms the core physical process, motivates channels with stronger focusing (smaller β⊥), lower-scattering windows, and integrated RF to restore longitudinal momentum. The lack of superior performance for LH2 in MICE highlights the importance of minimizing window thickness and aperture size; future lower-emittance channels with smaller bores should better exploit hydrogen’s advantages. The beam-sampling approach also shows a powerful methodology to probe optics-dependent cooling trends using particle-by-particle measurements.

MICE has quantitatively demonstrated transverse emittance reduction of muon beams via ionization cooling using both LiH and LH2 absorbers, with measurements consistent with theoretical models and full simulations. Effective equilibrium emittances of about 2.5 mm were determined, and empty-channel controls confirmed that observed changes arise from absorber-induced cooling. This represents a substantial advance toward practical muon cooling channels, an essential step for high-brightness muon sources.

Future work should develop a muon cooling demonstrator employing stronger focusing (smaller β⊥), optimized low-Z absorbers with minimal/thinner windows, and high-gradient RF cavities to restore longitudinal momentum and enable repeated cooling stages. Design studies are underway toward integrating multiple cells to achieve the transverse and longitudinal emittance targets required for muon colliders, with the MICE results providing critical validation and benchmarks.

• Optics mismatch from the transfer line increased β at the absorber compared with design, reducing cooling performance; mitigated by a sampling algorithm to select matched subsamples.
• A downstream spectrometer-solenoid matching coil was inoperable, necessitating compromises in optics and transmission.
• Scattering in aluminium windows (spectrometer and LH2-vessel windows) introduced heating that limited net cooling and diminished the relative advantage of LH2.
• The experiment did not include RF reacceleration; longitudinal momentum restoration is required in practical cooling channels.
• Systematic uncertainties were dominated by magnetic-field knowledge in tracking regions and, to a lesser extent, tracker material modelling and alignment; these contribute Δε systematics up to ~0.08 mm at higher input emittances.
• Results pertain to ~140 MeV/c beams and specific β* (~450 mm); extrapolation to other momenta and stronger focusing requires further dedicated studies.