[Paper Review] RF Cavities For The Muon and Neutrino Factory Collaboration Study

A. Moretti, N. Holtkamp+3 more|ArXiv.org|Aug 18, 2000

Particle accelerators and beam dynamics3 citations

TL;DR

This paper presents the design and cold test results of two high-gradient RF cavities—805 MHz for a muon collider and 201 MHz for a neutrino factory—using beam-matching iris apertures and thin-walled tube grids to maximize shunt impedance and enable efficient ionization cooling. The 805 MHz cavity achieved 33.5 MV/m/m with 77 MV/m peak surface field, while the 201 MHz design reached 32.0 MV/m/m with 25 MV/m peak field, both showing strong agreement with simulations and supporting high-power testing.

ABSTRACT

A multi-laboratory collaboration is studying the feasibility of building a muon collider, the first phase of which maybe a neutrino factory. The phase space occupied by the muons is very large and needs to be cooled several orders of magnitude for either machine, 100,000 to 1 million for the collider and ten to 100 for the factory. Ionization cooling is the base line method for muon cooling. This scheme uses hydrogen absorbers and rf re-acceleration in a long series of magnetic focusing channels to cool the muons. At Fermilab two rf cavity types are under study to provide the required cooling rf re-acceleration, a 805 MHz high gradient cavity for the collider and a 201 MHz high gradient cavity for the neutrino factory. The 805 MHz cavity currently under going cold testing is a non-periodic pi-mode cavity with the iris openings shaped to follow the contour of the beam. The 201 MHz cavity uses hollow thin metal tubes over the beam aperture to terminate the field in a pill-box type mode to increase its shunt impedance. This is possible because muons have little interactions with thin metal membranes. Details of these cavities and cold measurement data will be presented.

Motivation & Objective

• Develop high-gradient, high-shunt-impedance RF cavities to enable ionization cooling in muon and neutrino factory accelerators.
• Address the challenge of cooling muons from a large 6D phase space to meet luminosity requirements in a short time.
• Optimize cavity geometry to minimize beam interception and peak surface electric fields while maximizing shunt impedance.
• Validate cavity designs through 3D electromagnetic simulations and cold model testing to ensure performance before high-power operation.
• Enable high-power testing of 805 MHz copper cavities and prototype development of 201 MHz cavities for future accelerator complexes.

Proposed method

• Designed a 201 MHz gridded cavity with crossed hollow aluminum tubes (4 cm diameter, 125 µm thick) over the beam aperture to terminate fields in a pillbox-like mode, increasing shunt impedance.
• Used MAFIA 3D time-domain and 2D eigenmode solvers to optimize cavity geometry, focusing on shunt impedance, peak surface field, beam intercept, and inter-cavity coupling.
• Engineered an 805 MHz open-cell cavity with iris apertures shaped to follow the five-sigma beam contour to avoid material in the beam path and maximize shunt impedance.
• Simulated high-power RF couplers using a two-cell model with a rectangular waveguide and slot-coupling mechanism, adjusting slot width for critical coupling (β = 1).
• Conducted bead-pull measurements and field profile validation on a full-scale aluminum model to verify simulation accuracy within ±5 µm and ±5%.
• Calculated coupling coefficient β using the energy method with time-domain field data, achieving 97.6% agreement between measured and simulated β (0.976 vs. 1.000).

Experimental results

Research questions

• RQ1 How can RF cavity design be optimized to achieve high shunt impedance and low peak surface electric fields in large-aperture cavities for muon cooling?
• RQ2 To what extent does matching the iris aperture to the beam contour improve shunt impedance without introducing beam interception?
• RQ3 Can thin-walled metallic tubes effectively replace beryllium windows in high-gradient cavities to reduce mechanical and thermal challenges?
• RQ4 What is the achievable coupling coefficient and field profile accuracy in a prototype cavity when validated against 3D electromagnetic simulations?
• RQ5 Can cold model measurements of field profile and frequency agree with simulation within 5% and 5 µm, respectively, to support high-power testing?

Key findings

• The 201 MHz gridded cavity achieved a shunt impedance of 32.0 MOhm/m and required 4.5 MW to reach 15 MV/m, with a peak surface electric field of 25 MV/m, 1.7 times the Kilpatrick limit.
• The 805 MHz open-cell cavity achieved a shunt impedance of 33.5 MOhm/m and required 27.7 MW to reach 30 MV/m, with a peak surface electric field of 77 MV/m, 2.9 times the Kilpatrick limit.
• Cold model measurements of the 805 MHz cavity showed excellent agreement with simulations: frequency and field profile within 5 µm and 5%, respectively.
• The critical coupling slot dimensions were determined as (height, depth, width) = (6.2, 2.2, 8.2) cm, with a measured coupling coefficient β = 0.976, closely matching the simulated β = 1.000.
• The aluminum model's machining accuracy met the ±13 µm tolerance, and measurements confirmed the reliability of MAFIA and Superfish simulations for cavity design.
• High-power testing of a copper 805 MHz cavity is underway, with breakdown and vacuum conditioning studies planned at Fermilab’s new high-power test facility.