Accelerator R&D

Recent progress in overcoming technical challenges posed by the muon’s lifetime has generated a great deal of excitement for particle physicists. Current focus is on advancing a full design for a 10 TeV collider to prepare to build a demonstrator.

Target and Capture

The Muon Accelerator Program (MAP) has established the target proton beam intensity and the time structure to achieve the design muon collider luminosity. Specifically, the proton beam bunch length is extremely short (1-3 ns) and the proton beam density will be close to 10¹⁵ cm^-3. This density goes beyond any present operational target facility in the world. Past investigations of damage in beam irradiated materials suggest that survivability of the material is critically dependent on the magnitude of the instantaneous thermal impulse. Specific studies of the muon collider target that should be pursued in the 3-5 year time frame are as follows:

• Utilize high-performance computer simulations to identify potential target materials and dimensions, taking into account engineering stress tolerance and pion yields. Utilize Density Functional Theory (DFT) and Molecular Dynamics (MD) to simulate the lattice defects on a sub-pico second scale. Integrate the beam impact process model in the simulation tool.
• Design the optimization algorithm based on AI/ML for the muon collider target system. Conduct pion yield measurements in the thick target at the anticipated proton driver beam energy in order to integrate pion yield parameter into the algorithm.
• The current baseline target material is graphite, but fluidized or high-granular targets should also be studied. Development of a specialized circulatory system and a radiation-hard beam window are necessary in these scenarios.

Magnets

The accelerator and collider magnet goals for muon colliders are aggressive, but the fundamental machine requirements for a muon collider are more relaxed than those needed for the FCC-hh. Muon colliders will need significant advances in magnet design beyond currently available magnet technologies. Significant developments will need to be made in the HTS magnet space in order to fully optimize the collider design. Synergies with the Magnet Development Program (MDP), compact fusion and high field science magnets (40T NHMFL) help with this development and should be leveraged. Dialogue between machine and magnet designers is critical to explore many tradeoffs. Current efforts in the US (MDP) and EU (HFM) are inadequate to support muon collider magnet needs in a reasonable timeframe – tradeoff studies are needed to define the approach. IMCC contends that a technically limited scheduled would enable a 3 TeV Muon Collider to be ready shortly after the HL-LHC shutdown in early 2040s. A technically limited schedule will need a substantial increase in resources on both sides of the Atlantic to be realized. Specific efforts that should be pursued in the 3-5 year timeframe are as follows:

• Solenoid design and prototyping for the late 6D cooling stage parameters should be carried out and the test results should be integrated into the muon collider 6D cell prototype.
• Solenoid quench protection requirements both for the late 6d and final cooling stage should be used to develop a conceptual design and integrate this into the muon collider 6D prototype.
• Both a conceptual and then a technical design of the late 6D cryomodule (RF + magnet) design should be delivered that is ready for prototyping.
• A conceptual design and an R&D program for supporting a 40–50 T prototype for the final cooling stage should be undertaken.
• For the demonstrator (RF + magnet), specifications need to be developed, followed by a conceptual design and then a full technical design construction proposal.
• For the TeV-class accelerator design – an understanding of the limits of the peak field should be developed, followed by a fast-ramping magnet conceptual design and then a technical design for a fast ramp power supply and magnet demonstration.
• For the collider design – radiation shielding and combined function design options should be studied, followed by the conceptual and then technical design of muon collider dipoles (Nb3Sn, HTS) with a clearly defined cable and magnet R&D program.

Normal-Conducting RF

For a multi-TeV muon collider based on a proton-driven muon source, the normal conducting RF (NCRF) cavities are essential components for muon capturing and ionization cooling. These cavities operate at hundreds of MHz in a multi-tesla B-field background from the surrounding superconducting (SC) solenoids. Achieving the high gradient in these cavities is critical for the ionization cooling rate and eventually the luminosity of the muon collider.

The major question for the muon collider NCRF cavities development is how to overcome the RF breakdown and achieve high RF gradient in strong B field at hundreds of MHz. Other important topics include: the compact integration of the high-power RF cavities and the SC solenoids in the cooling channel, the development of the high-peak power short pulse length RF source at hundreds of MHz, the evaluation and mitigation of the higher-order-modes and the beam loading, etc.

The R&D in MAP and pre-MAP era has demonstrated the feasibility of achieving 50 MV/m surface gradient in a 3T solenoid field, as well as some key engineering features for such cavities. Still, significant progress is needed to achieve or even surpass the current baseline design requirements. For the near term in the next 3 to 5 years, the NCRF cavity R&D will be prioritized in the following areas:

• Design and prototype a multi-cell fully operational RF cavity module for the proposed demonstrating cooling cell. This cavity will be the culmination of the breakdown mitigation practices and the engineering experience learnt from the previous studies, and represent the best chance to achieve the required accelerating gradient (~25 MV/m) in the cooling cell magnets based on our current knowledge. Besides the cavity itself, this study will also address how to compactly integrate the cavity with the SC solenoids in the demonstrating cooling cell.
• Study novel methods to achieve high gradient in strong B field background in a vacuum cavity, such as cryogenic copper cavity, short RF pulse, breakdown-resilient materials such as copper alloy, possibly aluminum, etc. Theoretical analysis and multi-physics simulation will be carried out for testing designs. Explore the location and resources for establishing a dedicated testing facility. Explore the collaborating testing opportunities with other projects such as breakdown study for linear collider, photocathode development, etc.
• Explore the alternative non-vacuum cavities, including the high-pressure hydrogen gas-filled cavity and the dielectric loaded cavity.
• Study the interaction between the RF cavity and the intense muon beam, and if needed, the HOM/beam loading mitigation methods.
• Investigate the high peak power (~3 MW), short pulse length (~µs) and high efficiency RF power source at hundreds of MHz.

Super-Conducting RF

SRF cavities will be used in the muon acceleration chain from the SRF linac (0.255 – 1.25 GeV) through dog-bone RLAs (1.25 – 63 GeV) to RCSs (up to the final energy). Along this chain of accelerators, the RF frequency would change from 325 MHz to 1300 Hz and accelerating gradients from 20 MV/m to 38 MV/m.

There are significant challenges that need to be addressed via R&D and dedicated studies. Among these challenges are:

• A very high muon bunch intensity of ~2×10¹² and possibly higher would favor larger cavity apertures and hence lower RF frequencies.
• A relatively small aperture of 1300 MHz cavity may not be sufficient and might require switching to lower frequency, e.g., 800 MHz (potential synergy with FCC-ee).
• High gradient operation of multi-cell 800 MHz and 650 MHz cavities must be demonstrated (potential synergy with HEP/GARD program, FCC-ee, and ACE at FNAL).
• 325 MHz cavity most likely will utilize Nb/Cu SRF technology, in synergy with ongoing R&D at CERN for FCC-ee.
• Stray magnetic fields from high-field magnets may significantly degrade performance of SRF cavities – there is a need to developing efficient magnetic shielding and/or develop SRF cavities based on alternative superconductors.
• Effect of high-intensity radiation from muon decays on the performance of SRF cavities is unknown and must be studied.

Recent SRF R&D results – supported by HEP/GARD – demonstrated feasibility of high gradients at 1300 MHz (~40 MV/m in 9-cell cavities) and 650 MHz (~55 MV/m in single-cell cavity, still preliminary result). We need to maintain progress in this research.

Key R&D priorities for the next 3-5 years stem from the plan developed for P5 and were presented at the workshop. Here are the main points of the plan:

• Perform studies of beam interaction with SRF cavities at different frequencies, including acceleration, longitudinal beam dynamics, wake-fields, bunch length evolution, and energy spread control. Select RF frequencies for different accelerators.
• Using synergies with other programs, develop SRF cavity concept designs, select one or two most challenging to fabricate prototypes.
• Develop cavity treatment recipe for high gradient and low sensitivity to residual magnetic field. Demonstrate the cavity performance in vertical testing. Utilize synergies as much as possible.
• Potentially initiate collaboration with CERN on Nb/Cu low-frequency SRF.
• If there is a breakthrough in developing alternative superconductors for SRF, initiate R&D to achieve specific muon collider goals.

Ionization Cooling Cell Prototyping & Demonstrator

The majority of ionization cooling in a muon collider occurs in the rectilinear cooling channel. A prototyping and demonstration program for ionization cooling is largely focused on that type of cooling system. The beamline of this channel consists of chains of repeating cooling cells, whose parameters evolve from values that are relatively straightforward to achieve at the beginning to ones that are far more challenging toward the end. There are two programs that would be developed.

A cooling demonstrator would consist of a significant number of cells, probably in the range of 10 to 20, that one would transport a muon beam through and measure a significant amount of cooling. This would require a muon source providing sufficient current and an appropriate time structure for the experiment and a capture system to set up the initial distribution for the cooling channel. Cost considerations would lead one to construct this from cooling cells whose parameters are not especially challenging. The IMCC has begun work on the design of such a demonstrator.

A prototype cell would construct and power the most difficult ionization cooling cell. It would consist of a full cooling cell with the RF cavity in the center, absorbers on each side that would be between cells, and a half cell of magnets on each side so that the magnets and RF cavities are seeing fields and forces similar to what they would have in a full cooling channel. Designing, building, and powering this cell will force us to face the most challenging engineering issues and prove that we can build the system that will achieve the lowest emittances. The design process will also provide essential input to the beam physics design of the cooling channel, as we expect we will need to make adjustments to the collider cooling channel design to take into account engineering requirements.

The demonstrator and the prototype cell will require design and prototyping of the solenoids and the RF cavity. Studies of RF cavity performance in magnetic field for different RF cavity wall materials will be important input to the cooling channel design, and first solenoid prototypes for the prototype cell could be used for that RF cavity study program. An early program may look something like the following:

• The cooling demonstrator cooling cell would be designed. A proton source for the demonstrator would be chosen. Required diagnostics for the demonstrator would be described. A first solenoid for the prototype cell would be designed. The RF cavities for the prototype cell and the cavity performance test would be designed, and their RF power sources would be chosen.
• The cooling demonstrator cell design would be finalized. The remainder of the cooling demonstrator would be designed. A first solenoid for the prototype, that could also be used for the cavity performance test, would be built. Solenoids for the demonstrator would be designed. The remaining solenoids for the cooling cell prototype would be designed, along with their integration into the full prototype. The RF cavity for the demonstrator would be designed, and the performance test cavity would be built.
• Solenoids for the prototype cell and a second solenoid for the cavity performance test would be built. The cavity performance test program would begin. The cavity for the cooling prototype would be built. A design report for the cooling demonstrator would be produced.

Proton Driver and Synergies with SNS

The muon collider proton driver (MCPD) will deliver short, intense proton pulses to a target to generate muons through pion decay. Preliminary designs call for 2–4 MW of beam power on the target at 5–10 Hz repetition rate, 5–20 GeV energy, and 1–3 nanosecond bunch length. The MCPD will use an H- linac and charge-exchange injection to compress the bunch length to several hundred nanoseconds in an accumulator ring; a second ring will compress the bunch length to a few nanoseconds. The final proton beam intensity will be larger than in any existing accelerator. Potential issues include:

• Collective effects during accumulation and compression
• Injection foil heating, degradation, and scattering
• Halo formation and beam loss

The Spallation Neutron Source (SNS) mirrors the proton driver design and will be capable of 2.8 MW operation this year. We propose the following R&D priorities at the SNS to help solidify the MCPD design parameters:

• Study proton bunch compression experimentally and benchmark simulation models: Compressed proton bunch dynamics could be explored by modifying the ring RF system or installing new hardware. Collective effects should be comparable to the MCPD due to the inverse scaling of space charge with energy. Simulations will determine the feasibility of this scheme in the SNS, followed by experiments at full charge and low repetition rate. These experiments would provide benchmarks for the simulation models used to design the MCPD.
• Demonstrate full-pulse laser-assisted charge exchange (LACE) injection: Laser-assisted charge exchange (LACE) aims to replace carbon stripper foils with laser excitation and magnetic stripping. Full-pulse injection should now be possible because of reduced laser power requirements. A LACE injection demonstration is planned for the extended SNS shutdown in 2028. The SNS is the only facility capable of testing LACE due to the high linac energy requirement (> 1 GeV).
• Develop space-charge-driven beam loss prediction and minimization techniques: Several projects at the SNS aim to predict and minimize space-charge-driven halo formation and beam loss. Examples include novel phase space painting techniques and high-dimensional and high-dynamic-range phase space measurements. The SNS is open to collaborating on these topics where they benefit the muon collider program.