Tova Holmes, University of Tennessee Knoxville, and Diktys Stratakis, Fermi National Accelerator Laboratory
“Do you want to work towards the last chapter of a 20th century story, or the first chapter of one that will stretch into the 22nd century?” This question, posed by Lawrence Lee at the Inaugural US Muon Collider Meeting in early August, sums up the dilemma facing physicists imagining the next stage of our exploration of the energy frontier: Should we keep pushing on the limitations of proton colliders, or start work now on a new paradigm?
The last decade has seen a dramatic turnaround in the US effort towards a muon collider (MuC). A previous effort, the Muon Accelerator Program, made progress on designs in the early 2010s, but was shut down following a low prioritization in the 2014 P5 process. However, in the lead-up to the 2022 Snowmass process there was a resurgence of interest from across the community. Theorists banded together to argue the physics case of a multi-TeV muon collider. The European community continued efforts that had been put aside in the US, and formed an international collaboration. Interest snowballed throughout Snowmass, and US physicists across experiment, theory and accelerator got involved. There were T-shirts. In December 2023, the new P5 put up a muon collider as the long-term vision for the Fermilab complex, saying, “This is our muon shot.”
What changed? For one, the physics case. In its modern incarnation, the muon collider effort has turned its eye towards the 10 TeV scale: something far out of reach of any e+e- collider and pushing the limits of feasibility for a hadron collider. This is the scale at which the technical challenges of a metastable beam begin to be dwarfed by the constraints of any other alternative. It’s also the clear next target for the exploration of the energy frontier: not just a new order of magnitude of unexplored space, but straightforward targets like measurement of the shape of the Higgs potential and key WIMP dark matter models.
As the concept of a muon collider has pushed to higher energies, the technology needed has matured. For detectors, the preparations for the High Luminosity LHC has pushed R&D close to the requirements for a muon collider detector (see reports from ATLAS and CMS), pushing the bounds of precision timing and granularity (though more work is required to integrate those concepts together), lower power consumption and smarter on-detector processing to sift through the immense backgrounds of decaying muon beams.
The same is true for accelerator technology. Significant progress has been made over the last decade, which now suggests that there exists a viable path forward for each of the systems required to reliably produce, cool, accelerate, and collide muons.
Let’s start with the proton driver. Multi-MW proton sources such as those needed for a muon collider proton driver are now available globally. Examples are the Spallation Neutron Source (SNS) and Proton Improvement Plan II linacs in the US, the European Spallation Source in Sweden and the Japan Proton Accelerator Complex. Survivability of the muon production target during the M-scale beam impact has been an open question for many years. In 2007, a proof-of-principle experiment validated this concept with a liquid Hg target. While the technology was benchmarked, safety concerns pushed the later effort towards more operational-friendly materials. Recent studies indicate that a solid graphite, liquid metal or fluidized tungsten target are feasible options putting the MuC in synergistic path with many ongoing projects and proposed experiments. For example, MW scale graphite targets are needed to provide the required beam flux for the long- and short-baseline neutrino programs at Fermilab. Furthermore, the FCC-ee plans to use a liquid metal target to dump the beamstrahlung photons from the interaction region.
After the target, the newborn muons have a very large 6D emittance. This emittance must be reduced by six orders of magnitude in order to obtain high-luminosity collisions. Designs that can achieve this goal are now in place and rely on ionization cooling. Their performance was found to depend on the available accelerating gradient and focusing solenoidal field. Recently, a test program at Fermilab demonstrated operation of RF cavities with up to 50 MV/m gradient in a strong magnetic field. Moreover, a record field of 32 T was achieved in a SC solenoid with bore diameter like that needed for muon cooling. With these latest advancements in key cooling technology areas, a significant improvement in cooling performance is expected. One noteworthy breakthrough was the physics demonstration of ionization cooling by the Muon Ionization Cooling Experiment and the Fermilab Muon g-2 Experiment. Such demonstrations provide significant confidence boosts about the technique.
Regarding the collider ring itself, lattice designs for a 3 TeV ring are in place with optics and magnet parameters within existing technology limits. Preliminary designs for a 10 TeV collider ring have also been developed but more work is needed. Attention is needed on the intense neutrino flux originating from the muon decays. This flux exits the ground far from the ring and its interaction rate rises linearly with the energy of the collider. The impact of this neutrino-induced radiation can be mitigated by a mechanical system that produces “mechanical wobbling,” whereby the lattice is modified periodically so that the neutrino flux pointing to the surface is spread out. According to recent studies, this innovative method has the potential to make the environmental impact of the MuC negligible, similar, for instance, to the impact from the LHC
But despite this progress, accelerator R&D remains the bottleneck for a muon collider. Although the principles of ionization cooling are understood, several challenges associated with the cooling technology and its integration exist. For example, operation of accelerating cavities close to solenoidal magnets may compromise the cryogenic performance of the magnet. Installation of cooling absorbers may also be challenging in such compact assemblies. Moreover, mitigation approaches to manage the forces within and between the magnet coils need to be developed. To understand and circumvent the associated risks, a facility that contains a sequence of ionization cooling cells that closely resemble a realistic ionization cooling channel is required. Such a facility will allow the integrated performance of the systems to be tested as well, and will give us the input, knowledge and experience to design a buildable cooling channel for a MuC.
In the following years, a targeted effort should be carried out towards a conceptual design of a demonstrator for testing cooling technology as well as an effort towards exploration of candidate sites that can host such a facility. Fermilab is an ideal site for hosting such a demonstrator because of the existing accelerator infrastructure of a MW-scale proton source that currently enables a strong physics program with neutrino and muon beams, while plans are in place for the evolution of the complex towards a multi-MW proton beam.
Regarding the proton complex, Fermilab’s accelerator evolution plan may offer a path for a proton driver, however an R&D program must be developed to define additions to the plan that would produce protons with the desired power and time structure of the MuC. Dedicated R&D on bunch compression under extreme space-charge is also needed in order to establish the performance limits of the proton driver. The SNS accelerator is a close analog to the MuC PD. As a result, it could offer a valuable test-bed for demonstrating novel high-intensity technologies such as laser-assisted charge exchange injection, accumulation, bunch compression and space-charge mitigation techniques.
Continuing with the machine design, an integrated design of all subsystems needs to be developed. This includes a cooling design that reaches the desired luminosity as well as accelerator designs that can deliver TeV scale beams with minimum losses. The interaction of the beam with cavities needs to be examined and collective effects such as space-charge or beam loading need to be evaluated. Engineering designs of the most challenging parts of the beamline are needed as well.
Considerable advancements in the magnet design beyond currently available technologies are needed for a 10 TeV muon collider. Recent progress in High-Temperature SC (HTS) magnet design lead to hopes of achieving even higher fields. To accelerate muons before they decay, we require magnets with very fast ramp rates. The demonstration of a 300 T/s ramp rate matches the design specifications of the last acceleration ring for the MuC, albeit at a reduced peak field of 0.5 T. Further R&D is needed towards a full-scale pulsed magnet capable of reaching a three-fold higher field amplitude and ramp rate as compared to the values achieved as of today. For the collider ring, the development of high-field SC dipoles has received a strong boost from high-energy physics in the past decades. The current state of the art are the LHC dipole magnets made of Nb-Ti which operate at 1.9 K to produce a field of around 8 T. For a 10 TeV MuC the goal is to double the field strength, which calls for a different design compared to the one used in the LHC. Currently, Nb3Sn technology is being explored as a viable candidate for reaching this goal within a timeframe of 15 years. High-temperature superconductors, such as REBCO, are also being studied but such technologies may take longer than 15 years to fully mature.
Continuing RF cavity R&D is also crucial. We need to develop a design and prototype of a multi-cell NC cavity for the proposed demonstrator cooling cells. Moreover, it’s important to study novel cavity designs or novel methods to maximize their efficiency. For example, using cryogenic copper or breakdown resilient materials such as copper alloy or aluminum. The R&D program should also investigate power sources that can deliver high-peak power (3 MW) and short pulses at hundreds of MHz. For SC RF we need to progress towards conceptual designs as needed for accelerator lattices. Then cavities must be chosen for detailed engineering design and prototyping.
All of these challenges require a workforce ready to meet them. The next step is obvious: what we need is growth. According to rough estimates from Vladimir Shiltsev, the community needs to increase tenfold by the time we’re ready to start construction. Next summer in Chicago, we’ll host a Muon Collider Accelerator School (August 3-6, 2025), aimed at newcomers to the effort, including physicists from all collider-related fields looking to understand the big muon collider picture and get involved in accelerator research.
A muon collider, if we can build it, will be the single most powerful probe of the deep and urgent questions underlined by the LHC. But how can we embrace our “muon shot”? We will need a collaborative international effort, with the US playing a large role, hopefully even as the host. But before we get to that stage, we’ll need institutions around the world to work together in a collaboration, tackling each of these known R&D challenges and all of those that crop up along the way. We’ll need accelerator physicists, experimentalists, and theorists to blur the boundaries between their fields. To get involved, reach out to us, attend meetings of the International Muon Collider Collaboration, and start thinking about how your expertise, interests, or both could contribute to any part of a muon collider. We need you!