Superconductors for the energy frontier

Fill hundreds of copper tubes with a powder of niobium and tin, and then stack them in the form of a cylinder. Draw this out into a composite wire hundreds of kilometres long and barely a millimetre in diameter. Braid it into a rectangular cable and insulate it in fibreglass. Wind it into coils, bake for a week at precisely 650 °C and impregnate with resin. Assemble them with sub-millimetre precision under a compressive stress of one tonne per square centimetre, cool the magnet to a few kelvin and power it with tens of thousands of amps. This is not alchemy. This is a possible recipe for a Nb₃Sn magnet.

Whether made of Nb₃Sn or higher-performance superconductors, such devices promise to substantially improve the discovery potential of hadron colliders. Since their energy reach scales as the dipole field times the size of the tunnel, each additional tesla directly expands the energy frontier.

What makes these magnets unique is their compactness. Superconducting coils can carry a current density of order 500 A/mm², a factor 100 higher than what can be tolerated by copper with active cooling. A magnet based on superconductivity can therefore have coils that are narrower and lighter.

No application of superconductivity pushes this limit harder than an accelerator magnet. Larger coils mean larger magnets and an unaffordably large tunnel to accommodate them. Accelerator magnets must therefore be highly optimised in space and cost – the capsule hotels of superconductivity – and this extreme optimisation creates opportunities for spinoff applications, from lightweight motors for electric aircraft to power transmission beneath the pavement of a crowded metropolis. Superconducting accelerator devices have already paved the way for societal applications in medical imaging and advanced accelerators for cancer therapy, and the field continues to benefit from strong research synergies with fusion tokamaks, though their toroidal coils don’t need to push the limits of current densities in the same way.

Superconductors also save energy. At the LHC, more than a thousand niobium–titanium alloy (Nb–Ti) superconducting dipoles are powered by only 40 MW. This is much less than what is consumed by the LHC’s injectors.

As dipoles based on Nb-Ti superconductors are limited to a maximum achievable field of nearly 10 tesla, corresponding to an operational field of about 8 tesla with acceptable margins, accelerator physicists and engineers are exploring the use of better superconductors to roughly double their field. The options include Nb₃Sn, which will soon be used in an accelerator for the first time at the HL-LHC, and “high temperature” superconductors that promise much higher performance and a simplified accelerator infrastructure. But dipoles are much more difficult to design than solenoids. Though 30 tesla solenoid magnets are already available on the market, no one has yet succeeded in building a 20 tesla dipole magnet.

Shear complexity

An accelerator dipole poses several challenges compared to a solenoid. While a solenoid’s current loops generate an axial magnetic field, a dipole must use vertically separated coils to generate a vertical magnetic field; for the same total coil thickness and current density, a solenoid can provide twice the field strength of a dipole; and the field distribution and the forces exerted on the coils are much more difficult to control. In a solenoid, electromagnetic forces are perpendicular to the conductor, but in a dipole they push the coil towards the midplane and outwards, with a two-dimensional distribution that includes shear stresses.

**Superconductors for high-field accelerator magnets** Constant temperature (4.2 K unless specified) slices of the “critical surface” of several superconductors. Superconductivity is lost for higher values of current density and surface magnetic field, and a balance must be struck between compactness (high current density) and field strength. Credit: A Ballarino

The engineering challenge is increased by the need for dipoles to operate precisely during the ramp, when particles gain energy with every turn after being injected into the collider, requiring increasingly strong magnetic fields to bend them. To ensure that accelerator physicists can make tightly focused beams collide with high luminosity inside the experiments, the field must be uniform to better than one part in 10⁴ across two thirds of a dipole’s aperture as the field increases up to a factor 15. These challenges are not present in either medical-imaging magnets or the toroidal coils used for fusion, which must operate at a constant current, though the toroidal coils used for fusion are subject to rapidly varying external magnetic fields.

In the context of the 2026 update to the European Strategy for Particle Physics (ESPP), advanced high-field dipole magnets would be needed by the hadron-collider phase of the Future Circular Collider (FCC-hh) and the proposed muon collider. Due to its exceptionally large and unstable beams, a muon collider would also require a kilometre-long channel of superconducting solenoids with alternating gradient, and a final superconducting cooling solenoid with a strength of roughly 40 tesla before the collider ring. These challenges are complementary to what is required by the FCC-hh, and the community is devoting significant research and development in this direction.

The targets initially set for the FCC-hh in 2014 were based on round numbers: a 100 km tunnel and a centre-of-mass energy of 100 TeV. This required 16 tesla dipoles, one or two tesla above what can be done with adequate margins and costs with present technology. After a decade of studies, the tunnel size was reduced to 91 km to fit geological constraints, and the field was brought down to 14 tesla, allowing a centre-of-mass energy of 85 TeV after some optimisation of the lattice. This 15% reduction in the energy in the centre-of-mass frame has had a major effect on the energy consumption of the collider, as synchrotron radiation reduced by 50%. A similar tuning occurred for the LHC, which was initially imagined at 16 TeV with 10 tesla magnets rather than today’s 13.6 TeV and 8.1 tesla.

The baseline design for the FCC-hh dipole magnets is Nb₃Sn technology operated at 1.9 K, though the ESPP documents also note three other possibilities: hybrid magnets that use substitute Nb–Ti for Nb₃Sn in the lower field regions; operation at 4.5 K; and a high-temperature-superconductor option operating between 4.5 and 20 K with magnetic fields in the range 14 to 20 tesla.

The Nb₃Sn path

Nb₃Sn was discovered a few years before Nb-Ti and has the advantage of providing current densities in excess of 500 A/mm² up to 16 T (see “Superconductors for high-field accelerator magnets” figure). After 35 years of research, fields have now reached 14.5 tesla, close to the 15–16 tesla target needed to have magnets operating at 14 tesla in the FCC-hh with adequate margins (see “Niobium dipoles” figure). The main goal today is to produce a double-aperture short-model Nb₃Sn magnet with all features specified in the FCC-hh design. This should be achieved by 2030 and then scaled up in length.

**Niobium dipoles** The evolution of the achieved field in Nb-Ti and Nb₃Sn dipoles. Credit: E Todesco

A key challenge is to reduce the quantity of Nb₃Sn, thereby lowering both the cost and hysteresis losses during field ramping. As the magnetic field changes, currents are induced within the superconducting filaments, leading to energy dissipation that must be carefully controlled. Minimising these losses is one reason for the complex, multi-filamentary architecture of superconducting wires. The smaller filaments of Nb-Ti can significantly reduce the losses, and Nb-Ti costs five to 10 times less than Nb₃Sn.

A second engineering challenge is to achieve a mechanical structure capable of keeping the coil in compression during powering but not overstressing it. The stress limits of Nb₃Sn are of the order of 200 MPa, and the required precompression for a 14 tesla dipole is about 150 MPa.

Another challenge of the low-temperature path would be logistical: the production of roughly 5000 tonnes of Nb₃Sn. This corresponds to a 1 kA cable from the Earth to the Moon at a cost of several billions of dollars. These numbers are an order of magnitude larger than what was needed for the Nb-Ti coils of the LHC.

Despite these challenges, Nb₃Sn technology is now well established for small series, and will soon play a key role at the High-Luminosity LHC – the technology’s first use in a working accelerator, though for focusing beams rather than bending them (see “Nb₃Sn quadrupoles” figure). But newer superconductors may well prove competitive.

The high-temperature path

In 1986, Johannes Georg Bednorz and Karl Alexander Müller announced the discovery of superconductivity above 35 K, something not foreseen by theory, and well above the boiling point of liquid helium. “High-temperature” superconductors (HTS) not only remain superconducting at high temperatures, in many cases above the boiling point of liquid nitrogen (though at 77 K HTS performance is not yet adequate for our needs ), but also at high fields. HTS solenoids have been constructed with fields up to 40 tesla, and though the problem of degradation is not yet totally solved, progress has been outstanding.

Three families of superconducting conductors are currently available or emerging on the market: rare-earth barium copper oxides (REBCO), bismuth strontium calcium copper oxides (BSCCO) and iron-based superconductors (IBS).

Nb3Sn quadrupoles — **Nb₃Sn quadrupoles** The cross section of one of the new final-focus quadrupoles for the High-Luminosity LHC. Operating at peak fields of up to 11.5 tesla, the quadrupoles will provide significantly stronger focusing and larger apertures than the Nb-Ti magnets used in the LHC, enabling tighter beam squeezing and higher collision rates. When the upgraded collider comes online in 2030, these quadrupoles will become the first Nb₃Sn magnets to be used in a working accelerator. Credit: OPEN-PHO-ACCEL-2017-010-2

REBCO is of strong interest in the world of fusion. Billions of dollars of investment have reduced the cost by more than an order of magnitude in the past decades. REBCO comes in tapes (see “Frontier superconductors” figure). A 12 mm-wide tape has thickness of 0.1 mm and can carry 1500 A at 4.5 K, or about half that at 20 K. 20 tesla peak field coils have been built and tested for fusion applications, and private investors plan to build reactors that are much more compact than ITER, which is based on Nb₃Sn technology.

Manufacturing REBCO coils is greatly simplified compared to Nb₃Sn as the tape needs no temperature treatment; but the technology used to wind the tapes is not easy to adapt for accelerator dipole magnets, which are radically different from the toroidal coils designed for tokamaks. The challenge here is not to develop a conductor for accelerator magnets, but to adapt our magnet designs to this amazing tape. There is a long way to the 15–16 tesla target, but the potential is huge, with progress being made in Europe, the US and China (see “HTS dipoles” figure).

**HTS dipoles** The evolution of the achieved field in HTS dipoles. Credit: E Todesco

And what of the other HTS superconductors? BSCCO has the great advantage of round wires, but must be treated at 800 °C and it does not profit from synergies with fusion. At present, this path is only being pursued in the US, with achieved fields of just 1.8 T. IBS is being actively developed in China and Europe, but its current density has not yet matched the performance of REBCO, and the best results were obtained for tapes rather than wires.

HTS would allow operation at 20 K, with a simplification of the cooling scheme and a possible reduction in the energy consumption of the collider, though at 85 TeV half of the heat loads are due to synchrotron radiation, which does not depend on the operational temperature of the magnets. Moreover, REBCO tape has a single filament, as wide as the tape, and therefore the saving from the higher operational temperature could be compensated by larger heat losses. Estimating the energy balance is far from trivial: do not draw easy conclusions!

Optimal solution

Addressing these challenges is the work of the High Field Magnet (HFM) programme, an international collaboration with 15 institutes steered by CERN that was founded in 2021. HFM is exploring multiple different designs to find the optimal solution, from the most classical to the more exotic, and novel ideas should be explored in parallel to the most conservative paths. Though there are major challenges ahead, solving them promises societal benefits via a number of diverse spinoff applications.

High-field magnets remain one of the hardest problems in applied superconductivity. The next decade will be decisive for understanding the feasibility and cost of the FCC-hh.

The most important tool you’ve never heard of

Jos, FORM has been at the heart of precision calculations for decades. But the story starts earlier, with Martinus Veltman (see “The pioneer” image). What was he trying to do?

Jos Vermaseren In 1963, Veltman was interested in the renormalisation of Yang–Mills theories. He wanted to check whether certain models produced unphysical infinities that could not be removed. These calculations are a lot of work: you don’t do that by hand. So he built himself a program, which he called Schoonschip, to do that calculation.

What was computing like in those days?

Vermaseren Very primitive by current standards. When Veltman started at CERN, they had a CDC 6600, which was for a while the biggest computer in the world. But you had to share it with maybe a few thousand people, so you had to wait for your program to come out (see “The first supercomputer” image). At Nijmegen University in the early 1970s, we had an IBM computer where you had to hand in your computer cards, then wait a few hours for output. If your program was big, it would only run during the night. Make a typo, and you’d find out the next day that nothing had happened. That kind of primitive computing was left behind when personal computers came in the 1980s. I bought an Atari ST in late 1985, and the fun part was that at Nikhef, the Dutch National Institute for Subatomic Physics, we had a CDC 173, but my Atari had more memory! That was quite amazing. Every decade, the computers became more powerful, and with that the calculations became larger. I’ve been involved in calculations where the intermediate formulas were terabytes big. That is kind of hard to imagine. But if you put in enough effort and enough checking, you still get the correct answer. There is simply no way you could ever do that by hand. No way. That’s why we absolutely need these algebra programs.

**The pioneer** Martinus Veltman (1931–2021) was a Dutch theoretical physicist who, together with Gerard ’t Hooft, elucidated the quantum structure of electroweak interactions and showed how to renormalise the underlying gauge theory, enabling precision calculations that helped make the emerging Standard Model predictive. For this work, they shared the 1999 Nobel Prize in Physics. Beyond the core theory, Veltman was a pioneer of computer-assisted quantum field theory. Credit: CERN PhotoLab

Where did Schoonschip – I apologise for my pronunciation – fit in the landscape of early computer algebra?

Vermaseren Ah, Veltman did that intentionally to tease all the foreigners. [chuckles] There were already ideas about algebraic software in the 1960s – Feynman was suggesting something in the 1950s – but nothing really usable for physics calculations when Veltman started. Around the same time, Tony Hearn started with the REDUCE program, which was formally more elegant but less powerful. Those were the main players for a while, but they all had limitations. REDUCE wasn’t nearly as fast as Schoonschip and couldn’t handle very big expressions. Schoonschip’s limitation was that Veltman had written it in assembly, so you could only use it if you had the correct computer.

How did you enter this story?

Vermaseren I was very much used to Schoonschip and was quite a good programmer with it, but CDC computers were expensive and being phased out. So there I was, faced with the idea that I wouldn’t have Schoonschip any longer. I also wanted to make a giant system for doing automated calculations that would need computer algebra in a more flexible way than Schoonschip provided. If I needed new features, I’d have to go to Veltman and wait probably a year. Veltman had built in what he needed and was so nice to provide other people with his program. But if you get a free program, you shouldn’t come up with too many demands. The conclusion was that if I really wanted to make what I needed, I would need my own program.

**The first supercomputer** The remote input/output station to CERN’s CDC 6600 in 1972. The card reader on the left and the line printer on the right were operated by programmers on a self-service basis. Credit: CERN-CO-7202053

Schoonschip had a couple of weak points. One was the sorting mechanism, which meant that with very large expressions, the program became outrageously slow. The handling of functions and function arguments was not flexible at all. And then there was the whole business of computer availability. I asked Nikhef management if they would allow me to take some time out to work on it, and they thought it was a good idea, so my back was covered.

This may resonate with early-career researchers who want to build long-lived tools today. What would you tell them?

Vermaseren You have to put in an enormous amount of time, and if you want to get a job in physics, you can only get credit for that if at the same time you use what you make for good calculations that draw attention. You need physics publications. If you go in as a postdoc to just write useful software, you have a problem, unless somebody has already promised you a decent job.

People like to count citations, and organisations usually look at citations in the first two years. But when you have a paper about a calculation, the opposite usually occurs. In the beginning you don’t get very many citations because people aren’t using it yet. I have a lot of papers that started with hardly anything, and then after a few years they pick up and keep growing. But for a postdoc, that is a disaster.

Thomas Gehrmann I’d add to this that recognition for contributions to scientific software is usually underrated when evaluating a researcher’s performance. It’s not recognised at the same level as publications or plenary talks. We should really try to communicate to senior people making funding decisions the importance of the whole body of scientific output. Scientific software development is very useful to the community but much less easily quantifiable than citations.

Vermaseren Although, for universities it is very nice to eventually have somebody there who is generating a lot of citations and educating people to do big calculations, they just don’t recognise it. The world of theory software development needs more institutional support.

Thomas, can you describe FORM’s impact on particle physics?

Gehrmann FORM enabled calculations that would never have been possible with any other tool. At each given moment in time, ever since the inception of FORM version one in the late 1980s, early 1990s, the cutting-edge calculations were usually done with FORM. Many of these calculations were redone a few years later with other tools, but what had changed was that computers became more powerful, had more memory, more storage space and were faster, so you could also do similar calculations in Mathematica or Maple. However, FORM was always at the avant-garde of the calculations.

In groups that are performing multi-loop calculations, the first-week’s task for a new student is usually: learn FORM on a simple example, compute the scattering matrix elements in FORM to get you used to its environment. For students working on cutting-edge projects – the next loop on a scattering amplitude, the next order on a benchmark cross-section – it’s made clear from the very onset that FORM is the tool to be used, because it’s only with this tool that there’s a realistic chance to get through the project in a finite amount of time.

Can you give an example of a particularly important calculation?

Gehrmann The LHC is a proton–proton collider, but the hard scattering processes underlying the collisions are not proton–proton but collisions of quarks and gluons. To make precise predictions for anything you observe at the LHC, you need to know how quarks and gluons are distributed inside the proton. These parton distribution functions are extracted from combined fits to huge sets of data from different experiments at vastly different energy scales. I mean, from a 35 GeV electron beam at SLAC up to multi-TeV collisions at the LHC. That’s almost three orders of magnitude.

Parton distributions evolve with energy scales via the Altarelli–Parisi evolution equations: knowing the Altarelli–Parisi splitting functions to sufficient theoretical precision is one of the cornerstones enabling these fits. The calculation that enabled the current level of precision was done in the early 2000s by Jos and his collaborators Sven Moch and Andreas Vogt. It went alongside the development of FORM version three, and was a crucial result for the entire LHC physics programme.

Looking ahead to the High-Luminosity LHC and a potential FCC, how important is FORM’s continued development?

Gehrmann Both are extremely high-statistics, high-luminosity machines. They’ll give us measurements at a statistical precision never achieved before in a collider experiment. Researchers need to be empowered with proper tools to make the most of the physics, with a whole new generation of precision calculations. FORM has grown with the field, due to both the ingenious design choices Jos made at inception, when a lot was already conceived in a scalable fashion, and through continuous development addressing bottlenecks. It’s very hard to predict what will be the bottlenecks for High-Luminosity LHC calculations, and it’s even harder for the FCC. But they will require adaptations to how we do computer algebra. And, of course, committed developers.

Josh, you’ve been working on FORM 5. Why is a major release necessary now?

Joshua Davies Being able to release new versions helps convey to the community that there’s progress. Most users stick to a released version rather than rebuilding from GitHub. Being able to say “this is a new version with well-tested new features” is important for users to trust it for their work.

What are the major new features?

Davies The first is a Feynman graph generator built into FORM, from a collaborator of Jos, Toshiaki Kaneko. FORM now has an interface to this generator that lets you produce graphs from within the code without relying on external tools. It’s written in a more flexible way, which lets you add features or modify it much more easily than other tools. I also put in an interface that improved polynomial arithmetic performance. This is increasingly necessary now that people study processes with higher multiplicities or more mass scales. You end up with computations depending on many more variables than in the past.

Vermaseren The third main feature is the ability to have floating-point coefficients as opposed to rational numbers. Modern algorithms still can’t determine everything through normal calculations. You’re restricted to doing certain parts in arbitrary-precision floating point. But these capabilities have other good features. If you want to do a calculation for the LHC, in the end these run in Monte Carlo integration programs: you take a very big formula and sample it billions of times. But how numerically stable is that formula? If I have floating-point capability, I can figure out the numerical stability before I evaluate it billions of times in another program. I can determine whether I’ll run into disasters.

What does the future hold for FORM’s development?

Davies It seems unlikely that anyone is suddenly going to fund a permanent job where the main role is looking after FORM. But if we can foster an environment where postdocs or PhD students feel they can contribute and be recognised for it, and it helps them apply for their next position, this needs to be the way packages like FORM are developed. I’m a postdoc trying to apply for longer-term positions, but the future of FORM isn’t secure. I’ve put in a lot of effort, alongside Coenraad Marinissen and Takahiro Ueda, to get FORM to version five, but it’s not guaranteed people working on FORM will be able to continue.

Do we need a different institutional framework to support this kind of development?

Davies We need more recognition from the people who decide where funding goes for contributions to software work. On the experimental side, there are people whose job is the LHC software that goes into the analysis chain. We don’t really have this equivalent on the theory side. People work on software alongside their physics projects, and you always have to have physics results coming out if you want to continue to get jobs. No one can truly focus one hundred percent on the tools. What would really help is if contributing to a project like FORM was clearly recognised as a valuable scientific output in its own right, alongside physics papers. If young researchers felt that contributing to core tools genuinely strengthened their career prospects rather than putting them at risk, it would completely change how sustainable projects like this are.

**FORM before meaning** Melencolia I (1514) by Albrecht Dürer is often read as an allegory of mathematical thought confronting its limits: the tools of calculation. Credit: A Dürer, Melencolia I, 1514. Public domain. Image adapted by the editors

Gehrmann This is exactly right. Over the years, it was crucial to have Jos as a developer in the background regularly talking to the community, getting feedback: “This is the current bottleneck we’re up against.” But that only worked because Jos could actually focus on it. We’ve been trying to improve community involvement over the past five years with dedicated workshops, bringing together developers with users pushing FORM to their limits and students coming into the field. This format has started to take off successfully. At these workshops, in the mornings the senior developers explain the internal structure of the code. And then in the afternoons people work on concrete exercises like bug fixes or small features, almost like a hackathon. But this is a bottom-up initiative. It needs a top-down approach to make the project sustainable and create career perspectives for FORM developers like Josh. I can only hail the visionary decisions Nikhef management made 40 years ago when they decided to leave Jos alone for a few years to develop version one. Without institutional recognition that creates actual career paths for theory software developers, we risk losing the very people who can secure FORM’s future – and with it, our ability to make the most of the next generation of colliders.

New directions for bent crystals

Soviet accelerator physicists were the first to bend particle beams using bent crystals. Under controlled conditions, the technique can produce beam deflections equivalent to those generated by magnetic fields of hundreds of tesla, far exceeding the limits of superconducting magnets.

Even more strikingly, genuinely enormous magnetic fields also arise in a more subtle way. At LHC energies, the electric fields between crystal planes are Lorentz-boosted into effective magnetic fields of hundreds to thousands of tesla in the rest frame of passing particles. This opens up some unique possibilities for particle physics: probes of new physics once limited to long-lived particles in conventional, orders-of-magnitude weaker magnets may now come within reach for short-lived baryons.

A bobsleigh on a track

Energy loss and multiple scattering are the fate of most charged particles in matter. If carefully aligned to particle trajectories, crystals can be an exception: as positively charged particles fly past nuclei in the planes of the crystal lattice, they experience an averaged electrostatic potential that channels them between the crystal planes. Provided they don’t have enough transverse energy to cross the potential barrier to a neighbouring crystal plane, the particles oscillate between the atomic planes like a bobsleigh on a track (see “Guided paths” figure). If the crystal is mechanically bent, the entire track curves, steering the particles along with it.

**Guided paths** Positively charged particles (red) can be “channelled” along the trough of the electrostatic potential (shaded surface) between planes of nuclei in a bent crystal, achieving a far stronger curvature than conventional magnets. In this artist’s impression, length scales have been adjusted for clarity. Credit: D De Biasio

Crystal channelling was predicted in simulations by Robinson and Oen in 1963, experimentally confirmed the same year by Piercy, and given its theoretical foundation by Lindhard in 1965. The idea of using bent crystals for beam control was first proposed in 1976 by Tsyganov. Proof-of-principle experiments at JINR Dubna in 1979 demonstrated the channelling of 8.4 GeV protons, achieving deflections equivalent to an 81-tesla magnetic field, and practical applications followed soon after.

A key modern application of bent crystals is the selective extraction of particles from the beam halo rather than the beam core, to produce a secondary beam. Crystal-based beam extraction was demonstrated up to 8.4 GeV at JINR in Dubna in 1984, then with higher energy protons at IHEP Protvino in 1989, and at CERN’s Super Proton Synchrotron (SPS) in 1993. Later in that decade, Fermilab’s Tevatron extracted beam particles using crystals at a record energy of 900 GeV.

Bent crystals are also used in modern accelerators’ collimation systems to deflect stray particles in the beam halo into shielding blocks that safely absorb them. The exploration of bent crystals for beam collimation began in the 1990s at Brookhaven National Laboratory and Fermilab, but the field underwent a step change in 2006 with the experimental observation of volume reflection at Petersburg Nuclear Physics Institute. This advance was enabled by new manufacturing techniques for high-quality bent silicon crystals. Predicted in the mid-1980s by Taratin and Vorobiev, volume reflection occurs when a particle is coherently deflected by the collective field of bent crystal planes without becoming trapped in a channel, effectively rebounding from the planar potential barrier.

Crystal clear

These breakthroughs motivated the UA9 Collaboration and experts in beam collimation to undertake a systematic programme of crystal-based beam manipulation at the SPS. This effort culminated in 2023, when crystal collimation became an operational reality at the LHC (see “Heavy-ion collimation” figure).

**Heavy-ion collimation** A crystal collimator is installed at the LHC, where it is used to deflect halo particles onto an absorber located roughly 90 metres downstream. Credit: J M Ordan/CERN-PHOTO-202111-185-3

This technique addressed a critical limitation of heavy-ion operation: conventional amorphous collimators fragment heavy nuclei into lighter ions, some of which escape the collimation system and can quench downstream superconducting magnets. Bent crystals, by contrast, coherently and deterministically steer beam halo particles onto dedicated absorbers. As a result, crystal collimation was demonstrated to reduce heavy-ion beam losses at LHC magnets by factors of 5 to 13 compared with standard collimation.

New frontiers

The success of TeV-scale beam collimation at the LHC laid the groundwork for another ambitious goal: using bent crystals in the LHC not just to steer beams, but also to probe the spin of short-lived particles. In the intense internal fields between crystal atomic planes, a particle’s spin behaves much like a spinning top in a gravitational field. Rather than simply tipping over, the top’s angular momentum rotates slowly – precesses – under the action of a torque. In close analogy, the magnetic moment of a relativistic particle traversing a bent crystal precesses under the torque generated by the effective magnetic field experienced in its rest frame.

In 1992, the E761 collaboration used the fixed-target proton beam from the Tevatron to perform the first experimental demonstration of the effect by measuring the magnetic moment of the Σ⁺ hyperon (uus). This pioneering work used two 4.5 cm-long bent silicon crystals to induce spin precession, proving that the technique could effectively substitute for massive conventional magnets.

Bent crystals could open new frontiers in particle physics at the LHC

Bent crystals could open new frontiers in particle physics at the LHC. The TWOCRYST collaboration is exploring whether the technique can be extended to study the spin of short-lived charm baryons. The idea dates back to 1996, when Samsonov extended the E761 findings to charm baryons and demonstrated that despite their extremely short lifetimes, the intense effective fields of bent crystals could induce measurable spin precession. In 2016, Scandale and Stocchi proposed to use this technique to measure the magnetic dipole moments of charm baryons at the LHC.

The lightest charm baryon, the Λ_c⁺ (udc), has an extremely short lifetime of roughly 200 femtoseconds. Even at 1 TeV, it only travels a few centimetres before decaying. The magnetic fields needed to study its spin precession cannot be provided by conventional magnets, but are well within reach if bent crystals are used. If produced at a fixed target, a clean sample of its decays to a proton, a kaon and a pion can be obtained via tracking and invariant-mass reconstruction, with decay angles yielding spin information.

Such measurements promise a unique opportunity to explore QCD at the interface between heavy and light quarks. Measurements of its spin precession would also provide exceptional sensitivity to a possible electric dipole moment – a potential signature of physics beyond the Standard Model. The ALADDIN (An LHC Apparatus for Direct Dipole moments INvestigation) experimental proposal aims to measure the electromagnetic dipole moments of charm baryons, the Λ_c⁺ and the Ξ_c⁺ (usc), using a double-crystal scheme in the LHC. In this concept, a first bent crystal extracts a small fraction of the LHC beam halo and guides 7 TeV protons onto a fixed target located inside the LHC vacuum pipe, producing, amongst other particles, the charm baryons of interest. The particles would then impinge on a second bent crystal, whose intense inter-planar fields would induce a measurable spin precession.

Such an experiment must deal with challenging demands on the crystal alignment. Channelling only occurs if particles enter a crystal within a narrow angular range, known as the Lindhard angle, which decreases with increasing beam energy. At TeV energies in the LHC, this angle is only a few microradians, meaning that misalignments far smaller than the width of a human hair over a metre are sufficient to suppress channelling entirely. This alignment will be particularly challenging for ALADDIN, which will rely on protons that have scattered off the primary collimators.

TWOCRYST was installed at Insertion Region 3 (IR3) in early 2025 (see “Halo extraction” figure). The experiment marks a significant leap in complexity compared to previous LHC crystal tests. Last year, the experiment successfully channelled LHC protons through two crystals (see “Double channelling” figure). These measurements marked the first controlled deployment of a double-crystal setup in the LHC, demonstrating the technique at 450 GeV, 1 and 2 TeV – a new world record, surpassing the 270 GeV achieved by the UA9 collaboration at the SPS and corresponding to an equivalent magnetic field of 600 tesla. Preliminary analyses of the recorded data indicate that more than 20% of protons were channelled successfully at 1 TeV.

Bent crystals have come a long way since the pioneering experiments at JINR Dubna in 1979. TWOCRYST’s demonstration of double-channelling at a record energy of 2 TeV represents an important step toward using the technique for precision particle-physics measurements with bent crystals at the LHC.

Measurements of spin precession have long played a central role in particle physics, providing deep insights into fundamental interactions and symmetries. The anomalous magnetic moments of the proton and neutron – measured in the 1930s and 1940s – remained unexplained for decades until the emergence of the quark model in the 1960s. While conventional magnet-based techniques remain highly effective for relatively long-lived particles such as the muon (CERN Courier March/April 2025 p21), particles as short-lived as charm baryons have so far remained experimentally inaccessible. The results from TWOCRYST suggest that bent crystals may allow the first direct experimental probe of electromagnetic dipole moments in charm baryons, opening a new window on QCD dynamics and offering a sensitive test for physics beyond the Standard Model.

HiLumi magnets face full-scale test

CERN has reached a crucial milestone in the advancement of the High-Luminosity Large Hadron Collider (HiLumi LHC) project with the start of the cryogenic cooldown to 1.9 K of its 95-metre-long test stand – a full-scale replica of the innovative equipment that will transform the LHC in the coming years. The test stand is designed to validate the novel magnet system (the inner triplet beam-focusing magnets) and its complex infrastructure, which is a key element in a major upgrade of the LHC that is set to enter operation in 2030.

This summer will mark the start of a four-year-long intensive work period to transform the LHC into the HiLumi LHC – a groundbreaking accelerator that will usher in a new era for high-energy physics. The HiLumi LHC will increase the number of particle collisions by a factor of 10, increasing the volume of physics data available for researchers. This leap forward will allow physicists to explore the behaviour of the Higgs boson and other elementary particles with unprecedented precision and to uncover rare new phenomena that might reveal themselves.

Exploring the unknown

“I don’t think it is possible to overstate the importance and excitement of the High-Luminosity LHC, which is the largest project undertaken by CERN for the past 20 years,” explains Mark Thomson, CERN Director-General. “Coupled with advanced new data tools and upgraded detectors, it will allow us to understand, for the first time, how the Higgs boson interacts with itself – a key measurement that will shed light on the first instants and possible fate of the universe. The HiLumi LHC will also explore uncharted territory and could reveal something completely new and unexpected. That’s the whole point of exploring the unknown: you don’t know what’s out there.”

Many of the technologies developed for the HiLumi LHC – such as superconducting crab cavities that tilt the particle beams before they collide, crystal collimators designed to remove errant particles and high-temperature superconducting electrical transfer lines to power the HiLumi magnets as efficiently as possible – have never been used in a proton accelerator before. Among these new key technologies, the inner triplet beam-focusing magnets are made of a superconducting compound based on niobium and tin (Nb₃Sn), enabling magnetic fields higher than those achieved with the current LHC niobium–titanium (NbTi) magnets (see “Superconductors for the energy frontier”). These new magnets will be deployed on both sides of the ATLAS and CMS experiments, alongside new cryogenic, powering, protection and alignment systems, and will operate at a temperature of 1.9 K, just like the LHC magnets.

The entire accelerator complex and associated experiments will benefit from the improvements

To ensure seamless integration, CERN has built, in an above-ground test hall, a full-scale test stand called the Inner Triplet String (IT String), which mirrors the underground configuration (CERN Courier March/April 2025 p8).

“All the systems have already been tested individually. The goal of the IT String is to validate their integration and their collective performance under operational conditions,” explains Oliver Brüning, CERN Director for Accelerators and Technology. “The connection and operation of all the equipment in the IT String give us a chance to optimise our procedures before the actual installation in the tunnel, so that we will be prepared and ready for an efficient and smooth installation.”

Harnessing potential

The large LHC experiments ATLAS and CMS will also undergo a major upgrade to enable them to harness the full scientific potential of the HiLumi LHC collisions – work that is being carried out in close coordination with hundreds of institutes worldwide. Additionally, the entire accelerator complex and associated experiments will benefit from improvements, says the lab, solidifying CERN’s leadership in high-energy physics.

The cooldown of the HiLumi LHC test string, which is achieved using a liquid-helium refrigeration and distribution system, is expected to take several weeks to complete.

ICABU fishes for accelerator innovations in Pohang

The 27th International Conference on Accelerators and Beam Utilizations (ICABU2025) attracted 300 experts to Pohang, South Korea, from 12 to 14 November 2025. Once a small fishing village, Pohang has developed into a major research hub and now hosts more than 22 R&D institutions. These include Pohang University of Science and Technology (POSTECH), the Pohang Accelerator Laboratory – home to the 3 GeV PLS-II synchrotron radiation source and PAL-XFEL hard X-ray free-electron laser – and the Asia-Pacific Center for Theoretical Physics. ICABU itself began in 1997 as the International Proton Accelerator Workshop, hosted by the Korea Atomic Energy Research Institute. Since 2009, it has grown into an international conference.

Particle beams are becoming increasingly important to materials engineering. Yunseok Kim (Sungkyunkwan University) discussed how helium-ion irradiation can be used to manipulate hafnium oxide, a material widely employed as an insulating layer in modern microelectronics. In very thin films, hafnium oxide can sustain a switchable electric polarisation that allows information to be stored, known as ferroelectricity. Yet, this state is normally fragile. Kim showed that controlled irradiation with low-energy helium ions can introduce and rearrange atomic-scale defects in the crystal lattice, stabilising the polarised state.

The meeting also addressed applications in nuclear medicine. A team from the Institute for Rare Isotope Science (IRIS) reported progress towards a domestic production route for the therapeutic alpha-emitter actinium-225, based on irradiation of thorium-232 targets with 50–70 MeV protons. Actinium-225 is both expensive and scarce, with current clinical use relying heavily on imports. Even an initial domestic supply would improve clinical availability and support the wider adoption of targeted alpha therapies.

Alongside applications, there was also a focus on progress in accelerator hardware itself

Alongside applications, contributions also focused on progress in accelerator hardware itself. Garam Hahn (PAL) and collaborators reported on a compact 5 T magnet system based on high-temperature superconductors (see p30). Operating without liquid cryogens, it is designed to shift the wavelength of synchrotron radiation, since stronger magnetic fields force tighter beam curvature and raise the characteristic photon energy. The system drew substantial attention from the accelerator-technology community, as it has the potential to increase high-energy photon brilliance by many orders of magnitude.

Beyond technical developments, ICABU2025 also addressed the evolving policy landscape for large-scale research infrastructure. In South Korea, the Korea Large Accelerator Act was recently established to manage, support and govern large accelerator facilities. Dongsoo Jang, deputy director of the Ministry of Science and ICT (MSIT), outlined strategies aimed at improving coordination, access and long-term planning across the country’s accelerator infrastructure.

Next year, the event will be hosted by the Korea Multi-purpose Accelerator Complex (KOMAC) and held in Gyeongju. Often described as a “museum without walls,” Gyeongju is one of Korea’s most historic cities and a symbol of cultural diplomacy, aligning well with the spirit of ICABU.

Photon detectors light up Bologna

The 7th international workshop on new Photon-Detectors (PD2025) took place from 3 to 5 December 2025 at Bologna’s Palazzo d’Accursio, attracting more than 150 researchers working on the development and application of photon-detection technologies. The medieval city-hall library, with its transparent floor above archaeological remains spanning more than two millennia, provided a striking setting for three days of discussion on state-of-the-art detector technologies.

Photon detectors lie at the heart of modern experimental physics. Their ability to measure extremely faint light signals, down to the single photons, makes them indispensable in areas ranging from high-energy and nuclear physics to astroparticle physics, astronomy, medical imaging and emerging quantum technologies. In recent years, rapid progress in devices such as silicon photomultipliers (SiPMs), avalanche photodiodes (APDs) and microchannel-plate (MCP-PMT) detectors has delivered improvements in timing resolution, radiation tolerance and large-scale integration. PD2025 provided a timely snapshot of this evolving field, combining technology-driven discussions with reports from experiments already exploiting these advances.

A significant fraction of the invited talks focused on the latest developments in SiPM technology, which has become the workhorse photodetector for many contemporary experiments. Alberto Gola (FBK) and Edoardo Charbon (EPFL) highlighted progress in custom SiPM and digital SPAD devices, respectively, stressing their improvements in photon-detection efficiency and sub-100 ps timing performance, as well as ongoing efforts to mitigate correlated noise and radiation-induced degradation. These technological developments were complemented by reports from large-scale experiments – such as ALICE3, CMS, DARKSIDE, DUNE, ePIC and JUNO-TAO – in high-energy and astroparticle physics, outlining the status of ongoing developments and the anticipated role of SiPM-based systems in large-area calorimetry, precision timing and Cherenkov imaging in future detectors.

Equally prominent were contributions on vacuum photodetectors and on enabling technologies. Albert Lehmann (University of Erlangen-Nürnberg) reviewed the status and future prospects of microchannel-plate photomultiplier tubes (MCP-PMT), while Angelo Rivetti (INFN Torino) addressed the challenges of fast, low-power front-end electronics capable of handling the ever-increasing channel counts of modern detectors. Modelling of photon-detection devices was discussed by Werner Riegler (CERN), who introduced an analytic description of timing and efficiency in SPADs and SiPMs, clarifying their performance limits for single-photon and charged-particle detection.

Several contributions underlined the increasingly close relationship between academia and industry in photon-detector development, touching on technology transfer, production scalability and long-term reliability, issues that are becoming central as detectors transition from small-scale prototypes to systems comprising hundreds of thousands, or even millions, of channels, such as in the case of the use of digital SiPMs for physics experiments.

The next edition of the conference will take place in May 2027 in Beijing.

Space radiobiology

Astronauts are exposed to elevated levels of cosmic radiation during spaceflight. As missions become longer and venture farther from Earth, understanding how this radiation affects the human body has become a pressing scientific challenge. This emerging field of space radiobiology has strong and perhaps unexpected links to the far better established discipline of radiobiology in medical physics, where physicists work closely with clinicians to design and optimise cancer treatments using ionising radiation. In both contexts, the central question is the same: how does radiation interact with living cells, and how can its harmful effects be predicted, mitigated and controlled?

Space Radiobiology is authored by Alessandro Bartoloni (INFN Roma) and Lidia Strigari (University Hospital of Bologna), whose combined expertise spans astroparticle physics, radiation transport and clinical radiobiology. The book explores a meeting point between two fields that have long followed separate paths but are now clearly converging around shared questions in radiation science.

At its core, the book argues for a closer integration of astroparticle physics and medical physics, demonstrating how both fields benefit from a common radiobiology perspective and a shared concern for radiation protection. At the heart of the volume is a thorough and well balanced discussion of space radiation and its implications for human spaceflight. The authors guide the reader through the complexity of the space-radiation environment – galactic cosmic rays, solar-particle events and their interactions – without losing clarity. These elements are consistently linked to real concerns for astronaut health, both for short missions and for the long-duration journeys that are becoming increasingly realistic. By connecting radiation sources, transport mechanisms and biological effects, the book builds a clear picture of where the risks lie and how they might be managed, making it especially relevant at a time when deep-space missions are moving from concept to planning.

What makes the book particularly engaging is that it never treats space research as an isolated niche. Instead, it repeatedly shows how ideas and tools developed for space can feed back into medical physics. From dosimetry and radiation monitoring to risk assessment, the authors highlight how methods refined for astroparticle experiments can be applied in clinical and research settings on Earth. Advances in detectors, modelling and data analysis developed for space missions are presented not as abstract achievements, but as practical contributions that can improve radiation therapy and diagnostic imaging.

From space to the hospital

This interdisciplinary spirit comes through especially well in the case study of the Alpha Magnetic Spectrometer group at INFN Roma Sapienza. Operating aboard the International Space Station, AMS was designed to study cosmic rays and search for signs of dark matter and antimatter. The book shows, however, that its high-precision measurements of charged-particle spectra, particle composition and energy deposition in low-Earth orbit have direct relevance for space radiobiology and radiation-protection research. In particular, AMS data helped characterise the flux, charge and energy distribution of galactic cosmic rays and solar energetic particles, key parameters for modelling dose, dose-rate and track-structure effects in biological tissue. These measurements inform risk assessments for astronaut exposure, improve shielding models, and support more realistic simulations of DNA damage and long-term health effects associated with chronic low-dose, high-energy radiation in space. Rather than serving as a standalone example, this case study acts as a concrete illustration of how cross-disciplinary collaboration actually works in practice: how shared technologies, experimental approaches and theoretical frameworks can produce insights that matter across fields.

Space Radiobiology — Credit: World Scientific

The sections on radiobiology strike a careful balance between accessibility and depth. Topics such as DNA damage, cellular responses and long-term health effects are explained clearly, without oversimplifying issues that are inherently complex (CERN Courier November/December 2025 p27). One of the book’s strongest messages is that space radiobiology, with its extreme and unconventional exposure conditions, offers a unique lens for understanding radiation effects that are also relevant to clinical and occupational environments on Earth.

By focusing on shared biological endpoints and common dosimetric challenges, the book shows how progress in one area can meaningfully inform the other. The discussion on developing common platforms for radiation measurement and monitoring reinforces this point, arguing that integrated approaches are not only efficient but scientifically necessary in increasingly complex radiation environments.

Space Radiobiology succeeds in bringing together different scientific communities around a common language and set of challenges. It will resonate with researchers in physics, space science, radiobiology and medical physics, as well as with graduate students looking for a broader, more connected view of radiation science. At a moment when deep-space exploration is becoming a tangible goal rather than a distant idea, the book offers a thoughtful and convincing picture of how lessons learned beyond Earth can shape safer and more effective uses of radiation here at home.

Seven colliders for CERN

Seven ambitious, diverse and technically complex colliders have been proposed as options for CERN’s next large-scale collider project: CLIC, FCC-ee, FCC-hh, LCF, LEP3, LHeC and a muon collider. The European Strategy Group tasked a working group drawn from across the field (WG2a) to compare these projects on the basis of their technical maturity, performance expectations, risk profiles, and schedule and cost uncertainties. This evaluation is based on documentation submitted for the 2026 update to the European Strategy for Particle Physics (CERN Courier May/June 2025 p8). With WG2a’s final report now published, clear-eyed comparisons can be made across the seven projects.

CLIC

The Compact Linear Collider (CLIC) is a staged linear collider that collides a polarised electron beam with an unpolarised positron beam at two interaction points (IPs) which share the luminosity (see figures and “Design parameters” table). It is based on a two-beam acceleration scheme where power from an intense 1 GHz drive beam is extracted and used to operate an X-band 12 GHz linac with accelerating gradients from 72 to 100 MV/m. The potential of two-beam acceleration to achieve high gradients enables a compact linear-collider footprint. Collision energies between 380 GeV and 1.5 TeV can be achieved with a total tunnel length of 12.1 or 29.4 km, respectively. The proof-of-concept work at the CLIC Test Facility 3 (CTF3) has demonstrated the principles successfully, but not yet at a scale representative of a full collider. A larger-scale demonstration with higher beam currents and more accelerating structures would be necessary to achieve full confidence in CLIC’s construction readiness.

The project has a well developed design incorporating decades of effort, and detailed start-to-end (damping ring to IP) simulations have been performed indicating that CLIC’s design luminosity is achievable. CLIC requires tight fabrication and alignment tolerances, active stabilisation, and various feedback and beam-based correction concepts. Failure to achieve all of its tight specifications could translate into a luminosity reduction in practical operation. CLIC still requires a substantial preparation phase and territorial implementation studies, which introduces some uncertainty on its proposed timeline.

FCC-ee

The electron–positron Future Circular Collider (FCC-ee) is the proposed first stage of the integrated FCC programme. This double-ring collider, with a 90.7 km circumference, enables collision centre-of-mass energies up to 365 GeV and allows for four IPs.

FCC-ee stands out for its level of detail and engineering completeness. The FCC Feasibility Study, including a cost estimate, was recently completed and has undergone scrutiny by expert committees, CERN Council and its subordinate bodies (CERN Courier May/June 2025 p9). This preparation translates into a relatively high technical-readiness level (TRL) across major subsystems, with only a few lower-level/lower-cost elements requiring targeted R&D. The layout has been chosen after a detailed placement study considering territorial, geological and environmental constraints. Dialogue with the public and host-state authorities has begun.

Performance estimates for FCC-ee are considered robust: previous experience with machines such as LEP, PEP-II, DAΦNE and SuperKEKB has provided guidance for the design and bodes well for achieving the performance targets with confidence. In terms of readiness, FCC-ee is the only project that already possesses a complete risk-management framework integrated into its construction planning.

FCC-hh

The hadron version of the Future Circular Collider (FCC-hh) would provide proton–proton collisions up to a nominal energy of 85 TeV – the maximum achievable in the 90.7 km tunnel for the target dipole field of 14 T. As a second stage of the integrated FCC programme, it would occupy the tunnel after the removal of FCC-ee, and so could potentially start operation in the mid-2070s. FCC-hh’s cost uncertainty is currently dominated by its magnets. The baseline design uses superconducting Nb₃Sn dipoles operating at 1.9 K, though high-temperature superconducting (HTS) magnets could reduce the electricity consumption or allow higher fields and beam energies for the same power consumption. Both technology approaches are active research directions of Europe’s high-field magnet programme.

The required Nb₃Sn technology is progressing steadily, but still needs 15 to 20 years of R&D before industry-ready designs could be available. HTS cables satisfying the specifications required for the magnets of a high-luminosity collider, although extremely promising, are at an even earlier stage of development. If FCC-hh were to proceed as a standalone project, operations could possibly start around 2055 from a technical perspective. In that case the magnets would need to be based on Nb₃Sn technology, as HTS accelerator-magnet technology is not expected to be available in that timeframe.

FCC-hh’s performance expectations draw strength from the LHC experience, though the achievable integrated luminosity would depend on the required “luminosity levelling” scenario that might be determined by pile-up control at the experiments. Luminosity levelling is a technique used in particle colliders such as the LHC to keep the instantaneous luminosity approximately constant at the maximum level compatible with detector readout, rather than letting it start very high and then decay rapidly.

LCF

The Linear Collider Facility (LCF) is a linear electron-positron collider, based on the design of the International Linear Collider (ILC), in a 33.5 km tunnel with two IPs sharing the pulses delivered by the collider and with double the repetition rate of ILC. The first phase aims at a centre-of-mass energy of 250 GeV, though the tunnel is sized to accommodate an upgrade to 550 GeV. LCF’s main linacs incorporate 1.3 GHz bulk-Nb superconducting radiofrequency (SRF) cavities for acceleration, operated at an average gradient of 31.5 MV/m and a cavity quality factor twice that of the ILC design at the same accelerating gradient. The quality factor of an RF cavity is a measure of how efficiently the cavity stores electromagnetic energy compared with how much it loses per cycle. LCF can deliver polarised positron and electron beams. Its engineering definition is solid and its SRF technology widely used in several operational facilities, most prominently at the European XFEL, however, the specific performance targets exceed what has been routinely achieved in operation to date. Demonstrating this combination of high gradient and high quality remains a central R&D requirement.

Several lower-TRL components – such as the polarised positron source, beam dumps and certain RF systems – also require focused development. Final-focus performance, which is more critical in linear colliders compared to circular colliders, relies on validation at KEK’s Accelerator Test Facility 2, which is being extended and upgraded. The overall schedule is credible but depends on securing the needed R&D funding and would require a preparation phase including detailed territorial implementation studies and geological investigations.

LEP3

The Large Electron Positron collider 3 (LEP3) proposal explores the reuse of the existing LEP/LHC tunnel for a new circular electron–positron (e⁺e^–) collider. LEP3 has two IPs and the potential for collision energies ranging from 91 to 230 GeV; its luminosity performance and energy range are limited by synchrotron radiation emission, which is more severe than in FCC-ee due to its smaller radius and the limited space available for the SRF installation.

The LEP3 proposal is not yet based on a conceptual or technical design report. Its optics and performance estimates depend on extrapolations from FCC-ee and earlier preliminary studies, and the design has not undergone full simulation-based validation. The current design relies on HTS combined quadrupole and sextupole focusing magnets. Though they would be central to LEP3 achieving a competitive luminosity and power efficiency, these components currently have low TRL scores.

Although tunnel reuse simplifies territorial planning, logistics such as dismantling HL-LHC components introduce non-trivial uncertainties for LEP3. In the absence of a conceptual design report, timelines, costs and risks are subject to significant uncertainty.

LHeC

The Large Hadron–Electron Collider (LHeC) proposal incorporates a novel energy-recovery linac (ERL) coupled to the LHC. High-luminosity collisions take place between a 7 TeV proton beam from the HL–LHC and a high-intensity 50 GeV electron beam accelerated in the new ERL. The LHeC ERL would consist of two linacs based on bulk-Nb SRF 800 MHz cavities, connected by recirculation arcs, resulting in a total machine circumference equal to one third that of the LHC. After acceleration, the beam will collide with the proton beam and will be successively decelerated in the same SRF cavities, “giving back” the energy to the RF system.

The LHeC’s performance depends critically on demonstrating high-current, multi-pass energy recovery at multi-GeV energies, which has not yet been demonstrated. The PERLE (Powerful Energy Recovery Linac for Experiments) demonstrator under construction at IJCLab in Orsay will test critical elements of this technology. The main LHeC performance uncertainties relate to the efficiency of energy recovery and beam-loss control of the electron beam during the deceleration process after colliding with the proton beam. Schedule, cost and performance will depend on the outcomes demonstrated at PERLE.

Muon collider

Among the large-scale collider proposals submitted to the European Strategy for Particle Physics update, a muon collider offers a potentially energy-efficient path toward high-luminosity lepton collisions at a centre-of-mass energy of 10 TeV. The larger mass of the muons, as compared with electrons and positrons, reduces the amount of synchrotron radiation emitted in a circular collider of a given energy and radius. The muons are generated from the decays of pions produced by the collision of a high-power proton beam with a target. “Ionisation cooling” of the muon beams via energy loss in absorbers made of low-atomic-number materials and acceleration by means of high-gradient RF cavities immersed in strong magnetic fields is required to reduce the energy spread and divergence of this tertiary beam. Fast acceleration is then needed to extend the muons’ lifetimes in the laboratory frame, thereby reducing the fraction that decays before collision. To achieve this, novel rapid-cycling synchrotrons (RCSs) could be installed in the existing SPS and LHC tunnels.

Neutrino-induced radiation and technological challenges such as high-field solenoids and operating radiofrequency cavities in multi-Tesla magnetic fields present major challenges that require extensive R&D. Demonstrating the required muon cooling at the required level in all six dimensions of phase space is a necessary ingredient to validate the performance, schedule and cost estimates.

**Design parameters** Key characteristics of the seven large-scale collider proposals considered by WG2a, based on inputs to the 2026 update to the European Strategy for Particle Physics. For the LHeC, the length is divided into the circumference of the HL-LHC and an additional 50 GeV ERL. The power consumption indicated for the LHeC does not include that of the HL-LHC injectors. For the muon collider, two configurations are presented for each collision energy. Full details are available in WG2a’s report. Credit: G Arduini et al. 2025 CERN-ESU-ESG-WG2a-full-report

WG2a’s comparison, together with the analysis conducted by the other working groups of the European Strategy Group, notably that of WG2b, which is providing an assessment of the physics reach of the various proposals, provides vital input to the recommendations that the European particle-physics community will make for securing the future of the field.

In pursuit of the post-inflation axion

**High-mass haloscope** Graduate student Heather Jackson at work on a prototype metamaterial plasma resonator for the ALPHA collaboration at UC Berkeley. Novel designs such as ALPHA’s plasma haloscopes and the MADMAX collaboration’s dielectric haloscopes are pushing axion searches into parameter space inaccessible to traditional designs. Credit: A J Gubser

One hundred µeV. 25 GHz. 10 m. This is the mass, frequency and de Broglie wavelength of a typical post-inflation axion. Though well motivated as a potential explanation for both the nature of dark matter and the absence of CP violation in the strong interaction, such axions subvert the “particle gas” picture of dark matter familiar to many high-energy physicists, and pose distinct challenges for experimentalists.

Axions could occupy countless orders of magnitude in mass, but those that result from symmetry breaking after cosmic inflation are a particularly interesting target, as their mass is predicted to lie within a narrow window of just one or two orders of magnitude, up to and around 100 µeV (see “Introducing the axion”). Assuming a mass of 100 µeV and a local dark-matter density of 0.4 GeV/cm³ in the Milky Way’s dark-matter halo, a back-of-the-envelope calculation indicates that every cubic de Broglie wavelength should contain more than 10²¹ axions. Such a high occupation number means that axion dark matter would act like a classical field. Moving through the Earth at several hundreds of kilometres per second, the Milky Way’s axion halo would be nonrelativistic and phase coherent over domains metres in width and tens of microseconds in duration.

Axion haloscopes seek to detect this halo via faint electric-field oscillations. The same couplings that should allow axions to decay to pairs of photons on timescales many orders of magnitude longer than the age of the universe should allow them to “mix” with photons in a strong magnetic field. The magnetic field provides a virtual photon, and the axion oscillates into a real photon. For several decades, the primary detection strategy has been to seek to detect their resonant conversion into an RF signal in a microwave cavity permeated by a magnetic field. The experiment is like a car radio. The cavity is tuned very slowly. At the frequency corresponding to the cosmic axion’s mass, a faint signal would be amplified.

The ADMX, CAPP and HAYSTAC experiments have led the search below 25 μeV. These searches are dauntingly difficult, requiring the whole experiment to be cooled down to around 100 mK. Quantum amplifiers must be able to read out signals as weak as 10^–24 W. The current generation of experiments can tune over about 10% of the resonant frequency, remaining stable at each small frequency step for 15 minutes before moving onto the next frequency. The steps are determined by the expected lineshape of the axion signal. Axion velocities in the Milky Way’s dark-matter halo should follow a thermal distribution set by the galaxy’s gravitational potential. This produces a spread of kinetic energies that broadens the corresponding photon frequency spectrum into a boosted-Maxwellian shape with a width about 10^–6 of the frequency. For a mass around 100 μeV, the expected width is about 25 kHz.

The trouble is that the resonance frequency of a cavity is set by its diameter: the larger the cavity, the smaller the accessible frequency. Because the signal power scales with the cavity volume, it is increasingly difficult to achieve a good sensitivity at higher masses. For a 100 µeV axion with frequency 25 GHz that oscillates into a 25 GHz photon, the cavity would have to be of order only a centimetre wide.

Probing this parameter space calls for novel detector concepts that decouple the mass of the axion from the volume where axions convert into radio photons. This realisation has motivated a new generation of haloscopes built around electromagnetic structures that no longer rely on the resonant frequency of a closed cavity, but instead engineer large effective volumes matched to high axion masses.

Two complementary approaches – dielectric haloscopes and plasma haloscopes – exploit this idea in different ways. Each offers the possibility of discovering a post-inflation axion in the coming decade.

The MADMAX dielectric haloscope

**A work in progress** A MADMAX prototype setup in the shielded laboratory at DESY/University of Hamburg. Microwaves from the booster (above, top right and enhanced image far right) are reflected from the focusing mirror (left) into a horn antenna (foreground right). Credit: J Egge/MADMAX Collab. 2025 *PRL* **134** 151004

Thanks to their electromagnetic coupling, a galactic halo of axions would drive a spatially uniform electric field oscillation parallel to an external magnetic field. For 100 µeV axions, it would oscillate at about 25 GHz. In such a field, a dielectric disc will emit photons perpendicular to its surfaces due to an electromagnetic boundary effect: the discontinuity in permittivity forces the axion-induced field to readjust, producing outgoing microwaves.

The Magnetized Disc and Mirror Axion (MADMAX) collaboration seeks to boost this signal through constructive interference. The trick is multiple discs, with tuneable spacing and a mirror to reflect the photons. As the axion halo would be a classical field, each disc should continuously emit radiation in both directions. For multiple dielectric discs, coherent radiation from all disc surfaces leads to constructive interference when the distance between the discs is about half the electromagnetic wavelength, potentially boosting axion-to-photon conversion in a broad frequency range. The experiment can be tuned for a given axion mass by controlling the spacing between the discs with micron-level precision. Arbitrarily many discs can be incorporated, thereby decoupling the volume where axions can convert into photons from the axion’s mass.

The MADMAX collaboration has developed two indirect techniques to measure the “boost factor” of its dielectric haloscopes. In the first method, scanning a bead along the volume maps the three-dimensional induced electric field, from which the boost factor is then computed as the integral of the electric field over the sensitive volume. This method yielded 15% uncertainty for a prototype booster with a mirror and three 30 cm-diameter sapphire discs (see “A work in progress” figure). By studying the response of the prototype in the absence of an external magnetic field, the collaboration set the world’s best limits on dark-photon dark matter in the mass range from 78.62 to 83.95 μeV.

The MADMAX collaboration has developed two indirect techniques to measure the “boost factor” of its dielectric haloscopes

The boost factor can alternatively be obtained by modelling the booster’s response using physical properties extracted from reflectivity measurements and the behaviour of the power spectrum in the given frequency range. This method was applied to MADMAX prototypes inside the world’s largest warm-bore superconducting dipole magnet. Named after the Italian physicist who designed it in the 1970s, the Morpurgo magnet is normally used to test subdetectors of the ATLAS experiment using beams from CERN’s North Area. Since MADMAX requires no beam, a first axion search using the diameter aperture took place during the 2024 winter shutdown of the LHC. The prototype booster included a 20 cm-diameter mirror and three sapphire discs separated by aluminium rings. Frequencies around 19 GHz were explored by adjusting the mirror position. No significant excess consistent with an axion signal was observed. Despite coming from a small prototype, these results surpass astrophysical bounds and constraints from the CERN Axion Solar Telescope (CAST), demonstrating the detection power of dielectric haloscopes.

As a next step, a prototype booster with a mirror and up to twenty 30 cm-diameter discs is expected to deliver a factor 10 to 100 improvement over the 2024 tests. The positions of its discs will be adjusted inside its stainless-steel cryostat using cryogenic piezo motors. The setup is currently being commissioned and is set for installation in the Morpurgo magnet during the third long shutdown of the LHC from mid-2026 to 2029. An important goal is to prove the broad-band scanning capacity of dielectric haloscopes at cryogenic temperatures and conditions close to those of the final MADMAX design. Operating at 4 K will enhance MADMAX’s sensitivity by reducing noise from thermal radiation. A prototype has already been successfully tested inside a custom-made glass fibre cryostat in the Morpurgo magnet in cooperation with CERN’s cryogenic laboratory.

The final baseline detector foresees a 9 T superconducting dipole magnet with a warm bore of about 1.3 m. A first design has been developed and important aspects of its technological feasibility have already been tested, such as quench protection and conductor performance. As a first step, an intermediate 4 T warm-bore magnet is being purchased. It should be available around 2030. Once constructed, the magnet will be installed at DESY’s axion platform inside the former HERA H1 iron yoke, where preparations for the required cryogenic infrastructure are underway.

With MADMAX’s prototype booster scaling towards its final size, and quantum detection techniques such as travelling-wave parametric amplifiers and single-photon detectors being developed, significant improvements in sensitivity are on the horizon for dielectric haloscopes. MADMAX is on a promising path to probing axion dark matter in the 40 to 400 µeV mass range at sensitivities sufficient to discover axion dark matter at the classic Dine–Fischler–Srednicki–Zhitnitsky (DFSZ) and Kim–Shifman–Vainshtein–Zakharov (KSVZ) theory benchmarks.

The ALPHA plasma haloscope

**Plasma tuning** A resonator with a spiral design at Stockholm University. Credit: J W Jeoung

In a plasma, photons acquire an effective mass determined by the plasma frequency, which depends on the density of charge carriers. If the plasma frequency is close to the axion’s Compton frequency, axion–photon mixing is resonantly enhanced. As the plasma could in principle be of any volume, the volume in which the axion field converts into photons has been decoupled from the axion mass – but tuning the plasma frequency is not feasible, preventing a detector based on this effect from scanning a wide range of masses.

In 2019, Matthew Lawson, Alexander Millar, Matteo Pancaldi, Edoardo Vitagliano and Frank Wilczek proposed performing this experiment using a metamaterial plasma with a tunable electromagnetic dispersion which mimics that of a real plasma. In a plasma haloscope, this metamaterial is a lattice of thin metallic wires embedded in vacuum. By adjusting the wire spacing, the diameter of the wires and their arrangement, the resonant plasma frequency can be tuned over a wide range.

The ALPHA collaboration was formed in 2021 to build a full-scale plasma haloscope capable of probing axion masses from 40 to 400 μeV, corresponding to axion frequencies from 10 to 100 GHz. While challenges related to detecting an extremely feeble signal remain, the simplicity of the cavity design, particularly in the magnet geometry and the tuning mechanism, offers flexibility.

ALPHA’s design can be pictured as a large-bore superconducting solenoid magnet, and a resonator housing an array of thin copper or superconducting wires stretched along the field direction. Photons are extracted through waveguides and fed into an ultra-low-noise microwave receiver chain, cooled by a dilution refrigerator to below 100 mK, developing quantum-sensing techniques developed in close collaboration with the HAYSTAC collaboration. Photons are amplified with Josephson parametric amplifiers – the same technique used for qubits used in quantum computers, and the topic of the 2025 Nobel Prize in Physics awarded to John Clarke, Michel Devoret and John Martinis. Tests at room temperature in 2022 and 2023 demonstrated that the response of the meta-plasma can be tuned across the 10 to 20 GHz range with a modest number of configuration changes, and that the quality factors exceed 10⁴ even before cooling down to cryogenic temperatures.

Two designs are being pursued to design a tuning mechanism that allows precise adjustment of the plasma frequency with minimal mechanical intervention: a spiral design where a single rotating rod tunes a set of three spiral arms relative to another set of fixed spiral arms (see “Plasma tuning” figure); and a design with multiple spinners rotating groups of wires relative to a fixed grid of wires.

It is an exciting time for axion searches

ALPHA’s development plan proceeds in two main stages. Phase I is currently being constructed at Yale University’s Wright Laboratory, and focuses on employing established technology to demonstrate the technique and search for axions with masses from 40 to 80 μeV. Phase I’s cavity, consisting of copper plasma resonators, will be immersed in a 9 T magnet, 17.5 cm in diameter and 50 cm tall. The expected conversion power in ALPHA’s frequency range is of order 10^–24 W – comparable to the thermal noise in a 50 Ω resistor cooled to 50 mK. The read-out chain therefore employs Josephson parametric amplifiers whose noise temperatures approach the standard quantum limit. The system is designed to scan continuously while maintaining sensitivity close to the KSVZ axion-photon coupling, a benchmark for well-motivated axion models. The data-acquisition strategy builds on techniques developed in ADMX and HAYSTAC: fast Fourier transforms of the time-stream, coherent stacking across overlapping frequency bins and real-time evaluation of excess-power statistics.

Several improvements are being developed in parallel for Phase II. Quantum sensing techniques have the potential to boost the signal while reducing noise. Such techniques include HAYSTAC-style noise squeezing, using cavity entanglement and state swapping to enhance the signal, and single-photon detection. Dramatically increasing the quality factor of superconducting plasma resonators will also significantly boost the signal. Last but not least, magnets with a larger bore and higher field, such as the ones being deployed at the neutron scattering facilities at Oak Ridge National Laboratory, are expected to expand the experimental reach up to 200 μeV and push the sensitivity to below the axion–photon coupling of the DFSZ model, another classic theoretical benchmark.

Beginning in 2026, ALPHA Phase I will start taking its first physics data, initially searching for dark photons – a dark-matter candidate that interacts with plasma without requiring the presence of a magnetic field. After commissioning ALPHA’s magnet, a full axion search will commence during 2027 and 2028.

It is an exciting time for axion searches. New experiments are coming online, implementing new ideas to expand the accessible mass ranges. Groups in Italy, Japan and Korea are exploring alternative metamaterial geometries, including superconducting wire meshes and photonic crystals that replicate plasma behaviour at higher frequencies. European teams linked to the IAXO collaboration are considering hybrid systems that couple plasma-like resonators to strong dipole magnets. ALPHA will search for axions in the well-motivated region, first focusing between 40 and 80 μeV, and then between 80 and 200 μeV.

Intense efforts are underway. Discoveries may be just around the corner.

Trigger-level search for dijet resonances

ATLAS figure 1 — **Fig. 1.** Observed (solid lines) and expected (dashed lines) 95% confidence upper limits on the coupling between quarks and an axial-vector mediator to the dark sector, as a function of the mass of the mediator. The TLA (thick blue line) places the strictest limits across a wide mass range. (Analysis references can be found in ATL-PHYS-PUB-2025-041.) Credit: ATLAS Collab 2025 ATL-PHYS-PUB-2025-041

The LHC’s increased collision energies have opened new territory for TeV-scale searches, but its vast datasets also provide unparalleled opportunities to thoroughly explore the electroweak scale. A new ATLAS result uses an unconventional trigger-level analysis (TLA) of the full Run 2 dataset to achieve record sensitivity to low-mass particles decaying into quarks or gluons. ATLAS employs a two-stage trigger system, with a fast hardware-based first-level trigger selecting about 100 kHz of events from the 40 MHz bunch-crossing rate, followed by a software high-level trigger (HLT) that performs detailed event reconstruction and further reduces the accepted event rate by about two orders of magnitude. By recording a much reduced event format at the trigger level, TLA preserves a substantially larger fraction of events than would normally be output by the HLT.

New particles that decay with a two-jet final state feature in many Standard Model (SM) extensions. For example, the properties of “dark mediators” that couple to both quarks and dark matter could explain the present abundance of dark matter by controlling how much of it remains after falling out of equilibrium with normal matter in the early universe. At the LHC, the coupling of dark mediators to quarks would enable both production and decay into quark–antiquark pairs. This should appear as resonances in the dijet mass distribution.

Searching for dijet resonances at low mass is challenging. Dijet production from strong interactions is one of the LHC’s most abundant signatures. Beyond requiring a precise understanding of these enormous backgrounds and the detector response, the low-mass dijet rate far exceeds what ATLAS can record. Only the most energetic dijet events can be kept, limiting conventional dijet searches to masses above approximately 1 TeV.

To access the low-mass region, ATLAS used TLA to record multi-jet events throughout Run 2. By dropping the raw detector data from the readout, these TLA events were ~200 times smaller than standard events while retaining all high-level jet and calorimeter-based variables reconstructed in real-time by the HLT.

The size reduction allowed ATLAS to record TLA events at rates of up to 27 kHz – compared to an average 1.2 kHz for the full detector readout. This rate was achieved in conjunction with the additional trigger bandwidth allocated to TLA at the end of LHC fills and a more efficient use of this bandwidth for dijet events. In Run 2, this was aided by ATLAS’s L1Topo trigger processor, which applies simple topological selections – such as angular correlations between jets – already at first level. The new result uses 1 billion dijet events, or up to 75 times the data sample available to the equivalent conventional search, achieving unprecedented statistical precision.

The new result achieves record sensitivity to low-mass particles decaying into quarks or gluons

This enormous dataset demands excellent control of systematic uncertainties. ATLAS developed a dedicated multi-step calibration for trigger-level jets, achieving a jet energy scale precision of 1 to 4%, comparable to calibrations using full detector readout. The overwhelming SM background was modelled using a data-driven fitting technique, reaching a relative precision better than 1 part in 10⁴.

The search has found the dijet invariant-mass distribution to be consistent with the background expectation. The analysis provides numerical results that can be used to constrain any of the numerous models of dijet resonances, as well as explicit constraints on a specific dark mediator model used as a common benchmark for many ATLAS and CMS searches. The result sets ATLAS’s most stringent exclusion limits to date on the potential coupling of such a mediator to quarks, across a broad range of mediator masses reaching as low as 375 GeV (see figure 1).

The dijet TLA during Run 2 has established a foundation for an expanded trigger-level physics programme. In Run 3, trigger-level jets incorporate tracking information, allowing flavour tagging and improving jet energy resolution and robustness against pile-up. ATLAS also records trigger-level photons and uses them in combination with partial detector readout at full granularity. These and other advances in TLA should enable future ATLAS searches to probe a wider variety of signatures at the electroweak scale.

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