Particle accelerators and colliders are crucial tools for advancing scientific research. They accelerate and collide highly energetic beams of particles to enable discoveries in particle and high-energy physics, material science, medicine, and many other fields. Modern accelerators use superconducting magnets to bend and focus the beam as it is accelerated to speeds approaching that of light before collision.

While most accelerators use magnets with bores that have circular apertures, magnets with elliptical apertures are better suited for a wide range of accelerator applications, such as fixed-field accelerators (FFAs), where the magnetic field remains fixed, and multiple beams of different energies are accelerated simultaneously.

Now, researchers from the Accelerator Technology & Applied Physics (ATAP) Division at Berkeley Lab have developed a new analytic framework for designing elliptical bore-shaped superconducting magnets and elliptically-shaped superconducting windings. The work could lead to smaller, more efficient, cost-effective magnets for FFAs and other accelerator technologies, including heavy ion synchrotrons. It also aligns with the goals of the U.S. Magnet Development Program, led by Berkeley Lab, and the recommendations of the recently released P5 Report, which outlines a pathway for particle physics over the next decade and includes strong support for accelerator R&D.

“In FFAs, because the particle beams move back and forth in the horizontal plane of the magnets, they sample a larger area of the magnet’s bore in this direction,” explains Lucas Brouwer, a research scientist in ATAP’s Superconducting Magnet Program who developed the analytic framework. “This results in a beam-prescribed region better matched to an elliptic rather than circular-shaped magnet bore.”

Brouwer says magnets with circular apertures produce magnetic fields in spaces that are not needed for these accelerators, leading to inefficiencies in the magnet design. However, magnets with elliptical apertures produce fields in a region “that better matches the area sampled by the beams, potentially allowing for more efficient accelerators that are more compact and cheaper to build and operate than current technologies.”

Furthermore, he adds that magnets with an elliptical aperture offer a more efficient design for incorporating materials that absorb the radiation accelerating beams produce. This makes them a potential option for addressing the challenges associated with the high radiation loads of future accelerators for high-energy physics research.

However, analytically modeling the characteristics of these magnetic fields is more challenging than for those with circular apertures. So, how to produce the desired magnetic fields for accelerator applications using superconducting magnets with elliptical apertures remains uncertain.

To model these magnetic fields, Brouwer first mathematically derived the natural form of the magnetic fields for an elliptical-shaped magnet aperture (elliptic field harmonics) and how these relate to an “idealized” current density—which determines the shape and strength of the magnetic field generated by the magnet’s superconducting coils. He then used the transformation between the elliptic and circular field harmonics to determine the elliptically-shaped current density, which produces the circular magnetic fields used in traditional accelerators.

He then applied this framework to the geometry of canted cosine-theta (CCT) accelerator magnets. First proposed in the 1970s, CCT magnets have attracted considerable interest over the last two decades because they can generate precisely shaped, high-strength magnetic fields required by accelerators, effectively manage conductor stress, and can be fabricated using simpler manufacturing processes, potentially making them much less expensive to produce than other magnets. Additionally, their versatile coil geometry can generate the different magnetic field distributions desired in accelerators. They can be used for dipole, quadrupole, sextupole, and octupole magnets and for magnets that require a combination of functions, such as part dipole and part quadrupole, which are desired for FFAs.

“We then investigated how magnet cost parameters scale with aperture ellipticity to determine the benefits of using an elliptical bore in cases where the beam’s prescribed field region is non-circular,” explains Brouwer. “Finally, we utilized this general method for the specific winding geometry of CCT magnets, which provided an analytical path to practical coil designs for elliptic bore accelerator magnets.”

According to Paolo Ferracin, senior scientist and deputy of ATAP’s Superconducting Magnet Program, the concept of magnets with elliptical apertures “represents a beautiful example of an innovative and original design and is perfectly suited to address some of the demanding requirements of the next generation of particle accelerators like the muon collider.”

The work, supported by funding from the Department of Energy Office of High Energy Physics Early Career Research Program, provides a robust analytic path for designing superconducting accelerator magnets constructed with elliptic bore magnets. Moreover, the method offers a practical tool for accelerator scientists and engineers to determine the correct coil geometry for the desired field characteristics for elliptic apertures.

“We plan to undertake a design study for a prototype magnet that will allow us to test and optimize the parameters for making elliptical-shaped superconducting magnets for specific accelerator applications like FFAs,” says Brouwer.

Commenting on the research, ATAP Division Director Cameron Geddes said, “The development of magnets with elliptical apertures promises new accelerator technologies for driving scientific research, enabling new discoveries, and advancing technologies for future colliders.”


To learn more …

L. Brouwer. “Producing circular field harmonics inside elliptic magnet apertures with superconducting Canted-Cosine-Theta coils,” Phys. Rev. Accel. Beams 27, 022402, 2024,



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