Proton Compression for the Muon Collider Project

Abstract

A muon collider is a promising future collider concept for particle physics. The International Muon Collider Collaboration (IMCC) and the Muon Collider Collaboration (MuCol) are currently conducting a design study to investigate the feasibility of such a facility. To produce muons, a high-intensity, short pulse proton beam produced in a proton complex is directed onto a target, where pions are produced, which subsequently decay into muons. This proton complex includes a compressor before final transport to the target. The collective repulsion between the protons, referred to as space-charge, is expected to be significant in the compressor, where proton bunches are to be compressed to pulse lengths below 2 ns.

Previous studies of the compressor have modeled space-charge using 2.5D Particle-in-Cell (PIC) simulations in Xsuite, whose space-charge implementation employs a static mesh, i.e., the mesh does not adapt to an evolving beam size. However, 2.5D space-charge may not be sufficient to accurately describe the effects of space-charge in the compressor. In addition, a 3D model with a static mesh would be computationally inefficient due to the compression.

In this thesis, an adaptive-mesh space-charge implementation has been developed for Xsuite. Using both static- and adaptive-mesh configurations, 2.5D and 3D space-charge models have been compared for the compressor. The results indicate that 3D modeling is required to capture important aspects of the compressor dynamics. A four-fold structure has been observed in the absence of space-charge, and its cause has been investigated. Further studies have been conducted using adaptive-mesh 3D modeling, including a convergence study and a tune scan, where the latter aided in the exploration of a new working point for the compressor. No fundamental obstacle to sub-2 ns compression was identified. However, it is not fully clear whether observed microbunching phenomena are numerical or physical in nature.

Popular Abstract

Want to detect dark matter? Or understand more about the Higgs boson? To accomplish these and many other goals in modern physics, we would need new particle colliders stronger than the ones we have today. One such particle collider would be the so-called Muon Collider, which would collide the particles called muons. Colliding muons would be very energy efficient, as they do not consist of several building blocks compared to protons, where their parts all use some of the useful energy. Muons would also be much more efficient compared to colliding electrons, as muons would lose much less energy when bent in a circular accelerator. However, muons come with one big drawback: a limited lifetime, which means that it is not as easy to get many of them to do meaningful collisions.

Thinking in analogy, imagine protons as colliding two round satellites together and electrons as colliding billiard balls. The satellites consist of many different parts and the energy will be spread across all of these, whereas for the billiard balls, the energy is shared only between the balls. The muons can perhaps be seen as big blocks of ice; bigger than the billiard balls yet, in a sense, still point-like. And as time progresses, the ice melts. The loss of energy at bending that is more significant for lighter objects is harder to analogize and is simply a fact to accept.

To deal with the limited lifetime of muons, several creative technical solutions are needed to make a muon collider possible. To create sufficient amounts of muons, many protons very close to each other will need to collide on a target. As equally charged particles, such as protons, repel each other, this implies significant challenges to make this possible. Before building something this expensive, we first use computer simulations to test different designs for how such a proton beam can realistically be produced. This work treats the last part of the proton complex, the compressor, where the protons are squeezed the closest together.

As some assumptions had been made in previous simulations, one goal was to see if these assumptions were realistic enough, and if not, what consequences this could have. By changing how the computer does some calculations and removing some assumptions, the results clearly differed. Following this, this work conducts several investigations:

- To make sure that the computer is not making things up, a ''convergence study'' is conducted, to determine which inputs consistently give the same output.
- In some cases, the particles underwent ''microbunching''. Think of an accordion: when you press together the accordion to produce sound, the bellows fold on themselves. In a sense, the proton beam sometimes underwent a similar ''folding'', but it is not clear whether this is caused by computer calculations or by real physics.
- Through further experiments, an observed ''four-fold'' structure was found to have an unexpected cause. It was initially believed to be caused by a resonance. In accelerator physics, a resonance can be compared to when you push someone on a swing: if you time it a certain way, the person that you are pushing will go further and further, and may even fall off. Resonance can build up for particle beams in a similar manner and may similarly cause us to lose particles. Therefore, this work also tries to find ways to remove the resonance mentioned.
- Lastly, think of an old-school radio: you turn on the wheel to adjust frequency and connect to the channel you want. Perhaps you need to adjust the wheel slightly to make the people speaking less ''noisy''. This work does a similar thing to the compressor, where we try to get the best results by slightly changing the structure of the compressor multiple times. Some of the best ''radio wheel'' positions were then compared.

This work in many ways improves on previous simulations, attempts to better understand how to improve the compressor, and provides suggestions on what may need to be investigated further.

• author: Sörqvist, Markus
• supervisor: Sofia Johannesson; Johan Lundgren
• organization: Department of Electrical and Information Technology
• alternative title: Protonkompression för en framtida myonaccelerator
• course: EITM01 20252
• year: 2026
• type: H2 - Master's Degree (Two Years)
• subject: Physics and Astronomy
• keywords: accelerator physics, beam physics, muon collider, mucol, imcc, high-intensity proton beam, proton driver, proton compressor, space-charge, collective effects, 2.5D space-charge, 3D space-charge, particle-in-cell, pic, Xsuite, adaptive mesh, resonances, tune scan
• report number: LU/LTH-EIT 2026-1121
• language: English
• id: 9228185
• date added to LUP: 2026-05-28 09:23:51
• date last changed: 2026-05-29 13:24:47