The 4th Annual Meeting of the International Muon Collider Collaboration and the 2nd MuCol Annual Meeting will take place in the week 12-16 May 2025. The meeting will be hosted by DESY in Hamburg, Germany. Participation via Zoom will be made possible for people who cannot attend in person.
The meeting will cover all areas of study and development. More details are available in the detailed agenda.
As for our previous meetings, we wish to profit from this opportunity to strengthen integration among the various activities and collaboration.
PLEASE BE AWARE that the event is being targeted by phishing emails. Never share your personal/payment data via email. The registrants list was made private to limit the phising attempts.
https://indico.desy.de/event/48594/
Input considerations to heat limits & warm-to-cold transitions
The RF system for the initial and 6D-muon-cooling channels consists of several RF cavities operating at 352 and 704 MHz. To meet the luminosity requirements of a muon collider, the maximum muon beam intensity at the end of the cooling channel is expected to be on the order of $10^{12}$ muons per bunch. At such high beam intensities, transient beam loading can severely impact the accelerating gradient and degrade beam quality. Based on input from the beam dynamics design, we estimated the beam loading effects in the proposed RF cavities and analyzed mitigation strategies to ensure that the maximum allowable surface fields remain within safe limits, reducing the risk of RF breakdown.
This study explores the implementation of an RF re-acceleration structure positioned between two final cooling cells. Various cavity configurations are analyzed under specific RF parameters to optimize the longitudinal beam dynamics. A detailed examination of the longitudinal phase space evolution within these RF systems is conducted, aiming to prepare the beam energy and adjust the energy spread to achieve optimal conditions for the subsequent final cooling cell. Additionally, solenoids placed between RF cavities ensure effective transverse beam guidance, further improving overall performance.
RF Breakdown is a critical factor driving the design and limiting the performance of high gradient RF cavities. Within these high E-field cavities, localised field enhancement effects can occur due to microscopic surface imperfections - resulting in field strength of orders of magnitude greater than the cavity's average - leading to plasma formation, material damage/degradation and field emission.
In the context of the muon collider's cooling channel, a strong external magnetic field is superimposed (2-5T) on the existing RF field, increasing the risk of RF breakdown and limiting maximum gradients.
This poster presents CST simulations, supported by investigation of secondary electron yield distributions, which can be applied to understand the role of the static magnetic field in the breakdown dynamic.
In the scenario of the Muon Collider, the short muon lifetime (2.2 μs at rest) poses several challenges in developing magnets, RF systems, targets, shielding, and cooling. One major concern is the flux of neutrinos produced by muon decay in the collider, which necessitates minimizing straight sections. This constraint makes conventional FoDo cells unsuitable, requiring the development of combined-function magnets that integrate bending with focusing/defocusing or chromaticity correction functions.
To address these challenges, magnets capable of combining a dipole field with either a quadrupole field (B1+B2) or a sextupole field (B1+B3) are currently under study. This work extends the Aperture-Field (A-B) plot methodology, previously applied to single dipoles or quadrupoles, to dipole-quadrupole combined-function magnets. It outlines feasible designs based on aperture, field strength, mechanical stress, quench protection, and cost. Using a Python-ANSYS tool, optimized configurations were simulated under the sector coil approximation, focusing on ReBCO coils operating at 4.5K, 10K, and 20K. The resulting Dipole Field – Quadrupole Gradient (B-G) plots illustrate the design space, highlighting the technological limits and feasibility of various dipole and quadrupole combinations.
The baseline design for the high-energy complex of a muon collider consists of a chain of Rapid Cycling Synchrotrons (RCS). The RCS chain examined in this study is based on CERN infrastructure: three RCSs are designed to reuse existing tunnels at CERN, the SPS and LHC tunnels. These synchrotrons cover an energy range from 63 GeV to 3.8 TeV and include both normal and hybrid types, featuring a combination of fixed-field superconducting magnets and pulsed normal-conducting magnets.
This poster presents the parameter optimization process and an initial optical design for this RCS chain. Additionally, it includes a preliminary comparison between the lattices of the SPS and LHC with that of the proposed RCSs.
Following the indications of the European Strategy for Particle Physics update (ESPP), the International Muon Collider Collaboration has been established to explore the viability of a muon collider with a center-of-mass energy of 10 TeV. This attempt presents significant technological developments to fast accelerate and efficiently collide muon beams before they decay if we consider the extremely short muon lifetime of just 2.2 microseconds at rest.
To reduce machine costs and enhance collider luminosity, the superconducting main arc dipole magnets of the collider ring must be both compact and capable of producing a strong, static high magnetic field. Additionally, the coil geometry needs to have wide aperture to accommodate tungsten shield structure that protects the superconducting coil volume from exposure to radiation and heat deposition generated by muon decays. Presently, high temperature superconductors represent the baseline magnets configuration for the 10 TeV collider due to the high performances and high operating temperature requirements considered. To optimize the electromagnetic field quality of the high field dipoles, magnetization of the HTS tape must be considered in the analysis due to the wide tape width.
This work presents the electromagnetic and mechanical design of a cos-theta dipole for the collider ring. In addition, the study focuses on the comparison of fem simulation model performed in COMSOL and analytical model of the magnetization effect of the persistent currents on field quality and hysteretic losses considering also the influence of transport current in the coil conductor.
Setup design is a critical aspect of experiment development, particularly in high-energy physics, where decisions influence research trajectories for decades. Within the MODE Collaboration, we aim to generalize Machine Learning methodologies to construct a fully differentiable pipeline for optimizing the geometry of the Muon Collider Electromagnetic Calorimeter.
Our approach leverages Denoising Diffusion Probabilistic Models (DDPMs) for signal generation and Graph Neural Networks (GNNs) for photon reconstruction in the presence of Beam-Induced Background from muon decays. Through automatic differentiation, we integrate these components into a unified framework that enables end-to-end optimization of calorimeter configurations. We present the structure of this pipeline, discuss key generation and reconstruction techniques, and showcase the latest results on proposed geometries.
Following the guidelines of the European Strategy for Particle Physics, the International Muon Collider Collaboration (IMCC) has outlined a plan for an innovative particle accelerator that exceeds the performance of the LHC and its luminosity upgrade, aiming to explore new frontiers in particle physics. This next-generation machine is a muon accelerator featuring a 10-km-long collider ring capable of reaching a center-of-mass energy of 10 TeV. The short average lifetime of muons (only 2.2 μs at rest), their challenging production and cooling processes, and the radiation issues caused by muon decay require the development of advanced and compact superconducting magnets that can generate extremely high magnetic fields within large apertures. To address these challenges, ReBCO has been identified as the most suitable superconducting material due to its outstanding critical current.
This contribution presents a preliminary 2D study of dipoles for the collider ring arc, utilizing a block-coil configuration with a novel cable stacked orientation and an innovative end winding design. The updated electromagnetic design achieves 16 T bore field within 140 mm diameter aperture, accompanied by an analytical estimation of the hysteretic losses, accounting for the transport current effects. Finally, an initial mechanical analysis of the magnet is presented using the Finite Element Method (FEM), exploring the application of a stress-management strategy to mitigate the effects of the high Lorentz forces.
A 10 TeV muon collider offers a combination of unprecedented energy collisions in a clean leptonic environment, providing both precision measurements and the highest energy reach. This endeavor will require novel detector technologies, designs, and software. Previous studies have analyzed 1.5 and 3 TeV muon collider detector designs adapted from CERN’s Compact Linear Collider (CLIC) detector with performances comparable to the LHC experiment. The MAIA detector concept is specifically optimized for 10 TeV to provide precision physics at this energy scale while suppressing the increased beam-induced-background (BIB) from muon decays at 10 TeV. The detector consists of an all-silicon tracker immersed in a 5T solenoidal field. High-granularity silicon-tungsten and iron-scintillator calorimetry is optimized to contain high-energy showers and allow for particle-flow reconstruction. To discriminate the BIB from physics signals, MAIA’s calorimeters must provide good timing information, fine spatial granularity, and high energy resolution. The MAIA collaboration calibrated and tested MAIA’s Hadronic Calorimeter (HCAL) performance through Anti-kT jet reconstruction efficiency and energy resolution.
Low energy cooling of positive muons has been demonstrated using a
modified Wien filter to deliver frictional cooling or by laser
ionisation cooling. These techniques have been shown experimentally to
deliver extremely cold - thermal - muon beams, but studies continue to
demonstrate efficiency and acceptance suitable for a muon collider. An
equivalent system for negative muons has not been demonstrated owing to
the formation of strongly bound muonic atoms at relatively high energy.
In this poster, we propose a novel low energy cooling technique for
positive muons. Our studies have shown delivery of cold muon beams with
acceptance and efficiency that is comparable to the rectilinear
"B-stage" cooling system in just a few metres of beamline and with
modest hardware requirements. Such a device could yield improvement in
the muon collider facility performance while reducing costs
significantly. It would also be promising as a source for low energy
positive muons for applications such as muSR.
Muon colliders offer high-luminosity, multi-TeV collisions without significant synchrotron radiation but require further exploration of muon production, acceleration, cooling, and storage techniques. A proposed 6D cooling demonstrator aims to extend the MICE experiment's validation of transverse ionization cooling to also reduce longitudinal emittance, using bunched muon beams and incorporating RF cavities for reacceleration. The cooling lattice includes solenoids for tight focusing, dipoles for beam dispersion, and wedge absorbers for differential energy loss. This paper presents a complete implementation of cooling channels for BDSIM, a Geant4-based accelerator simulation tool, using appropriate analytic field models to account for fringe-field-dominated magnets. Components have been tested individually and validated against other tracking codes such as G4BeamLine. A tracking study leveraging this implementation is presented, simulating and optimizing a rectilinear cooling channel for the 6D cooling demonstrator. The analysis incorporates beam parameters from existing proton drivers, using outputs from targetry and capture system designs.
We present a preliminary lattice design for a series of pulsed synchrotron rings to accelerate muon beams to their maximum collision energy at Fermilab. The rings are limited to a circumference of 15.5 km, which would allow them to fit just within the Fermilab site boundary. We wish to estimate the maximum energy that muons can be accelerated to on the Fermilab site based on a realistic lattice layout for the synchrotron chain. We consider the feasibility of beginning the synchrotron chain with Tevatron sized (6.28 km circumference) rings. To achieve high average fields, superconducting fixed field magnets are interleaved with iron-dominated magnets whose fields are rapidly ramped from negative to positive. We consider which rings in the acceleration chain benefit from using dipole and quadrupole magnets interleaved in this fashion. Multiple RF stations are required to ensure that the beam energy and the magnet fields are reasonably well synchronized and to avoid longitudinal losses due to the large synchrotron tune. We use FODO arc cells with dispersion suppressed into the RF straights. We will discuss tradeoffs between maximum energy, energy range, and muon decays.
To push the boundaries of physics beyond the capabilities of the LHC and its High-Luminosity Upgrade (HL-LHC), particle physicists are exploring advanced accelerators to enable more precise measurements and achieve higher energies. Following the recommendation of the Updated European Strategy for Particle Physics (ESPP), the International Muon Collider Collaboration has been established to assess the feasibility of a muon collider facility with a center-of-mass energy of 10 TeV. This initiative faces significant technical challenges, primarily due to the short muon lifetime at rest of just 2.2 µs. Overcoming this constraint requires the development of cutting-edge technologies, including complex magnets, RF systems, targets, shielding, and cooling techniques. This work focuses on optimizing the electromagnetic and mechanical design of high-temperature superconducting (HTS) dipoles with a large rectangular aperture for the accelerator ring, capable of generating a bore field of 10 T, using finite element methods. Key objectives include achieving precise magnetic field uniformity, conducting an initial assessment of the mechanical behavior of the HTS coils and a preliminary study of hysteretic losses. This research aligns with the ESPP's emphasis on technological advancements, particularly in high-field superconducting magnets, which are essential components for future circular colliders.
The Muon Cooling Complex is a key component of the future high-energy Muon Collider, utilizing ionization cooling to significantly reduce muon beam emittance. This process relies on RF-accelerating cavities operating within a multi-Tesla magnetic field, which necessitates the use of beryllium (Be) windows to ensure beam transmission while minimizing particle scattering.
Thermo-mechanical analyses indicate that the Be window is subject to significant temperature increases and mechanical stresses due to RF-induced heating and Lorentz forces. These effects lead to displacements that can cause frequency shifts beyond the cavity bandwidth, potentially compromising performance.
To address these challenges, the authors investigate the thermo-mechanical behaviour of the Be window to optimize its design. In particular, the impact of curvature and thickness variations is analysed to minimize temperature gradients, maintain structural integrity, and reduce deformations. By exploring different geometrical configurations, the study aims to enhance the mechanical stability of the window while preserving RF performance.
The results provide valuable insights for optimizing the design of Be windows in ionization cooling cavities, contributing to the overall feasibility and efficiency of the Muon Collider.
Intrabeam scattering (IBS) has widely been studied in the field of accelerator physics. It impacts the entire performance of storage and damping rings, as it causes emittance growth. Its effect on one-pass linear accelerators was not expected to be as large. However, recent studies have suggested that IBS can become critical in these machines, as it highly enlarges their energy spread, especially for low energy and dense beams. This work presents its implementation and benchmark on the CERN developed tracking-code, RF-Track, and predicts its effect on the final cooling stage of the Future Muon Collider.
The MAIA concept is a detector designed for a future Muon Collider operating at √s=10 TeV. The unique challenges of particle detection and reconstruction at a Muon Collider include mitigation of the beam-induced-background (BIB), requiring dedicated hardware and software solutions. Designing optimal detection and reconstruction software necessitates a detailed study of the effect of the BIB on various components of the detector, including the ECAL (electromagnetic calorimeter). A well-calibrated and well-resolved ECAL is especially crucial to reconstructing both electrons and photons, in addition to a broad range of final states with significant electromagnetic activity. This poster will detail the ability of the current MAIA detector software to reconstruct simulated photons, with a focus on efficiency and energy resolution. We will present results for simulated samples both with and without simulated BIB overlaid.
This study aims to determine the preliminary design parameters for developing a liquid lead target subjected to high peaks of deposited thermal power (10¹⁷ W/m³) and deposition pulses on the order of nanoseconds. Under such conditions, previous studies and experiments have shown the formation of shock waves and splashing into the liquid lead target. The study utilizes the Mie-Gruneisen and Tait equations of state starting from the distribution of thethermal source on the target. CFD (Computational Fluid Dynamics) simulations are developed employing the VOF (Volume of Fluid) model. The simulations include a cavitation model for lead in low-pressure regions. A possible target configuration is also presented to mitigate the impact of shock waves on the structures. The results represent an initial steptoward developing more robust and efficient liquid metal targets. Further analyses will becarried out to refine the physical model of lead cavitation and to integrate it more accurately with the other physical phenomena involved.
Unlike their low temperature counterparts, high temperature superconductors (HTS) can retain excellent RF perfomance in the demanding conditions of some emerging high-energy physics technologies, which require high quality factors at frequencies in the GHz range under strong magnetic fields (16-20 T). In particular, we have demonstrated that REBa2Cu3O7-x (RE = Y, Gd, Eu) (REBCO) offers outstanding, better than-Cu RF response in such conditions [1,2]. If in addition, HTS materials would sustain very high accelerating gradients (100-150 MV/m) keeping low RF properties, they could represent a promising solution accelerating cavities like those of the cooling stage of the muon collider. Unfortunately, up to now the usage of REBCO in RF applications is hindered by its complicated material growth, which makes it virtually impossible for it to be grown directly on the geometrically complex surfaces required for many applications.
To achieve a low surface impedance REBCO coating in RF cavities, we have developed a coating methodology based on soldering and delaminating coated conductors (CC). Up to now, our coating methodology was employed for the fabrication of axion dark matter detection haloscopes [3,4], a superconductor pulse compressor and prototypes for the Future Circular Collider (FCC-hh) beam screen [5]. Our findings place REBCO CC-based coatings as a solid candidate to replace Cu as the low surface-impedance coating in many high-energy physics applications.
In this work, we have investigated the RF response of REBCO coatings up to 10 MV/cm at cryogenic temperatures and zero magnetic field and we are proceeding towards 100 MV/m experiments and later to superimpose a high magnetic field. All these experiments should generate data regarding the opportunities of HTS CC to replace Cu also in some cooling cavities of the Muon Collider feasibility study.
We acknwoledge the iFAST project, the RADES collaboration and the FCC feasibility study.
References:
[1] T. Puig et al 2019 Supercond. Sci. Technol. 32 094006, doi: 10.1088/1361-6668/ab2e66.
[2] A. Romanov et al. Sci Rep 10, 12325 (2020), doi: 10.1038/s41598-020-69004-z.
[3] J. Golm et al, IEEE TAS, vol. 32, no. 4, pp. 1-5, Art no. 1500605, doi: 10.1109/TASC.2022.3147741.
[4] S. Ahyoune et al, 2024. https://arxiv.org/abs/2403.07790
[5] G. T. Telles et al, 2023 Supercond. Sci. Technol. 36 045001, doi: 10.1088/1361-6668/ac97c9.
Muon collider (MuC) is a promising, yet challenging, pathway to achieve a 10TeV collider at the energy frontier. The current MuC design requires ionization cooling to shrink the beam emittance and accomplish the target luminosity. One key component in the ionization cooling channel is the NCRF cavity which replenishes the longitudinal energy and provides the longitudinal focusing. Overcoming the limit on the cavity gradient imposed by the surrounding strong magnetic field is critical for the performance of the MuC. One unique feature of this cavity is the thin beam window covering the cavity aperture. The beam window increases the cavity shunt impedance and reduces RF breakdown probability. In this poster, we will present recent study progress on two effects of the beam window, the emittance growth due to the scattering and the wakefield enhanced by the closed aperture.
To study the muon scattering in the beam window and the resulting emittance dilution, we use GEANT4 simulation with analytical benchmarking. We simulate the window at different stages in the rectilinear cooling lattice, and it is shown that the scattering effect is negligible at the early stages and becomes significant in the later stages of the post-merging section. The comparison between two window materials, Be and Al, indicates the Al window needs to be at about a quarter of the thickness of the Be window to have the same amount of emittance dilution.
We also show that with the beam aperture completely covered by the window, the CST wakefield solver is no longer suitable for this calculation. Instead, we deploy the CST PIC solver to calculate the EM field generated by the muon beam passing through the cavity and use post-processing methods to resolve the wake potential with a Python wrapper script. The wakefields due to the cavity geometry and the beam space charge are separately characterized.
The tau lepton plays a crucial role in studying the Standard Model, providing access to the Higgs and leptonic sectors of physics. Unlike other proposed future collider experiments, a muon collider has the potential to reach high center of mass energies with colliding leptons, which are fundamental particles, ensuring that the totality of the beam energy is available for the production of new particles, such as taus. However, the inherent instability of muons poses significant challenges in detector design and particle reconstruction for this machine. Muon decays generate substantial beam-induced background (BIB), dominated by soft secondary particles which can obscure collision products in the detector volume. Regardless of the environment, tau reconstruction is already challenging to perform due to the fact that the taus decay before reaching the detector region and must be reconstructed through their decay products, approximately 65% of which are hadronic. Tau reconstruction has been investigated for a 3 TeV muon collider, but no dedicated study exists for a 10 TeV machine. In this study, we assess the performance of the $\texttt{TauFinder}$ reconstruction algorithm in the MAIA (Muon Accelerator Instrumented Apparatus) detector geometry, intended for $\sqrt{s} = 10$ TeV $\mu^+\mu^-$ collisions. We evaluate the reconstruction efficiency of one-prong and three-prong hadronically decaying taus. Our results provide a benchmark performance of tau reconstruction in a 10 TeV muon collider, demonstrating the physics potential of this machine.
Accurately modeling the transient behavior of non-insulated (NI) ReBCO superconducting coils is crucial for fully assessing their potential for high-field magnet applications. 3D Finite Element (FE) models are among the most promising approaches for capturing the thermal-electrodynamics of these coils. However, most popular mathematical formulations of Maxwell’s equations for superconductors, such as the well-known H-φ formulation, are currently too computationally expensive to simulate large-scale systems like accelerator magnets.
To address this challenge, we present a novel mathematical formulation that couples a 3D FE magnetic module with a 1D FE + 2D Finite Difference (FD) electric module, implemented in COMSOL Multiphysics. The formulation has been used to develop a model that simulates the electrodynamics of large ReBCO NI pancake coils. Although still under development, the model has been validated against other models across various test cases, and preliminary results demonstrate its ability to efficiently capture critical phenomena such as persistent current effects while significantly reducing the computational time required for large-scale 3D FE transient simulations.
The formulation has then been applied to simulate the energization of the Muon Collider 40 T Solenoid, offering valuable insights into: (1) the relationship between energization time and turn-to-turn contact resistance, and (2) the impact of magnetization on the Lorentz forces acting on the conductor. These results highlight the potential of this 3D magnetic and electric coupling approach to advance the understanding of NI superconducting coils.
The incorporation of thermal behaviour into this model is currently underway to investigate quench phenomena and evaluate advanced protection strategies.
Ongoing conceptual studies for a 10TeV muon collider
identified rapid cycling synchrotrons as major engineering
challenge. Due to the muon’s short lifetime of only 2.2µs
at rest, normal-conducting bending magnets with field rise
rates of well beyond 1kT/s are indispensable to support ac-
cordingly fast acceleration cycles. Energies of 100MJ will be
interchanged between magnets and capacitor banks within
few milliseconds. Accurate models of the magnets are thus
required to optimize the overall system performance. The
non-uniform temperature distribution in the magnet strongly
affects material properties like the electrical conductivity
of copper and must therefore be considered in the electro-
magnetic field problem. This contribution presents recent
advancements in addressing this multi-physical problem by
using problem-specific finite-element tools allowing to de-
scribe the inherently transient behavior. The ferromagnetic
yoke is accurately resolved by using a novel combination
of a Bergqvist hysteresis and a homogenized eddy current
model. Finally, different magnet design concepts are com-
pared in terms of material costs, magnetic energy, losses,
field quality and temperature buildup.
I will show a current design of a green field proton driver. It uses a flexible momentum compaction factor lattice. The momentum compaction is optimised in accumulator and compressor rings separately. Space charge effects during the bunch rotation will be estimated in the longitudinal and transverse directions. Possible beam experiments to demonstrate a bunch rotation with the high intensity effects are proposed.
A principal challenge associated with the realisation of the muon collider is the rapid acceleration of muons from injection to top energy within their lifetime. Rapid-cycling synchrotron (RCS) designs proposed thus far suffer limitations based on magnet ramp rates, power efficiency and power supply, and path length/time of flight differences (for the hybrid RCS proposals).
As an alternative, we outline acceleration schemes based on the Vertical-Excursion Fixed-Field Accelerator (vFFA) concept, wherein muons can be accelerated over equivalent energy ranges to RCS designs using exclusively time-independent superconducting magnets – whilst maintaining constant tunes and a zero path length difference. Stable vFFA lattices with comparable footprints to RCS1 and RCS4 are proposed, revealing the possibility for an energy-efficient machine without limits on acceleration rate imposed by magnet and power supply constraints. Moreover, the quasi-isochronous operation of the vFFA enables the possible use of on-crest acceleration, enabling a more efficient use of the available RF power and potentially eliminating the need to tune RF cavities over the acceleration cycle.
However, vFFAs suffer from complications associated with intrinsically coupled transverse optics. This poster additionally details methods whereby the coupled optics can be circumvented in straight sections to allow the construction of dispersion suppressors, as well as simplified injection and extraction systems. Ultimately, a vFFA ring with a number of ‘decoupled straights’ containing injection and extraction systems, as well as dispersion-suppressed high-gradient RF insertions, presents a viable and competitive alternative to RCS designs for muon acceleration – though further numerical simulation of transverse optics and longitudinal stability must now be conducted.
It's 65 km.
Find out why :)
https://indico.cern.ch/event/1547636/
Steering Board, IMCC Collaboration Board, Governing Board