Consolidated Parameters

MuCol Consortium, 2024 Grant Agreement 101094300 PUBLIC 1 / 2 Grant Agreement No: 101094300 MuCoL A Design Study for a Muon Collider complex at 10 TeV centre of mass Horizon Europe Framework Programme MILESTONE REPORT CONSOLIDATED PARAMETERS MILESTONE NO 7 Document identifier: MuCol_Mil_7_WP1_v1-0.pdf DOI: 10.5281/zenodo.17476875 Due date of milestone: 31/10/2025 (End of Month 32) Justification for delay: New deadline approved by EU Project Officer Work package: WP1 – Coordination and Communication Lead beneficiary: CERN Report release date: 30/10/2025 Document version: 1.0 Document status: Final Abstract: This document is comprised of a collection of consolidated parameters for the key parts of the muon collider. These consolidated parameters follow on from the October 2024 Preliminary Parameters Report. Attention has been given to a high-level consistent set of baseline parameters throughout all systems of the complex, following a 10 TeV center-of-mass design. Additional details of the designs contributing to this baseline design are featured in the appendix. Likewise, explorative variations from this baseline set can be found in the appendix. The data is collected from a collaborative spreadsheet and transferred to overleaf. Grant Agreement 101094300 PUBLIC 2 / 2 MuCol Consortium, 2025 For more information on MuCol, its partners and contributors please see https://mucol.web.cern.ch/ Funded by the European Union (EU). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the EU or European Research Executive Agency (REA). Neither the EU nor the REA can be held responsible for them. Delivery Slip Name Partner Date Authored by IMCC & MuCol Authors All 21/10/2025 Edited by R. Taylor CERN 21/10/2025 Reviewed by D. Schulte [Project Leader] C. Rogers [Deputy Project Leader] V. Shiltsev [USMCC Reviewer] CERN UKRI Fermilab 27/10/2025 Approved by MuCol Management Committee 30/10/2025 Consolidated Parameters Report – October 29, 2025 IMCC authors Carlotta Accettura1, Simon Adrian2, Rohit Agarwal3, Claudia Ahdida1, Chiara Aime’4,5, Avni Aksoy6,1, Gian Luigi Alberghi7, Simon Albright1, Siobhan Alden8, Luca Alfonso9, Muhammad Ali10,11, Anna Rita Altamura12,13, Nicola Amapane13,12, Kathleen Amm14, David Amorim15,1, Paolo Andreetto16, Fabio Anulli17, Ludovica Aperio Bella18, Rob Appleby19, Artur Apresyan20, Pouya Asadi21, Mohammed Attia Mahmoud22, Bernhard Auchmann23,1, John Back24, Anthony Badea25, Kyu Jung Bae26, E.J. Bahng27, Lorenzo Balconi28,29, Fabrice Balli30, Laura Bandiera31, Carmelo Barbagallo1, Daniele Barducci32,5, Roger Barlow33, Camilla Bartoli34, Nazar Bartosik12, Emanuela Barzi20, Fabian Batsch1, Matteo Bauce17, Michael Begel35, J. Scott Berg35, Andrea Bersani9, Alessandro Bertarelli1, Francesco Bertinelli1, Alessandro Bertolin16, Pushpalatha Bhat20, Clarissa Bianchi34, Michele Bianco1, William Bishop24,36, Kevin Black37, Fulvio Boattini1, Alex Bogacz38, Maurizio Bonesini39, Bernardo Bordini1, Patricia Borges de Sousa1, Salvatore Bottaro40, Luca Bottura1, Steven Boyd24, Johannes Braathen18, Marco Breschi34,7, Francesco Broggi29, Matteo Brunoldi41,4, Xavier Buffat1, Laura Buonincontri11,16, Marco Buonsante42,10, Philip Nicholas Burrows43, Graeme Campbell Burt44,45, Dario Buttazzo5, Barbara Caiffi9, Ilkay Turk Cakir6, Orhan Cakir6, Rama Calaga1, Sergio Calatroni1, Marco Calviani1, Simone Calzaferri41, Daniele Calzolari1,16, Kyle Capobianco-Hogan146, Vieri Candelise46,46, Silvio Candido1, Ali Can Canbay6, Claudio Cantone47, Rodolfo Capdevilla20, Christian Carli1, Carlo Carrelli48, Fausto Casaburo49,17, Massimo Casarsa46, Luca Castelli49,17, Maria Gabriella Catanesi10, Lorenzo Cavallucci34,7, Gianluca Cavoto49,17, Francesco Giovanni Celiberto50, Luigi Celona51, Alessia Cemmi48, Sergio Ceravolo47, Alessandro Cerri52,53,5, Francesco Cerutti1, Gianmario Cesarini47, Cari Cesarotti54, Antoine Chancé30, Nikolaos Charitonidis1, mauro chiesa4, Paolo Chiggiato1, Vittoria Ludovica Ciccarella47,49, Pietro Cioli Puviani55, Anna Colaleo42,10, Francesco Colao48, Francesco Collamati17, Marco Costa56, Nathaniel Craig57, David Curtin58, Laura D’Angelo59, Giacomo Da Molin60, Heiko Damerau1, Sridhara Dasu37, Jorge de Blas61, Stefania De Curtis62, Herbert De Gersem59, Andre de Gouvea63, Tommaso Del Moro49,48, JeanPierre Delahaye1, Dmitri Denisov35, Haluk Denizli64, Radovan Dermisek65, Paula Desiré Valdor1, Charlotte Desponds1, Luca Di Luzio16, Elisa Di Meco47, Karri Folan Di Petrillo25, Ilaria Di Sarcina48, Eleonora Diociaiuti47, Tommaso Dorigo16,66, Karlis Dreimanis67, Tristan du Pree68,69, Hatice Duran Yildiz6, Juhi Dutta70, Thomas Edgecock33, Mamad Eshraqi71,72, Siara Fabbri1, Marco Fabbrichesi46, Stefania Farinon9, Davide Fazioli1, Javier Fernandez Roncal1, Guillaume Ferrand30, Samuel Ferraro73, Jose Antonio Ferreira Somoza1, Marco Ferrero12, Max Fieg74, Frank Filthaut75,68, Patrick Fox20, Roberto Franceschini76,77, Rui Franqueira Ximenes1, Frank Gaede18, Simone Galletto12,13, Michele Gallinaro60, Maurice Garcia-Sciveres3, Luis Garcia-Tabares78, Rocky Bala Garg79, Ruben Gargiulo49, Cedric Garion1, Maria Vittoria Garzelli80, Marco Gast81, Lisa Generoso42,10, Cecilia E. Gerber82, Luca Giambastiani11,16, Alessio Gianelle16, Eliana Gianfelice-Wendt20, Stephen Gibson8, Simone Gilardoni1, Dario Augusto Giove29, Valentina Giovinco1, Carlo Giraldin16,11, Alfredo Glioti17, Arkadiusz Gorzawski71,1, Mario Greco77, Christophe Grojean18, Alexej Grudiev1, Edda Gschwendtner1, Emanuele Gueli17,17, Nicolas Guilhaudin1, Tao Han83, Chengcheng Han84, John Michael Hauptman27, Matthew Herndon37, Adrian D Hillier36, Micah Hillman85, Gabriela Hoff86, Tova Ray Holmes85, Samuel Homiller87, Walter Hopkins88, Lennart Huth18, Sudip Jana89, Laura Jeanty21, Sergo Jindariani20, Sofia Johannesson71, Benjamin Johnson85, Owain Rhodri Jones1, Paul-Bogdan Jurj90, Yonatan Kahn20, Rohan Kamath90, Anna Kario69, Ivan Karpov1, David Kelliher36, Wolfgang Kilian91, Ryuichiro Kitano92, Felix Kling18, Antti Kolehmainen1, K.C. Kong93, iii Jaap Kosse23, Jakub Kremer18, Georgios Krintiras93, Karol Krizka94, Nilanjana Kumar95, Erik Kvikne1, Robert Kyle96, Stephan Lachnit18, Emanuele Laface71, Elleanor Lamb1, Kenneth Lane97, Andrea Latina1, Anton Lechner1, Lawrence Lee85, Junghyun Lee26, Seh Wook Lee26, Thibaut Lefevre1, Emanuele Leonardi17, Giuseppe Lerner1, Gabriele Levati98, Filippo Levi9, Peiran Li99, Qiang Li100, Tong Li101, Wei Li102, Roberto Li Voti49,47, Giulia Liberalato46, Mats Lindroos†,71, Ronald Lipton20, Da Liu83, Zhen Liu99, Miaoyuan Liu103, Alessandra Lombardi1, Shivani Lomte37, Kenneth Long90,36, Luigi Longo10, José Lorenzo104, Roberto Losito1, Ian Low63,88, Xianguo Lu24, Donatella Lucchesi11,16, Tianhuan Luo3, Anna Lupato11,16, Yang Ma105, Shinji Machida36, Edward MacTavish1, Thomas Madlener18, Lorenzo Magaletti106,10,106, Marcello Maggi10, Tommaso Maiello9, Helene Mainaud Durand1, Abhishikth Mallampalli37, Fabio Maltoni105,34,7, Jerzy Mikolaj Manczak1, Marco Mandurrino12, Claude Marchand30, Francesco Mariani29,49, Stefano Marin1, Samuele Mariotto28,29, Simon Marsh1, Stewart Martin-Haugh36, David Marzocca46, Maria Rosaria Masullo107, Giorgio Sebastiano Mauro51, Anna Mazzacane20, Andrea Mazzolari31,108, Patrick Meade109, Barbara Mele17, Federico Meloni18, Xiangwei Meng110, Matthias Mentink1, Rebecca Miceli34, Natalia Milas71, Abdollah Mohammadi37, Dominik Moll59, Francesco Montagno Bozzone111,112, Alessandro Montella113, Manuel Morales-Alvarado46, Mauro Morandin16, Marco Morrone1, Tim Mulder1, Riccardo Musenich9, Toni Mäkelä74, Elias Métral1, Krzysztof M˛ekała114,18, Emilio Nanni79,115, Marco Nardecchia49,17, Federico Nardi11, Felice Nenna11,10, David Neuffer20, David Newbold36, Daniel Novelli9,49, Maja Olvegård116, Yasar Onel117, Domizia Orestano76,77, Inaki Ortega Ruiz1, John Osborne1, Simon Otten69, Yohan Mauricio Oviedo Torres86, Daniele Paesani47,1, Simone Pagan Griso3, Davide Pagani7, Kincso Pal1, Mark Palmer35, Leonardo Palombini16, Alessandra Pampaloni9, Paolo Panci5,32, Priscilla Pani18, Yannis Papaphilippou1, Rocco Paparella29, Paride Paradisi11,16, Antonio Passeri77, Jaroslaw Pasternak90,36, Nadia Pastrone12, Kevin Pedro20, Antonello Pellecchia10, Fulvio Piccinini4, Henryk Piekarz20, Tatiana Pieloni15, Juliette Plouin30, Alfredo Portone104, Karolos Potamianos24, Joséphine Potdevin15,1, Soren Prestemon3, Teresa Puig118, Ji Qiang3, Lionel Quettier30, Tanjona Radonirina Rabemananjara119,68, Emilio Radicioni10, Raffaella Radogna10,42, Ilaria Carmela Rago17, Angira Rastogi3, Andris Ratkus67, Elodie Resseguie3, Juergen Reuter18, Pier Luigi Ribani34, Cristina Riccardi41,4, Stefania Ricciardi36, Caroline Riggall85, Tania Robens120, Youri Robert1, Chris Rogers36, Juan Rojo68,119, Marco Romagnoni108,31, Kevin Ronald96,45, Benjamin Rosser25, Carlo Rossi1, Lucio Rossi28,29, Leo Rozanov25, Maximilian Ruhdorfer79, Richard Ruiz121, Farinaldo S. Queiroz86,122, Saurabh Saini52,1, Filippo Sala34,7, Claudia Salierno34, Tiina Salmi123, Paola Salvini4,41, Ennio Salvioni52, Nicholas Sammut124, Carlo Santini29, Alessandro Saputi31, Ivano Sarra47, Giuseppe Scarantino29,49, Hans Schneider-Muntau125, Daniel Schulte1, Jessica Scifo48, Sally Seidel126, Claudia Seitz18, Tanaji Sen20, Carmine Senatore127, Abdulkadir Senol64, Daniele Sertore29, Lorenzo Sestini62, Vladimir Shiltsev128, Ricardo César Silva Rêgo86,122, Federica Maria Simone106,10, Kyriacos Skoufaris1, Elise Sledge129, Valentina Sola12,13, Gino Sorbello130,51, Massimo Sorbi28,29, Stefano Sorti28,29, Lisa Soubirou30, Simon Spannagel18, David Spataro18, Anna Stamerra42,10, Marcel Stanitzki18, Steinar Stapnes1, Giordon Stark131, Marco Statera29, Bernd Stechauner132,1, Shufang Su133, Wei Su84, Ben Suitters36, Xiaohu Sun100, Alexei Sytov31, Yoxara Sánchez Villamizar86,135, Jingyu Tang136,110, Jian Tang84, Rebecca Taylor1, Herman Ten Kate69,1, Pietro Testoni104, Leonard Sebastian Thiele2,1, Rogelio Tomas Garcia1, Max Topp-Mugglestone1, Toms Torims67,1, Riccardo Torre9, Luca Tortora77,76, Ludovico Tortora77, Luca Tricarico34,48, Sokratis Trifinopoulos54, Donato Troiano42,10, Alexander Naip Tuna137, Sosoho-Abasi Udongwo2,1, Ilaria Vai41,4, Riccardo Umberto Valente29, Giorgio Vallone3, Ursula van Rienen2, Rob Van Weelderen1, Marion Vanwelde1, Gueorgui Velev20, Rosamaria Venditti42,10, Adam Vendrasco85, Adriano Verna48, Gianluca Vernassa1,138, Arjan Verweij1, Piet Verwilligen10, Ludovico Vittorio135, Paolo Vitulo41,4, iv Consolidated Parameters Report – October 29, 2025 Isabella Vojskovic71, Biao Wang117, Dayong Wang100, Lian-Tao Wang25, Xing Wang76,77, Manfred Wendt1, Robert Stephen White12, Markus Widorski1, Mariusz Wozniak1, Juliet Wright21, Yongcheng Wu139, Andrea Wulzer140,112, Keping Xie83, Yifeng Yang141, Yee Chinn Yap18, Katsuya Yonehara20, Hwi Dong Yoo142, Zhengyun You84, Zaib Un Nisa44,1, Marco Zanetti11, Angela Zaza42,10, Jinlong Zhang88, Liang Zhang96, Ruihu Zhu142,143, Alexander Zlobin20, Davide Zuliani11,16, José Francisco Zurita145 1CH - CERN, 2DE - UROS, University of Rostock, 3US - LBL, Lawrence Berkely National Laboratory, 4IT - INFN - Pavia, Istituto Nazionale di Fisica Nucleare Sezione di Pavia, 5IT - INFN - Pisa, Instituto Nazionale Di Fisica Nucleare - Sezione di Pisa, 6TR - AU, Ankara University, 7IT - INFN - Bologna, Instituto Nazionale Di Fisica Nucleare - Sezione di Bologna, 8UK - RHUL, Royal Holloway and Bedford New College, 9IT - INFN - Genova, Istituto Nazionale di Fisica Nucleare Sezione di Genova, 10 IT - INFN - Bari, Instituto Nazionale Di Fisica Nucleare - Sezione di Bari, 11 IT - UNIPD, Università degli Studi di Padova , 12 IT - INFN - Torino, Istituto Nazionale di Fisica Nucleare Sezione di Torino, 13 IT - UNITO, Università di Torino, 14 US - FSU, Florida State University, 15 CH - EPFL, École Polytechnique Fédérale de Lausanne, 16 IT - INFN - Padova, Istituto Nazionale di Fisica Nucleare Sezione di Padova, 17 IT - INFN - Roma, Istituto Nazionale di Fisica Nucleare Sezione di Roma, 18 DE - DESY, Deutsches Elektronen Synchrotron, 19 UK - UOM, University of Manchester, 20 US - FNAL, Fermi National Accelerator Laboratory - Fermilab, 21 US - UO, University of Oregon, 22 EG - CHEP-FU, Center of High Energy Physics, Fayoum University, 23 CH - PSI, Paul Scherrer Institute, 24 UK - UWAR, The University of Warwick, 25 US - UChicago, University of Chicago, 26 KR - KNU, Kyungpook National University, 27 US - ISU, Iowa State University, 28 IT - UMIL, Università degli Studi di Milano, 29 IT - INFN - Milano, Istituto Nazionale di Fisica Nucleare Sezione di Milano, 30 FR - CEA, Commissariat à l’Energie Atomique, 31 IT - INFN - Ferrara, Istituto Nazionale di Fisica Nucleare Sezione di Ferrara, 32 IT - UNIPI DF, Univesità di Pisa, Dipartimento di Fisica , 33 UK - HUD, University of Huddersfield, 34 IT - UNIBO, Università degli Studi di Bologna , 35 US - BNL, Brookhaven National Laboratory, 36 UK - RAL, Rutherford Appleton Laboratory, 37 US - University of Wisconsin-Madison, 38 US - JLAB, Jefferson Laboratory, 39 IT - INFN - Milano Bicocca, Istituto Nazionale di Fisica Nucleare Sezione di Milano Bicocca, 40 IL - TAU, Tel Aviv University, 41 IT - UNIPV, Università degli Studi di Pavia , 42 IT - UNIBA, University of Bari, 43 UK - UOXF, University of Oxford, 44 UK - ULAN, University of Lancaster, 45 UK - CI, The Cockcroft Institute, v 46 IT - INFN - Trieste, Istituto Nazionale di Fisica Nucleare Sezione di Trieste, 47 IT - INFN - Frascati, Istituto Nazionale di Fisica Nucleare - Laboratori Nazionali di Frascati, 48 IT - ENEA, Agenzia Nazionale per le nuove tecnologie, l’energia e lo sviluppo economico sostenibile, 49 IT - Sapienza, Università degli Studi di Roma “La Sapienza”, 50 ES - UAH, Universidad de Alcalá, 51 IT - INFN - LNS, Istituto Nazionale di Fisica Nucleare - Laboratori Nazionali del Sud, 52 UK - UOS, The University of Sussex, 53 IT - UNISI, Università degli Studi di Siena, 54 US - MIT, Massachusetts Institute of Technology, 55 IT - POLITO, Politecnico di Torino, 56 CA - PITI, Perimeter Institute for Theoretical Physics, 57 US - UC Santa Barbara, University of California, Santa Barbara, 58 CA - U of T, University of Toronto, 59 DE - TUDa, Technische Universität Darmstadt, 60 PT - LIP, Laboratorio de instrumentacao e Fisica Experimental De Particulas, 61 ES - UGR, Universidad de Granada, 62 IT - INFN - Firenze - Istituto Nazionale di Fisica Nucleare - Sezione di Firenze, 63 US - Northwestern, Department of Physics and Astronomy, Northwestern University, 64 TR - IBU, Bolu Abant Izzet Baysal University, 65 US - IU Bloomington, Indiana University Bloomington, 66 SE - LTU, Luleå University of Technology, 67 LV - RTU, Riga Technical University, 68 NL - Nikhef, Dutch National Institute for Subatomic Physics, 69 NL - UTWENTE, University of Twente, 70 IN - The Institute of Mathematical Sciences, Chennai, 71 SE - ESS, European Spallation Source ERIC, 72 SE - LU, Lund University, 73 US - BROWN University, 74 US - UC Irvine, University of California, Irvine, 75 NL - RU, Radboud University, 76 IT - UNIROMA3, Università degli Studi Roma Tre, 77 IT - INFN - Roma 3, Istituto Nazionale di Fisica Nucleare Sezione di Roma Tre, 78 ES - CIEMAT, Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas, 79 US - Stanford University, CA, 80 DE - Uni Hamburg, Universität Hamburg, 81 DE - KIT, Karlsruher Institut Fur Technologie, 82 US - UIC Physics, Department of Physics, University of Illinois Chicago, 83 US - Pitt PACC, Pittsburgh Particle Physics, Astrophysics and Cosmology Center, 84 CN - SYSU, Sun Yat-Sen University, 85 US - UT Knoxville, University of Tennessee, Knoxville, 86 BR - UFRN - IIP, Universidade Federal do Rio Grande do Norte - International Institute of Physics, 87 US - Cornell University, 88 US - HEP ANL, High Energy Physics Division, Argonne National Laboratory, 89 DE - MPIK, Max-Planck-Institut für Kernphysik, 90 UK - Imperial College London, 91 DE - Uni Siegen, Universität Siegen, 92 JP - Yukawa Institute for Theoretical Physics, Kyoto University, 93 US - KU, University of Kansas, 94 UK - University of Birmingham, 95 IN - SGT U, Shree Guru Gobind Singh Tricentenary University, 96 UK - STRATH, University of Strathclyde, 97 US - BU, Boston University, vi Consolidated Parameters Report – October 29, 2025 98 CH - ITP Center, University of Bern , 99 US - UMN, University of Minnesota, 100 CN - PKU, Peking University, 101 CN - NKU, Nankai University, 102 US - Rice University, 103 US - Purdue University, 104 ES - F4E, Fusion For Energy, 105 BE - UCLouvain, Université Catholique de Louvain, 106 IT - POLIBA, Politecnico di Bari, 107 IT - INFN - Napoli, Istituto Nazionale di Fisica Nucleare Sezione di Napoli, 108 IT - UNIFE FST, Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, 109 US - YITP Stony Brook, Yang Institute for Theoretical Physics, Stony Brook University, 110 CN - IHEP, Institute of High Energy Physics, 111 ES - UAB, niversitat Autònoma de Barcelona, 112 ES - IFAE, Institut de Física d’Altes Energies, 113 SE - SU, Stockholm University, 114 PL - UW, University of Warsaw, 115 US - SLAC National Accelerator Laboratory , 116 SE - UU, Uppsala University, 117 US - UI, University of Iowa, 118 ES - ICMAB-CSIC, Institut de Ciencia de Materials de Barcelona, CSIC, 119 NL - VU, Vrije Universiteit, 120 HR - IRB, Institut Ru ¯ der Boškovi´c, 121 PL - IFJ PAN, Institute of Nuclear Physics Polish Academy of Sciences, 122 BR - UFRN, Universidade Federal do Rio Grande do Norte, 123 FI - TAU, Tampere University, 124 MT - UM, University of Malta, 125 FR - CS&T, Consultations Scientifiques et Techniques, La Seyne sur Mer, 126 US - UNM, University of New Mexico, 127 CH - UNIGE, Université de Genève, 128 US - NIU, Northern Illinois University, IL, 129 US - Caltech, California Institute of Technology , 130 IT - UNICT, Università di Catania, 131 US - SCIPP UCSC, Santa Cruz Institute for Particle Physics, University of California Santa Cruz, 132 AT - TUW, Technische Universität Wien, 133 US - UA, The University of Arizona, 134 FR - CNRS, Centre National de la Recherche Scientifique, 135 CN - USTC, University of Science and Technology of China, 136 US - UC San Diego, University of California, San Diego, 137 FR - Ecole des Mines de Saint-Etienne, 138 CN - NNU, Nanjing Normal University, 139 ES - ICREA, Institució Catalana de Recerca i Estudis Avançats, 140 UK - SOTON, University of Southampton, 141 KR - Yonsei University, 142 CN - Institute of Modern Physics, Chinese Academy of Sciences, 143 CN - UCAS, University of Chinese Academy of Sciences, 144 ES - IFIC, Instituto de Física Corpuscular 145 US - CASE Stony Brook, Center for Accelerator Science and Education, Stony Brook University, †deceased vii Contents 1 Introduction .......................................... 1 2 ProtonDriver ......................................... 4 3 Target&Front-End ...................................... 4 4 Cooling ............................................ 5 5 Acceleration.......................................... 6 6 Collider ............................................ 8 7 Detectors............................................ 9 8 Machine-DetectorInterface .................................. 13 9 Magnets ............................................ 13 10 RFCavities .......................................... 14 11 Impedance........................................... 14 12 RadiationShielding ...................................... 16 13 RadiationProtection...................................... 19 14 Demonstrators......................................... 22 A Appendix: Top-Level Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 B Appendix:ProtonDriver ................................... 30 C Appendix:Target&Front-End ................................ 33 D Appendix:Cooling ...................................... 37 E Appendix: Low Energy Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 F Appendix: High Energy Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 G Appendix: Machine-Detector Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 H Appendix:Magnets ...................................... 56 I Appendix: Radiofrequency Cavities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 J Appendix:PowerConverters ................................. 66 K Appendix:Impedance..................................... 71 L Appendix:Demonstrators................................... 73 M Appendix: CERN Civil Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 viii Consolidated Parameters Report – October 29, 2025 Tables 1.1 Consolidated target parameters for a muon collider at 10 TeV. .............. 2 1.2 Target Lengths, energies and transmission of each subsystem . . . . . . . . . . . . . . . 3 1.3 Estimated emittance and transmission of each subsystem . . . . . . . . . . . . . . . . . 3 2.1 H-LINACparameters.................................... 4 2.2 Baseline Accumulator and Compressor parameters . . . . . . . . . . . . . . . . . . . . 4 3.1 Assumed beam from proton driver via carbon target used in studies . . . . . . . . . . . . 5 3.2 Yield per unit energy proton beam [10−2GeV /p+].................... 5 4.1 Beam parameters of the cooling system for shortand long-rectilinear options. . . . . . . 6 5.1 RCS acceleration chain key parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 5.2 RCS acceleration chain lattice parameters . . . . . . . . . . . . . . . . . . . . . . . . . 8 6.1 Assumptions for the main parameters used in the design of a 10 TeV muon collider. . . . 9 6.2 Collider arcs, coil inner aperture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 7.1 Detector baseline and aspirational targets . . . . . . . . . . . . . . . . . . . . . . . . . 10 7.2 Detectorparameters..................................... 11 7.3 Assumed spatial and time resolution for MAIA and MUSIC tracking detector sub-systems 12 7.4 MAIAcalorimetersystems................................. 12 7.5 MUSICcalorimetersystems ................................ 12 8.1 Ionizing dose and neutron-equivalent fluence in MUSIC and MAIA detectors . . . . . . 13 8.2 Number of secondary particles entering the detector volume . . . . . . . . . . . . . . . 13 9.1 Summary of main magnet development targets . . . . . . . . . . . . . . . . . . . . . . . 14 10.1 RF frequencies and gradients to be used in the beam dynamics studies. . . . . . . . . . . 14 11.1 RCS normal conducting magnets vacuum chamber used in simulations . . . . . . . . . . 15 11.2 RCS Collective Effects Parameters used in simulations. . . . . . . . . . . . . . . . . . . 15 11.3 10 TeV collider parameters for impedance model simulations. . . . . . . . . . . . . . . 16 12.1 Radiation load on target solenoids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 12.2 Parameters for collider radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 12.3 Power load and radiation damage in collider . . . . . . . . . . . . . . . . . . . . . . . . 18 12.4 Final focusing magnets and dose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 13.1 Neutrino radiation at distances from muon decay (1.5 TeV beam) . . . . . . . . . . . . . 19 13.2 Neutrino radiation at distances from muon decay (5 TeV beam) . . . . . . . . . . . . . . 20 13.3 Effective dose for underground structures due to neutrinos from bending magnets (5 TeV w/movers) ......................................... 22 13.4 Effective dose for underground structures due to neutrinos from arc interconnects (5 TeV w/movers) ......................................... 22 14.1 Simulated cooling performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 ix Consolidated Parameters Report – October 29, 2025 Parameters Unit Baseline Range Beam power MW 2 1.5-3.0 Beam energy GeV 5 2-10 Pulse frequency Hz 5 5-50 Pulse intensity p+ 1014 5 3.7-7.5 Bunches per pulse 1 1-2 Pulse length ns 2 1-2 Beam size mm 5 1-7.5 Impinging angle ° 0 0-10 Table 3.1: Assumed beam from proton driver via carbon target used in studies FLUKA simulations were conducted, calculating the muon and the pion yield in each setting. For this purpose, it was assumed that all the muon and pions going in the chicane can be captured if their momentum is below 500 MeV/c. The obtained yields are summarized as a function of beam energy in Table 3.2, assuming a transverse beam sigma of 5 mm and a graphite target rod with a radius of 15 mm. Yield [10−2GeV /p+]345678910 µ+2.8 2.6 2.4 2.3 2.2 2.1 1.9 1.9 µ−1.8 1.8 1.8 1.8 1.7 1.7 1.7 1.7 π+1.3 1.2 1.1 1.1 1 0.98 0.92 0.9 π−0.84 0.81 0.84 0.82 0.83 0.8 0.8 0.81 Table 3.2: Yield per unit energy proton beam [10−2GeV /p+] 4Cooling The cooling channel is defined from the end of the RF capture system to the beginning of acceleration. Five sub-systems are part of the cooling apparatus. Details of the sub-systems can be found in Appendix D. 1. Charge separation, which splits the positive and negative muon species into separate beamlines; 2. Rectilinear cooling (A and B lattices) which cools the beam in 6D phase space. Detailed parameters on each of these stages are in Appendix D.2; 3. Bunch merge after the A lattice which merges the microbunches produced by the front end into a single bunch; 4. Final cooling, which cools in 4D phase space and produces the final low transverse emittance beam, at the cost of a larger longitudinal emittance. Detailed parameters on this sub-system including design alternatives are in Appendix D.3; 5. Re-acceleration, which accelerates the low energy beam up to 339 MeV/c momentum which is 250 MeV kinetic energy. Potential performance for re-acceleration is estimated in Table D.21. For this iteration, parameters are listed in Table 4.1 for the principal subsystems: rectilinear cooling and final cooling. This is for two alternative stagings: One with a shorter rectilinear cooling, finishing at stage 8 but with a longer final cooling. The other with a longer rectilinear cooling until stage 10, but with a shorter final cooling. A potential initial cooling stage is described in Section D.1. This system would be integrated prior to the charge separation. 5 5. Acceleration εTεTtarget εLεLtarget Mean pzTransm. µmµm mm mm MeV/c % End of charge separation 17000 46 288 95 6D Cooling end of Stage 80260 300 1.86 1.5 200 14.9 End of Final Cooling 22.5 22.5 42 – 72 64 28 6.4 End of Reacceleration 22.5 22.5 64 64 339 5.8 εTεTtarget εLεLtarget Mean pzTransm. µmµm mm mm MeV/c % End of charge separation 17000 46 288 95 6D Cooling end of Stage 10 140 300 1.56 1.5 200 10.5 End of Final Cooling 22.5 22.5 ex 22 ex 64 26.5 6.4 End of Reacceleration 22.5 22.5 22 64 339 5.8 Table 4.1: Beam parameters entering and leaving the cooling system for short-rectilinear (top) and longrectilinear (bottom) options. The target emittances are listed. They are 10 % more demanding than the nominal emittances in the RCS and collider, allowing for some emittance growth at some point in the acceleration chain. Note: 64 mm = 0.0225 eVs 5Acceleration 5.1 Low Energy Acceleration The low energy acceleration chain brings the muon beams from 250 MeV after the pre-accelerator to 62.5 GeV for injection into the high energy acceleration chain described in Section 5. Details of the Low Energy Acceleration systems are in Appendix E. They are composed of a single-pass superconducting LINAC outlined in Table E.1, followed by two recirculating linear accelerators (RLA), described in Table E.2. RLA2 has a preliminary optics design. No optics design exists for LINAC and RLA1. Both RLAs have an assumed racetrack geometry. The transmission through RLA2 is 92.6%. The target transmission for LINAC and RLA1 is 90%, which corresponds to an effective average gradient of 4.1 MV/m. 5.2 High Energy Acceleration Below is the main overview of the high energy acceleration system. Table 5.1 shows the general RCS parameters. We assume a survival rate of 90 % per ring and linear ramping only considering losses due to muon decay, even though these values are subject to further adjustments to optimize the RF and magnet powering parameters with respect to total costing, ramp shape, bunch matching, and the overall transmission of the entire chain. The lattice parameters based on the key parameters are shown in Table 5.2. The high energy acceleration parameters for site-based variations are summarized in Appendix F. Parameters for high energy acceleration performed with a fixed field accelerator are shown in Appendix F.2. Recent longitudinal tracking studies in both RLA2 and RCS1 revealed an important longitudinal mismatch at injection into the high-energy acceleration chain at 62.5 GeV. This mismatch, mainly due to the important difference in the aspect ratios of the RF buckets, could be mitigated by lowering the RF frequency of RCS1, presently 1.3 GHz, closer towards the frequency of the accelerating sections at 352 MHz in RLA2. To progress with the baseline optics study, an eightfold symmetry with eight long straight sections has 6 Consolidated Parameters Report – October 29, 2025 Parameter Unit RCS1 RCS2 RCS3 RCS4 Hybrid RCS - no yes yes yes Repetition rate Hz 5 5 5 5 Circumference m 5990 5990 10700 35000 Injection energy GeV 63 314 750 1500 Extraction energy GeV 314 750 1500 5000 Energy ratio 5.0 2.4 2.0 3.33 Assumed survival rate 0.9 0.9 0.9 0.9 Cumulative survival rate 0.9 0.81 0.73 0.66 Acceleration time ms 0.34 1.10 2.37 6.37 Revolution period µs 20 20 36 117 Number of turns - 17 55 66 55 Required energy gain/turn GeV 14.8 7.9 11.4 63.6 Average accel. gradient MV/m 2.44 1.33 1.06 1.83 Number of bunches 1 1 1 1 Inj. bunch population 1012 2.7 2.4 2.2 2 Ext. bunch population 1012 2.4 2.2 2 1.8 Beam current per bunch mA 21.67 19.5 9.88 2.75 Peak RF power MW 640 310 225 350 Vert. norm. emittance µm 25 25 25 25 Horiz. norm. emittance µm 25 25 25 25 Long. norm. emittance eVs 0.025 0.025 0.025 0.025 Bunch length at injection ps 31 22 18 14 Bunch length at ejection ps 22 18 14 10 Straight section length m 1012.4 536.4 793.6 4385.6 Length with pulsed dipole magnets m 3654 2539 4366 20376 Length with steady dipole magnets m - 1115 2358 4257 Max. pulsed dipole field T 1.8 1.8 1.8 1.8 Max. steady dipole field T - 10 10 16 Ramp rate T/s 4232 3272 1519 565 Main RF frequency GHz 1.3 1.3 1.3 1.3 Harmonic number 25900 25900 46300 151400 Table 5.1: RCS acceleration chain key parameters been assumed. As this would be insufficient from the longitudinal beam dynamics point of view, due to the large energy gain per long straight section, alternative options are being investigated to either lower the momentum compaction factor of the lattice or to introduce more straight sections for acceleration. Both approaches would smooth the impact of the discrete energy kicks by the RF system. The present assumption to reach a 90 % survival rate per RCS with an initial bunch intensity of 2.7· 1012 muons injected at 62.5 GeV simplified the preliminary choice of parameters given in this report. However, a global optimization of the beam transfer energies between the different RCS in the chain will be performed, with the objective to maximize the overall transmission for muons up to 1.5 TeV or 5 TeV. This optimization is also expected to adjust RF voltages, average accelerating gradients and horizontal apertures of all four synchrotrons. Of course, variations cannot be completely avoided in the upstream part of the chain due to the constraint of installing the first two RCS in the same accelerator tunnel. 7 6. Collider Parameter Unit RCS1 RCS2 RCS3 RCS4 Fill ratio dipole % 61 61 62.8 70.4 Cells per arc 17 17 29 36 Number of arcs 8 8 8 8 Cell length m 36.6 40.1 42.7 106.3 Total Arc length m 4977.6 5453.6 9906.4 30614.4 Arc Ratio - 0.83 0.91 0.93 0.87 Relative path length difference 10−60 5.1 0.9 1 Horizontal aperture mm 91.3 83.4 49.7 88.6 Vertical aperture mm 24.8 21.6 21.1 21.1 Transition gamma 31.02 33.36 55.85 68.78 Momentum compaction factor 10−410.4 9.0 3.2 2.1 Horizontal tune (ring) 41.02 39.56 64.54 82.40 Vertical tune (ring) 42.36 36.08 62.44 81.43 Mean horizontal beta m 36.54 35.42 38.31 97.94 Mean vertical beta m 38.31 36.02 37.84 92.75 Horizontal natural chromaticity (ring) -60.91 -53.96 -86.58 -112.94 Vertical natural chromaticity (ring) -61.11 -46.88 -82.11 -102.39 Table 5.2: RCS acceleration chain lattice parameters 6Collider The present work concentrates on the design of a 10 TeV center-of-mass collider. The aim is to maximize the luminosity to the two possible experiments, introduced in Section 7. The basic luminosity assumptions (in Section A.1) are extrapolations from lower energy starting with a relative rms momentum spread of σδ= 1 ·10−3. Together with the longitudinal emittance, this fixes the rms bunch length σz= 1.5 mm and the β∗= 1.5 mm to the same value, such that the hour glass luminosity reduction factor fhg = 0.758 starts to become significant. Maximization of the luminosity requires to choose the shortest possible circumference Ccompatible with feasibility of the magnets (average bending field assumed to be ¯ B≈10.48 T leading to C≈10 km). Note that extrapolation of parameters to higher energies lead to very large chromatic effects further increasing with energy. The main parameters are described in Table 6.1, which contains a set of target parameters which meet the performance of Table 1.1. The set of relaxed parameters considers a lattice with reduced beta oscillations and chromatic aberrations, to study imperfections and the effects of movers. The radial build of arc dipoles is described in Table 6.2. The radial build assumes a radiation shielding thickness of 3 cm, which can be accepted from a cryogenics point of view if the operating temperature is 20 K. The estimated heat load and radiation damage in arc dipoles is summarized in Table 12.3. 1Luminosities for Gaussian beams with hour glass reduction factor and without beam-beam effect. Multiturn beam simulations with the correct lattice and tunes are needed in addition to first single pass simulations resulting in a modest luminosity increase. 2The approximate circumference depends on the maximum achievable dipole field. The current lattice design assumes a collider arc peak field of 16 T, but will likely be updated later to reduce the field to 14 T. This change should not significantly affect the optics and will mainly result in an increased collider circumference. 3Assuming constant bending field of 16 T. The exact value will depend on the detailed lattice design and likely be lower. 4Assuming that only the synchrotron radiation losses have to be compensated. Some margin and no particular frequency requirements as long as the RF voltage does not vary too much over the bunch length of few 10s of ns. 8 Consolidated Parameters Report – October 29, 2025 version Parameter Unit relaxed target Center of mass energy TeV 10 Geometric Luminosity11034 cm−2s−15.77 19.2 Beam energy TeV 5 Relativistic Lorentz factor 47322 Circumference2km ≈10 Dist. of last magnet to IP m 6 Repetition rate Hz 5 Bunch intensity (one bunch per beam) 1012 1.80 Injected beam power per beam MW 7.2 Normalized transverse rms emittance µm 25 Longitudinal norm. rms emittance eVs 0.025 Relative rms momentum spread 10−30.3 1 RMS bunch length in space mm 5 1.5 RMS bunch length in time domain ns .017 0.005 Twiss betatron function at the IP mm 5 1.5 Energy loss per turn3MeV ≈27.2 Integrated RF gradient4MV 30 Table 6.1: Assumptions for the main parameters used in the design of a 10 TeV muon collider. Parameter Unit Thickness Outer radius Beam aperture mm 23.49 23.49 Coating (copper) mm 0.01 23.5 Radiation absorber (tungsten alloy) mm 30 53.5 Shielding support and thermal insulation mm 11 64.5 Cold bore mm 3 67.5 Insulation (Kapton) mm 0.5 68 Clearance to coils mm 1 69 Table 6.2: Collider arcs, coil inner aperture. For options using low temperature superconductor, i.e. at 3 TeV, the shielding thickness should be 40 mm and the other parameters changed accordingly. 7Detectors The design of the detector for √s= 10 TeV follows the concept already developed for √s= 3 TeV with modifications to account for the higher energy. Two distinct detector concepts are presented, MAIA (Muon Accelerator Instrumented Apparatus) and MUSIC (MUon System for Interesting Collisions), to fully exploit the two interaction points of the collider. Both designs share a similar structure, a cylinder 11.4m long with a diameter of 12.8m. The main detector components are: – Tracking system – Electromagnetic calorimeter (ECAL) – Hadron calorimeter (HCAL) – A superconducting solenoid – A muon sub-detector The origin of the space coordinates is the beam interaction point at the center of the detector. The z-axis 9 7. Detectors Requirement Baseline Aspirational √s= 3 TeV √s= 10 TeV Angular acceptance |η|<2.5|η|<2.5|η|<4 Minimum tracking distance [cm] ∼3∼3<3 Forward muons (η > 5) – tag σp/p ∼10% Track σpT/p2 T[GeV−1]4×10−54×10−51×10−5 Photon energy resolution 0.2/√E[GeV] 0.2/√E[GeV] 0.1/√E[GeV] Neutral hadron energy resolution 0.5/√E[GeV] 0.4/√E[GeV] 0.2/√E[GeV] Timing resolution (tracker) [ps] ∼30 −60 ∼30 −60 ∼10 −30 Timing resolution (calorimeters) [ps] 100 100 10 Timing resolution (muon system) [ps] ∼50 for |η|>2.5∼50 for |η|>2.5<50 for |η|>2.5 Flavour tagging bvs c b vs c b vs c,s-tagging Boosted hadronic resonance ID hvs W/Z hvs W/Z W vs Z Table 7.1: Preliminary summary of the “baseline” and “aspirational” targets for selected key metrics, reported separately for machines taking data at √s= 3 and 10 TeV. The reported performance targets refer to the measurement of the reconstructed objects in physics events after, for example, background subtraction and not to the bare detector performance. follows the direction of the clockwise-circulating µ+beam, the y-axis is parallel to gravity acceleration, and the x-axis is defined as perpendicular to both the yand zaxes. Table 7.1 summarises the baseline and aspirational performance and acceptance targets for the muon collider detectors. Table 7.2 summarises the detector parameters sub-system by sub-system for the two concepts. While the tracking system has a similar structure, the MAIA detector has the solenoid just after the tracker, before the ECAL while MUSIC places the solenoid magnet between ECAL and HCAL. 7.1 Tracking System The tracking detector is composed of the vertex and tracker sub-detectors, both of them structured in barrels and end-caps. The barrels consist of sensor modules arranged in cylindrical configurations with varying lengths and radii, whose axes align with the beamline, covering the central region of the detector. The endcaps are annuli centered on the zaxis, with variable distance from the interaction point and radii which cover the forward part of the detector. The major characteristics of this sub-system are described in Table 7.3. The vertex detector is close to the interaction point in order to allow a good resolution on track impact parameter. The building blocks of the barrel detection layers are rectangular staves of sensors, arranged to form a cylinder, while the endcaps are constituted by trapezoidal modules of sensors, arranged as "petals" to form a disk. The MAIA detector has 5 layers, with the first two structured as a double layer, while MUSIC has 5 distinct layers. The length of the MUSIC barrel is 26 cm, which is double that of MAIA. The barrel layers of the vertex detector have silicon pixels of size 25 ×25 µm2, and thickness 50 µm. The inner and outer trackers are based on the same technology for MAIA and MUSIC, single layer of silicon macro-pixels sensors of 100 µm thickness. 10 Consolidated Parameters Report – October 29, 2025 Detector Concept MuColl MUSIC MAIA √s= 3 TeV √s= 10 TeV √s= 10 TeV Inner Trackers Rmin – Rmax [mm] 30 – 1486 29 – 1486 30 – 1486 zmin – zmax [mm] 0 – 2190 0 – 2190 0 – 2190 Angular Acceptance [◦] 10 – 170 10 – 170 10 – 170 X/X00.3 0.1 0.1 L/L00.1 0.04 0.04 EM Calorimeters Rmin – Rmax [mm] 1500 – 1702 1690 – 1960 1857 – 2125 zmin – zmax [mm] 2307 – 2210 2307 – 2577 2307 – 2575 Angular Acceptance [◦] 10 – 170 10 – 170 10 – 170 X/X026 – 32 33 – 38 40 – 42 L/L01.2 – 1.5 1.4 – 1.7 1.8 – 1.9 Hadron Calorimeters Rmin – Rmax [mm] 1740 – 3330 2902 – 4756 2125 – 4113 zmin – zmax [mm] 2539 – 4129 2579 – 4434 2575 – 4562 Angular Acceptance [◦] 10 – 170 10 – 170 10 – 170 X/X082 – 87 89 – 116 100 – 114 L/L08.8 – 9.3 9.5 – 12.5 10.9 – 12.3 Muon Systems Rmin – Rmax [mm] 4461 – 6450 4806 – 6800 4150 – 7150 zmin – zmax [mm] 4179 – 5638 4444 – 5903 4565 – 6025 Angular Acceptance [◦] 10 – 170 10 – 170 10 – 170 Solenoid Rmin – Rmax [mm] 3483 – 4290 2000 – 2807 1500 – 1857 zmin – zmax [mm] 0 – 4129 0 – 2500 0 – 2307 X/X0– 18 6 L/L0– 2.7 1.4 Bz[T] 3.6 5 5 Nozzles Rmin – Rmax [mm] 10 – 600 10 – 550 10 – 550 zmin – zmax [mm] 60 – 6000 60 – 6000 60 – 6000 Table 7.2: Detector parameters for the MuColl (v1), MUSIC (v2) and MAIA (v0) concepts. Values that are left empty ("–") are not relevant for the specific detector. X/X0and L/L0are for a particle travelling from the nominal beam interaction point (IP). The origin of the space coordinates is the IP. The z-axis has direction parallel to the beam pipe, the y-axis is parallel to gravity acceleration and the x-axis is defined as perpendicular to both the yand zaxes. 7.2 Calorimeter System The calorimeter system is composed of the electromagnetic (ECAL) and hadronic (HCAL) subdetectors. A summary of the main characteristics are in Tables 7.4 and 7.5. The MAIA ECAL configuration is inspired by CLIC. It consists of a dodecagonal barrel and two endcap systems. It is composed of 50 alternating layers of Tungsten as absorber material 2.2mm thick and Si sensor as active material with 5.1×5.1mm2silicon detector cells. It is located outside of the superconducting solenoid. The MUSIC ECAL, has the same geometry as MAIA’s, but is positioned immediately after the tracking 11 7. Detectors Vertex Detector Inner Tracker Outer Tracker Sensor type pixels macro-pixels macro-pixels Barrel Layers 5 3 3 Endcap Layers (per side) 4 7 4 Cell Size 25 µm×25 µm 50 µm×1 mm 50 µm×10 mm Sensor Thickness 50 µm 100 µm 100 µm Time Resolution 30 ps 60 ps 60 ps Spatial Resolution 5µm×5µm 7 µm×90 µm 7 µm×90 µm Table 7.3: Assumed spatial and time resolution for MAIA and MUSIC Tracking Detector sub-systems. There is no resolution difference between the barrel and end-cap regions. The first layer of the Vertex barrel and all Vertex endcap layers of MAIA are implemented as double layers. system and within the superconducting solenoid. It is a semi-homogeneous longitudinally-segmented calorimeter based on lead-fluoride (PbF2) crystals read out by Silicon Photomultipliers. It represents a modern design approach that aims to combine the intrinsic high-energy resolution of homogeneous calorimeters with the longitudinal segmentation typically found in sampling calorimeters. MAIA and MUSIC currently share the same technology for HCAL. It consists of a dodecagonal barrel and two endcap systems, structured in alternating layers of iron absorber 20 mm thick and plastic scintillating tiles with cell size 30×30 mm2, 75 layers in MAIA and 70 in MUSIC. It allows the reconstruction of hadronic jets and helps in particle identification, to separate hadrons from leptons and photons. Electromagnetic Calorimeter Hadron Calorimeter Cell type Silicon - Tungsten Iron - Scintillator Cell Size 5.1 mm ×5.1 mm 30.0 mm ×30.0 mm Sensor Thickness 0.5 mm 3.0 mm Absorber Thickness 2.2 mm 20.0 mm Number of layers 50 75 Table 7.4: Cell and absorber sizes in the MAIA calorimeter systems, describing both the barrel and end-cap regions. Electromagnetic Calorimeter Hadron Calorimeter Cell type PbF2crystal Iron - Scintillator Cell Size 10 mm ×10 mm ×40 mm 30.0 mm ×30.0 mm Sensor Thickness - 3.0 mm Absorber Thickness - 20.0 mm Number of layers 6 70 Table 7.5: MUSIC calorimeter systems, describing both the barrel and end-cap regions. 7.3 Muon System The current configuration of the two detector concepts does not include a magnetic field outside the calorimetric system, so the role of the muon detector must be reconsidered. In particular, for high-energy muons, new methods based on machine learning, which combine tracking detector and calorimeter information, could be employed. In this case, the muon detector would primarily serve to identify that the particle is a muon. 12 Consolidated Parameters Report – October 29, 2025 8Machine-Detector Interface This section contains the main overview of the Machine-Detector Interface (MDI). An overview of the detectors can be found in Section 7. An indication of the ionization dose and neutron-equivalent fluence of both detector geometries can be found in Table 8.1. The results for the vertex detector, the inner tracker, as well as the electromagnetic calorimeter correspond to one year of operation, assuming 1.2×107seconds of operation (139 days). The studies considered only muon decay, while neglecting the contribution of collision products and beam halo losses. The results were computed for IR lattice version 0.8. Table 8.2 indicates the species of secondary particles that enter the detectors. Additional information and variations can be found in Appendix G. Dose 1 MeV neutron-equivalent Unit kGy fluence in Si 1014 n/cm2 MAIA MUSIC MAIA MUSIC Vertex (barrel) 900 2 Vertex (endcaps) 1800 7 Inner trackers (barrel) 61 4 3.5 Inner trackers (endcap) 26 10 8.8 ECAL 0.51 1.2 0.13 0.8 Table 8.1: Maximum values of the ionizing dose and the 1 MeV neutron-equivalent fluence (Si) in the MAIA and MUSIC detectors. All values are per year of operation (10 TeV) and include only the contribution of muon decay. The updated values assume a collider ring circumference of 11.4 km. Particle type Particles entering detector Threshold Photons 1.0×108100 keV Neutrons 1.1×1080.01 meV Electron/positrons 1.2×106100 keV Muons 1.1×104100 keV Charged hadrons 4.0×104100 keV Table 8.2: Number of secondary particles (muon decay) entering the detector volume (10 TeV). Only particles above the threshold values were included. The multiplicities include only the contribution of one beam and correspond to one bunch crossing. 9Magnets The below table summarizes the latest studies of the most challenging magnets of the muon collider. The main performance targets and target ranges (i.e., not yet to specification) of the most challenging magnets of the muon collider are shown Table 9.1. Though these targets are bound to adapt as the study proceeds, they already provide a good basis to feedback on beam optics and accelerator performance, and to identify outstanding issues to be addressed by future work and dedicated R&D. The whole accelerator complex functions in steady state, apart from the fast ramped magnets in the rapid cycling synchrotrons. Specific details on the 6D cooling solenoids can be found in Appendix H. 13 10. RF Cavities Complex Magnet No. Aper. Length Field Grad. Ramp rate Temp. Unit [mm] [m] [T] [T/m] [T/s] [K] Target, capture Solenoid Coils 23 1380 ≈0.4 – 0.8 2 – 20 SS 20 6D cooling Solenoid Coils ≈6000 90-1500 0.08 – 0.5 2 – 17 SS 4.2-20 Final cooling Solenoid Coils 20 50 0.5 >40 SS 4.2 RCS NC dipole ≈1500 30x100 5 ±1.8 4200 300 SC dipole ≈2500 30x100 1.5 10 SS 4.2-20 Collider arc Dipoles ≈1050 140 5 14* SS CF ≈628 140 5 – 10 4 – 8 ±100–±150* SS 4.2-20 IR quadrupoles ≈20 100 - 280 5 – 10 ±110 – ±330** SS 4.2-20 Table 9.1: Summary of main magnet development targets. For the collider magnet values marked with a * slightly higher values are assumed in the lattice design but no important changes are expected adjusting to the specified performances. The values marked with ** correspond to the lattice design but might be too high for the magnets; the lattice design will be updated accordingly. Specific configurations still need to be evaluated and this is a work in progress. CF stands for combined-function magnets. 10 RF Cavities The RF parameters which should be considered in the design are listed in Table 10.1. In the other sub-systems of the muon cooling complex: capture, bunch merge, final cooling, etc many different RF frequencies are necessary. It is recommended to keep these RF frequencies as high as reasonable possible from the beam dynamics point of view, since the size of the achievable gradient scales approximately as p(fRF ). Further details on the designs of the 6D cooling cavities and the RCS cavities can be found in Appendix I. Proton driver LINAC RF frequencies MHz 352 704 Muon cooling complex 6D Cooling Channels RF frequencies MHz 352 704 1056 Max accelerating field (conservative) MV/m 22 30 30 Max accelerating field (optimistic) MV/m 35 50 50 Acceleration complex LINAC RF frequencies MHz 352 704 1056 Max accelerating field (conservative) MV/m 20 25 30 Max accelerating field (optimistic) MV/m 30 38 45 RCS RF frequency MHz 704 1056, 1300 Max accelerating field (conservative) MV/m 25 30 Max accelerating field (optimistic) MV/m 38 45 Table 10.1: RF frequencies and gradients to be used in the beam dynamics studies. 11 Impedance This section is devoted to beam intensity limitations that could be encountered in the different machines due to collective effects. 14 Consolidated Parameters Report – October 29, 2025 geometry considered are two consecutive underground rooms that are aligned along the neutrino flux path. The resulting neutrino induced dose distributions for the interconnection and the bending regions are illustrated in Figs 13.2 and 13.3, respectively. Assuming a conservative annual exposure scenario with a 100% occupancy in the two underground rooms would lead to a respective effective dose for various relevant distances as given in Tables 13.4 and 13.3. Fig. 13.2: Side (left) and cross-sectional view (right) of the effective dose (in arb. units) for an underground building structure exposed to the neutrino flux from the decay of negative muons in an interconnection region, after the vertical deformation by the movers. Fig. 13.3: Side (left) and cross-sectional view (right) of the effective dose (in arb. units) for an underground building structure exposed to the neutrino flux from the decay of negative muons within a bending region, after the vertical deformation by the movers. Table 13.3 shows the dose contribution from a bending section, for which the collider is approximated as an ideal circle of 1.36 km radius. As can be seen in Fig. 13.3, the vertical smearing effect of the movers is overlapped with the horizontal bending of the muon beam resulting in neutrino flux uniformly distributed in the plane perpendicular to the neutrino direction. It was found that the neutrino-induced dose from a bending section is approximately proportional to the square of the muon beam energy. The dose evaluation for a straight section in an interconnection region is shown in Table 13.4. Assuming 1 m of a straight section length, the values for a single beam are comparable with the summed numbers of a bending section shown in Table 13.3. Due to overlaps, the dose from a bending section always has to take into account a contribution from both beams, while an interconnection straight section generally contributes from a single beam. More studies are needed to understand possible overlaps of neutrino fluxes emerging from the interconnection regions of a realistic collider lattice. 21 14. Demonstrators µ−µ+Summed Distance [km] Avg eff. dose [pSv m/decay] Avg eff. dose [pSv m/decay] [pSv m/decay] 15 1.37 ×10−91.38 ×10−92.75 ×10−9 20 7.70 ×10−10 7.79 ×10−10 1.55 ×10−9 30 3.43 ×10−10 3.47 ×10−10 6.90 ×10−10 40 1.93 ×10−10 1.95 ×10−10 3.88 ×10−10 60 8.58 ×10−11 8.67 ×10−11 1.73 ×10−10 80 4.82 ×10−11 4.88 ×10−11 9.70 ×10−11 100 3.09 ×10−11 3.12 ×10−11 6.21 ×10−11 200 7.72 ×10−12 7.81 ×10−12 1.55 ×10−11 300 3.43 ×10−12 3.47 ×10−12 6.90 ×10−12 Table 13.3: Effective dose in [pSv m/decay] of neutrino-induced radiation for an underground building structure at different baseline distances from the muon decay after the vertical deformation by the movers is applied. The muon beam energy is 5 TeV and the neutrinos are assumed to emerge from a bending magnet inside the collider arcs, where the mover system is employed. The dose unit comes from the convention where the quoted numbers have to be only multiplied by decays/meter/year to obtain the annual dose. The bending section length is already embedded in the calculation. µ−µ+ Distance [km] Avg eff. dose [pSv/decay] Avg eff. dose [pSv/decay] 15 6.55 ×10−96.66 ×10−9 20 4.74 ×10−94.88 ×10−9 30 3.04 ×10−93.14 ×10−9 60 1.32 ×10−91.35 ×10−9 100 6.55 ×10−10 6.58 ×10−10 Table 13.4: Effective dose in [pSv/decay] of neutrino-induced radiation for an underground building structure at different baseline distances from the muon decay after the vertical deformation by the movers is applied. The muon beam energy is 5 TeV and the neutrinos are assumed to emerge from a collider straight section inside the arcs, where the mover system is employed. 14 Demonstrators The Muon Cooling Demonstrator Programme will be an essential component of the muon collider R&D programme. Muon cooling is required in order to deliver the required luminosities but it is a technology that has not been fully proven. The muon cooling demonstrator will demonstrate – Successful integration of cooling equipment. – Operation of the cooling equipment with beam. – Delivery of required beam physics performance. Delivery of the demonstration of muon cooling will require a programme of R&D to understand and mitigate risks surrounding construction of the cooling lattice. The principle issues are: 1. The cooling cell has RF cavities and solenoids in close proximity. Solenoid fields are known to induce RF breakdown which must be understood in detail. 22 Consolidated Parameters Report – October 29, 2025 Fig. 14.1: Cooling Cell Schematic showing individual elements. 2. Warm-cold interfaces between adjacent RF cavities and solenoids require careful attention to thermal management. 3. Integration of ancillary equipment such as vacuum, RF power and beam instrumentation may be very challenging to implement in such a compact lattice. 4. Beam instrumentation must enable suitable commissioning of the equipment. For the beam demonstration in particular, where muon rates may be low compared to conventional beams, suitable instrumentation must still be implemented. 5. The integrated facility must be operable in a routine manner. In order to deliver this, a staged R&D programme is envisaged, with each stage demonstrating the technology more fully: 1. Several RF test stands will be constructed to understand the limits to RF gradient that can be achieved in the presence of high-field solenoids. 2. A one-cell module will be implemented in order to test the operation of RF cavities in an operational magnetic environment. 3. A multi-cell module will be implemented to demonstrate integration of absorber, RF and magnets. 4. The multi-cell module will be operated with beam in order to demonstrate commissioning and operation of the cooling equipment with beam. 5. A cooling line comprising several cooling modules will be implemented to demonstrate beam physics performance. The Collaboration has adopted the terminology in Fig. 14.1 to designate the elements of a cooling cell. The chosen cooling cell to implement is related to the B5 rectilinear cooling cell. Several important design differences have been implemented compared to B5. The Demonstrator cooling cell parameters are chosen as a compromise between cost and technical challenge. The design will inform subsequent design of the muon collider cooling system. The cooling channel would be composed of a series of cooling cells grouped into vacuum vessels, as shown in Fig 14.2. The cooling performance for two different cooling channel lengths is listed in Tab. 14.1, while the main parameters of the most recent demonstrator cell layout are reported in Tab. 14.2. 23 14. Demonstrators Fig. 14.2: Cooling demonstrator conceptual layout. Simulated cooling performance Unit Start value End value (50 m) Transverse emittance mm 1.85 1.46 Longitudinal emittance mm 3.20 2.81 Transmission % 100 95.4 Table 14.1: Simulated cooling performance. 24 Consolidated Parameters Report – October 29, 2025 Parameter Unit Value Cooling Cell Length mm 1000 Beam Physics Momentum MeV/c 200 Twiss beta function mm 130 Dispersion in X mm -61.5 Dispersion in Y mm -19.7 Beam Pipe Radius mm 81.6 Solenoid Parameters Unit Value Tol B0 T 7 0.2 B0.5 T 0 0.016 B1 T 1 0.02 B2 T 0 0.4 Coil Geometry Parameter Unit Coil 1 Coil 2 Geometry – B5-DEMO-MAG-2.4 Inner Radius mm 285 185 Length mm 211 63.4 Radial Thickness mm 76.2 71.7 Z Centre Position mm 251.8 88.1 Pancake length mm 12 12 Spacer length mm 7.9 13.7 Number pancakes – 11 3 Current Density A/mm2403.5 632.3 RF Cavity Centre-to-centre distance mm 177.5 Gradient E0 MV/m 30 Iris Radius mm 60 Number of RF Cells 3 Frequency GHz 0.704 Synchronous Phase degree 20 Window Thickness mm 0.1 Wedge Material LiH Opening Angle degree 10 Thickness mm 20 Alignment Horizontal Dipole Length mm 100 Polarity + - - + Field T 0.2 Z Centre Position mm 160 Field Direction Vertical Table 14.2: Cooling Cell Table 25 A. Appendix: Top-Level Parameters Appendices AAppendix: Top-Level Parameters Additional parameters relating to the Muon Collider staging options can be found in Table A.1. Parameter Symbol Unit Stage 1 Stage 2 Centre-of-mass energy Ecm TeV 3 10 Target integrated luminosity RLtarget ab−11 10 Estimated luminosity Lestimated 1034cm−2s−12.1 18 Collider circumference Ccoll km 4.5 11.4 Collider arc peak field Barc T11 14 Luminosity lifetime Nturn turns 1039 1363 Muons/bunch N1012 2.2 1.8 Repetition rate frHz 5 5 Beam power Pcoll MW 5.3 14.4 RMS longitudinal emittance ε∥eVs 0.025 0.025 Norm. RMS transverse emittance ε⊥µm 25 25 IP bunch length σzmm 5 1.5 IP betafunction βmm 5 1.5 IP beam size σµm 3 0.9 Protons on target/bunch Np1014 5 5 Proton energy on target EpGeV 5 5 Table A.1: Target parameters for a muon collider for Stage 1 at 3 TeV and Stage 2 at 10 TeV. The estimated luminosity refers to the value that can be reached if all target specifications can be reached, including beam-beam effects. A.1 Luminosity assumptions The luminosity of the muon collider is estimated taking into account several effects. The beams will perform collisions with the bunch charges Ndecreasing with time tfollowing N(t) = N0exp −t γτ (A.1) It should be noted that in the 10 TeV machine after 200 ms still about 15% of the charge remain, which corresponds to 2% of the integrated luminosity. One can inject a new bunch without removing the old one. However, for the current luminosity estimate, we assume that the beam is being removed. In contrast, for the radiation load on the detector and arcs as well as the neutrino flux, we assume that the bunch is not being removed. The hourglass effect reduces the luminosity by a factor 0.76 for round beams with the beta-function and the rms bunch length being equal, as can be easily estimated analytically. The beam-beam forces on the other hand increase the luminosity since the beams focus each other, this requires simulations since the disruption parameter is of the order of 1. A simple estimate of the combination of both effects is produced by running the muon version of GUINEA-PIG using the target beam parameters. The calculation is performed assuming a longitudinally "round" beam, i.e. all particles are distributed with equal density in the space ∆E σE2 +∆z σz2 ≤22(A.2) 26 Consolidated Parameters Report – October 29, 2025 The beam-beam enhancement factor varies with the bunch charge, and reaches up to 24% at 10 TeV and full charge. We perform the integration over time and find L ≈ 1.86 ×1035 cm−2s−1(A.3) The result depends on the actual charge distribution in the bunch, the full model is being developed. However, using other longitudinal profiles with the same RMS bunch length, such as Gaussian distributions or a constant charge profile yield very similar results. We thus use L ≈ 1.8×1035 cm−2s−1(A.4) For the 3 TeV parameters the disruption is higher. The above luminosity can be roughly estimated analytically using the following assumptions: – One bunch of µ+is colliding against one bunch of µ−(as for the same total number of particles, it is more efficient to have all the particles in one bunch), – Densities are uncorrelated in the three planes, – Gaussian distributions in the transverse planes, – Same parameters for both bunches, – Round (transverse) beam, – No crossing angle, – No transverse offset, – Ignoring the beam-beam enhancement. The Muon Collider luminosity formula is typically written as L=N2 0f0γ 4πβ∗ϵn FHG(β∗/σz)Fdecay ,(A.5) where N0is the initial number of muons colliding, f0is the revolution frequency, β∗is the beta function at the interaction point, ϵnis the normalised transverse emittance and σzis the rms longitudinal beam size. Furthermore, FHG(β∗/σz)describes the usual hourglass effect while Fdecay is a new term specific to the muons due to their decay and replenishment. For the first term, assuming that β∗=σzyields FHG(1) = 0.76. For the second term, as the muons decay rapidly and new muons arrive with the repetition frequency fr= 1/Tr, the number of muons needs to be averaged such that < N2>=1 TrZTr 0 (N0e−t γτµ0)2dt =N2 0Fdecay ,(A.6) with Fdecay =frγτµ0 2[1 −e−2 frγτµ0].(A.7) It is worth reminding that this scheme assumes that there is no muon beam once the new injection arrives, either because muons decayed or because the remaining ones were kicked out. Therefore, the luminosity 27 A. Appendix: Top-Level Parameters can be written fully as: L=N2 0f0γ 4πβ∗ϵn FHG(β∗/σz)frγτµ0 2[1 −e−2 frγτµ0].(A.8) Once applying the aforementioned assumption that β∗=σz, L=c 8π2 N2 0 ϵnϵl BavgγσE EFHG(1)frγτµ0 2[1 −e−2 frγτµ0].(A.9) Here we define ϵl[eVs] = σt σE EEand BavgR=p e, where Bavg is the average dipolar magnetic field, Ris the average machine radius, pis the muon momentum and eis the elementary charge. Doing the numerical application with the baseline parameters of Table A.1 (N0= 1.8×1012,ϵn= 25 µm, ϵl= 0.025 eVs, Bavg = 10.5T, E= 5 TeV, σE E= 0.1 %,FHG(1) = 0.76,fr= 5 Hz, β∗=σz= 1.5mm), yields L≈18.8×1034 cm−2s−1. Assuming that one year of run corresponds to 1.2×107s leads to Lint(1 year)≈2.2ab−1. This means that 10 ab−1can thus be reached in ∼5years (or ∼2.5years with two detectors), which should give enough margin for further design and technology studies and a realistic ramp-up of the luminosity. It is also interesting to normalise the luminosity per beam power, with P1beam [W] = E[J]×N0×fr[Hz], which yields the following: L P1beam =1 8π2mµ0c N0 ϵnϵl Bavg σE EFHG(1) ×Fenergy ,(A.10) where Fenergy =γτµ0 2[1 −e−2 frγτµ0].(A.11) Plotting Fenergy, the only factor dependant on energy, Fig. A.1 is obtained, from which three conclusions can be drawn. First, the derived luminosity formula of Eq. A.9, gives the same result as the linearised one in Eq. A.5(i.e. neglecting the exponential term linked to the muon decay) with the IMCC assumptions (E= 5 TeV and fr= 5 Hz). Second, these linearised assumptions would however not be true for higher energies and/or higher repetition rates, as the energy factor Fenergy converges towards 1/fr. Third, the (linear) luminosity formula can be recovered by using more than one bunch per beam, but then in this case we cannot consider our initial assumption of one bunch of µ+colliding against one bunch of µ−. Let’s consider an integer nand average N2over nTrinstead of Tr. This leads to: < N2>=1 nTrZnTr 0 (N0e−t γτµ0)2dt =N2 0Fdecay(n),(A.12) with Fdecay(n) = frγτµ0 2n[1 −e−2n frγτµ0].(A.13) To conclude: for any energy and repetition rate, one can choose a nsuch that the exponential term becomes negligible. One then just has to inject the bunches in ndifferent buckets and one recovers the 28 Consolidated Parameters Report – October 29, 2025 usual luminosity formula (without the exponential term). However, in this case all the beam studies should be performed with these nbunches of µ+colliding against nbunches of µ−. If multiple bunches are stored, a collider design may be implemented with additional interaction points leading to an increase in the physics capability of the facility beyond the baseline assumptions. Fig. A.1: Normalised luminosity per muon beam power as a function of the muon beam energy, assuming that (only) one bunch of µ+collides with one bunch of µ−. This is a worst-case scenario; in reality additional bunches will be stored if Fdecay becomes significant. A.2 Muon Decays Within the main document of Table 1.3, the total transmission of the muon beams throughout the muon collider complex has been listed. These values include both the losses due to decays and the losses due to beam dynamics effects. The transmission loss solely due to decays can be safely predicted as it depends only on the energy of the beam, and the length of each system the beam travels through. This is significant as it dictates the maximum intensity which is physically possible for a perfect system. In addition it allows for an integrated understanding of which systems contribute the most significant decay losses. System Energy In Energy Out Lengths Turns Transm. Cumul. Transm. Total Length GeV GeV m % % m Front End 0.121 0.200 150 1 90.5 90.5 150 Rectilinear A 0.200 0.162 363 1 80.3 72.7 513 Rectilinear B 0.162 0.124 487 1 70.6 51.3 1000 Final Cooling 0.124 0.005 100 1 86.0 44.2 1100 Pre-Accelerator 0.005 0.250 245 1 77.5 34.2 1345 LINAC 0.25 1.250 500 1 89.7 30.7 1845 RLA1 1.25 5 800 4.5 81.5 25.0 2645 RLA2 5 62.5 2430 4.5 92.6 23.2 5075 RCS1 62.5 314 5990 17 90.0 20.9 11065 RCS2 314 750 5990 55 90.0 18.8 17055 RCS3 750 1500 10700 66 90.0 16.9 27755 RCS4 1500 5000 35000 55 90.0 15.2 62755 Collider 5000 5000 10000 1000 72.6 11.0 72755 Table A.2: Transmission due to only decays assuming linear change in energy. Table A.2 shows the transmission for each system only due to decays, which is represented graphically in Figure A.2. The total length logarithmically represents the path the muon takes, which is the length of 29 B. Appendix: Proton Driver the system multiplied by the number of turns the beam takes. It is clear that the rate of decay increases most significantly throughout the cooling system. Fig. A.2: Decrease in survival rate throughout the complex only due to decays, estimated from energy and lengths of each system BAppendix: Proton Driver This section is devoted to the Proton Complex parameters choice. The proton driver of a future Muon Collider is required to deliver a proton-beam of at least 2 MW at a repetition rate of 5 Hz to the pionproduction target. The proton-beam energy must be in the multi-GeV range in order to maximize the pion yield. In addition, a particular time structure consisting of a single very short bunch, with a rms pulse length on the order of 2 ns, is needed to allow the muon beam to be captured efficiently in the cooling section. The proton bunch parameters are intimately connected and constrained by beam loading and longitudinal acceptance in the downstream muon accelerator systems and by the acceptance (in time, energy, and power) of the target and pion capture system. The study for the proton complex focused on two different options, the first considers a 5 GeV proton beam with a power of 2 MW and the high-level parameters are listed in 2.1 and 2.2, and the second considers a higher energy and higher power proton beam of 10 GeV and 4 MW, and the parameters are listed in Tables B.1 and B.2. These two options are equivalent to the luminosity scaling options. Figure B.1 is a schematics of the baseline for the proton complex for both energy options presented. A full energy linac delivers a pulse of H−to an accumulator ring, after that the pulses are transferred to a compressor ring and rotated longitudinally in order to reach the 2 ns rms bunch length. After the compressor a recombination transport line merge the bunches, which are 2 for now for both cases, and delivers a final single bunch to the target. 30 Consolidated Parameters Report – October 29, 2025 extracted in the middle of the chicane, by using solenoids with different diameters in order to create a gap for the high-energy protons. Shower simulation studies showed that such an extraction channel in the chicane needs to have a transverse size of a few tens of centimeters, which is challenging for the magnet design. In addition, an internal radiation shielding would be needed to protect the coils from particles, which are still lost in the chicane. The chicane design studies are presently still ongoing. Parameters Unit Num. micro bunches 21 Longit. emittance mm 46 Transv. emittance um 17000 Positive muon yield 1/GeV per p+ 0.024 Negative muon yield 1/Gev per p+ 0.018 Table C.8: Outgoing muon beam C.4 Buncher & Phase Rotator The buncher is comprised of a sequence of RF cavities. The cavity frequency is chosen to match the distance between nominal RF bunches, so that it varies along the length of the buncher. The phase is purely bunching. In the phase rotator, cavities are dephased so that the low energy tail of the beam sees an accelerating gradient and the high energy front of the beam sees a decelerating gradient. Cavities are placed in a two-cavity LINAC with 0.25 m separation between adjacent cavity pairs. Each cavity in the pair is independently phased. Transversely, the beam is contained in a 2 T field. DAppendix: Cooling D.1 Initial Cooling The Helical FOFO Snake (HFOFO) is a design for initial (pre-charge separation) 6D cooling of both signs of muon in a single channel. The HFOFO lattice is composed of alternating-polarity, inclined solenoids, as well as RF cavities and LiH wedge absorbers. Periodic rotations about both the xand z-axes are applied to the solenoids, as defined by the pitch and roll angles respectively. The effect of these rotations is the generation of a rotating dipole field which enables charge-agnostic focusing. A “matching section” comprising the first nine solenoids, characterized by unique parameters, is necessary to induce the hallmark helical orbits particles execute in the HFOFO channel. The subsequent portion of the channel, referred to here as the “steady-state," is built from repeated periods of six units corresponding to six periodic solenoid rotations (where a unit is defined as a set of one solenoid, the RF cavity within it, and the wedge absorber placed after it). Table D.1 contains those parameters which vary along the channel — that is, the rotations of solenoids in the matching and steady-state sections, in addition to the RF gradient. In Table D.2, a list of parameters which are consistent for the entire channel is given, including the solenoid geometries and further descriptions of the RF system. The set of six repeated z-rotations (described by roll angles) of solenoids in the steady-state channel are given in Table D.3, as are the angles of the repeated wedge absorber rotations (about the z-axis). 37 D. Appendix: Cooling Position of unit in lattice Coil pitch [deg] Coil roll [deg] RF gradient [MV/m] 1 0 0 20 2 0 0 20 3 0.0886 -122.4 20 4 0.1246 -23.6 20 5 0.0863 122.3 20 6 0.0817 -102.0 25 7 0.0969 25.3 25 8 0.1672 137.8 25 9 0.1226 -97.0 25 10-end 0.14 periodic (see additional table) 25 Table D.1: HFOFO full-channel variable parameters for matching (units 1–9) and steady-state (units 10–end) sections. Parameter Unit Value Number of solenoids per period 6 Period length mm 4200 Number of periods per channel 30 Coil length mm 300 Coil inner radius mm 420 Coil outer radius mm 600 Spacing between coil centers mm 700 RF frequency MHz 325 RF length mm 249 GH2density g/cm30.014 Table D.2: HFOFO full-channel constant parameters for matching and steady-state sections. Position of unit in period Periodic coil rolls [deg] Periodic wedge angles [deg] 1 240 -26.97 2 0 93.03 3 120 213 4 240 333 5 0 453 6 120 573 Table D.3: HFOFO periodic parameters. Finally, Table D.4 provides performance results from present G4beamline simulations of HFOFO. The emittances have been calculated using the ICOOL emitcalc script. Notably, these simulations use a MAP-era beam file containing only positive muons — though further studies are ongoing to assess the performance and acceptance of the design with more modern input beams. Corrections may be in order to adequately compare the performance to that of other designs. 38 Consolidated Parameters Report – October 29, 2025 Ntotal N150<p<350 MeV ε⊥[m] εL[m] Initial 11452 7666 0.01604 5.748 Final 5348 5139 0.003595 2.908 47% transmission 67% transmission Factor of 4.46 Factor of 1.98 Table D.4: HFOFO performance (with MAP-era µ+beam). Emittances calculated with emitcalc. D.2 Baseline Rectilinear Cooling The rectilinear cooling section consists of a number of solenoid magnets with dipole field superimposed. In the MAP design the dipole field was achieved by means of introducing a tilt in the solenoids but separate dipoles are proposed for this IMCC design. The rectilinear cooling lattice described below is stored in the MuonCollider-WG4 GitHub group, rectilinear repository as release (branch) 2024-09-27_release and described in [23]. The solenoid field is approximately sinusoidal with a period given by the cell length Lso that Bz(z, r = 0) = Bpeak sin(2πz/L). Cells in the Rectilinear B lattices are increasingly non-sinusoidal, with a component Bz(z, r = 0) = Bpeak sin(4πz/L)that gets stronger further down the B lattice. The peak Bzlisted in Table D.6 is the peak field on the axis of the solenoid. Fields may be higher in the conductor volume. RF cavities are modelled as perfect cylindrical pillbox cavities operating in TM010 mode. Several RF cavities are included within each cell. A thin conductive window electromagnetically seals the RF cavities so that the pillbox model is an adequate approximation to the real cavity field and the cavities can be assumed to be independently phased. The RF gradient listed in Table D.7 is the peak gradient. Updates for the A and B stages of the rectilinear cooling system have been developed, comprising of 10 "B-type" stages, denoted S1 through S10 that yields improved performance over the MAP lattice listed above and has been designed using 352 MHz RF and harmonics. The performance is summarised in Table D.5. Hardware parameters are described in Table D.6. In this lattice, the dipoles were simulated as a magnet independent of the solenoids which were not tilted and the dipole field is listed. 39 D. Appendix: Cooling εTεLε6D Stage Cumulative mm mm mm3Transmission Transmission % Start 16.96 45.53 13500 100 A-Stage 1 5.17 18.31 492.60 75.2 75.2 A-Stage 2 2.47 7.11 44.03 84.4 63.5 A-Stage 3 1.56 3.88 9.59 85.6 54.3 A-Stage 4 1.24 1.74 2.86 91.3 49.6 Bunch merge 5.13 9.99 262.5 78.0 38.7 B-Stage 1 2.89 9.09 76.07 85.2 33.0 B-Stage 2 1.99 6.58 26.68 89.4 29.4 B-Stage 3 1.27 4.05 6.73 87.5 25.8 B-Stage 4 0.93 3.16 2.83 89.8 23.2 B-Stage 5 0.70 2.51 1.32 89.4 20.7 B-Stage 6 0.48 2.29 0.55 88.4 18.2 B-Stage 7 0.39 2.06 0.31 92.8 17.0 B-Stage 8 0.26 1.86 0.13 87.9 14.9 B-Stage 9 0.19 1.72 0.06 85.2 12.7 B-Stage 10 0.14 1.56 0.03 87.1 11.1 Table D.5: Rectilinear cooling performance in terms of emittance reduction (transverse, longitudinal and 6D) and transmission per stage. Cell Stage Pipe Max. BzInt. β⊥DxOn-Axis Wedge Length Length Radius On-Axis ByWedge Len. Angle m m cm T Tm cm mm cm deg A-Stage 1 1.8 104.4 28 2.5 0.102 70 -60 14.5 45 A-Stage 2 1.2 106.8 16 3.7 0.147 45 -57 10.5 60 A-Stage 3 0.8 64.8 10 5.7 0.154 30 -40 15 100 A-Stage 4 0.7 86.8 8 7.2 0.186 23 -30 6.5 70 B-Stage 1 2.3 50.6 23 3.1 0.106 35 -51.8 37 110 B-Stage 2 1.8 66.6 19 3.9 0.138 30 -52.4 28 120 B-Stage 3 1.4 84.0 12.5 5.1 0.144 20 -40.6 24 115 B-Stage 4 1.2 66.0 9.5 6.6 0.163 15 -35.1 20 110 B-Stage 5 0.8 44.0 6 9.1 0.116 10 -17.7 12.5 120 B-Stage 6 0.7 38.5 4.5 11.5 0.087 6 -10.6 11 130 B-Stage 7 0.7 28.0 3.75 13 0.088 5 -9.8 10 130 B-Stage 8 0.65 46.15 2.85 15.8 0.073 3.8 -7 7 140 B-Stage 9 0.65 33.8 2.3 16.6 0.069 3 -6.1 7.5 140 B-Stage 10 0.63 29.61 2.0 17.2 0.069 2.7 -5.7 6.8 140 Table D.6: Rectilinear cooling cell hardware in terms of cell geometry, solenoid fields, dipole fields and wedge geometry 40 Consolidated Parameters Report – October 29, 2025 RF Frequency Num. RF RF Length RF Gradient RF phase MHz cm MV/m deg A-Stage 1 352 6 19 27.4 18.5 A-Stage 2 352 4 19 26.4 23.2 A-Stage 3 704 5 9.5 31.5 23.7 A-Stage 4 704 4 9.5 31.7 25.7 B-Stage 1 352 6 25 21.2 29.9 B-Stage 2 352 5 22 21.7 27.2 B-Stage 3 352 4 19 24.9 29.8 B-Stage 4 352 3 22 24.3 31.3 B-Stage 5 704 5 9.5 22.5 24.3 B-Stage 6 704 4 9.5 28.2 22.1 B-Stage 7 704 4 9.5 28.5 18.4 B-Stage 8 704 4 9.5 27.1 14.5 B-Stage 9 704 4 9.5 29.7 11.9 B-Stage 10 704 4 9.5 24.9 12.2 Table D.7: Rectilinear cooling cell RF parameters. 0ophase is bunching mode. Beam Size σx(σy) Beam Size σx(σy) Cell Center (max) Cell Start (min) mm mm A-Stage 1 48.6 (35.4) 38.6 (47.2) A-Stage 2 25 (22.1) 23.9 (23.6) A-Stage 3 15.6 (15.4) 15.7 (14.6) A-Stage 4 13 (11.9) 12.6 (12) B-Stage 1 28.4 (27.5) 23.9 (23.3) B-Stage 2 20 (20.3) 19.5 (17.4) B-Stage 3 16.4 (16.3) 12.3 (11.2) B-Stage 4 13.5 (13.9) 8.9 (7.9) B-Stage 5 9.8 (10) 6.2 (5.8) B-Stage 6 8.6 (8.4) 3.9 (3.8) B-Stage 7 7.7 (7.6) 3.3 (3.2) B-Stage 8 5.8 (5.6) 2.3 (2.3) B-Stage 9 5.2 (5.1) 1.7 (1.8) B-Stage 10 4.7 (4.2) 1.4 (1.4) Table D.8: Rectilinear cooling cell beam size at the start and center of the beam. Horizontally (and vertically). 41 D. Appendix: Cooling D.2.1 Low-Stress Rectilinear Cooling Upon review of the above solenoids, the radial stress was calculated, as shown in Table H.1. In response to this, a low-stress lattice option has been produced, the performance of which is displayed in Table D.9. The cell details in each stage is listed in Table D.10, and the resulting RF cavity parameters are in Table D.11. VARIANT εTεLε6D Stage Cumulative Low Stress mm mm mm3Transmission Transmission Start 16.96 45.53 13500 100 A-Stage 1 4.977 17.83 447.3 72.6 72.6 A-Stage 2 2.486 7.06 44.24 82.8 60.1 A-Stage 3 1.609 3.616 9.604 84.1 50.6 A-Stage 4 1.247 1.74 2.863 87.4 44.2 Bunch merge 5.13 9.99 262.5 78 34.6 B-Stage 1 2.892 9.239 77.77 85.3 29.5 B-Stage 2 2.025 6.418 26.96 90.9 26.8 B-Stage 3 1.214 3.972 5.943 87.2 23.4 B-Stage 4 0.8987 3.021 2.476 91.6 21.4 B-Stage 5 0.6868 2.528 1.224 90 19.3 B-Stage 6 0.4683 2.29 0.5099 85.3 16.5 B-Stage 7 0.3642 2.035 0.2718 88.4 14.5 B-Stage 8 0.2659 1.843 0.1307 84.5 12.3 B-Stage 9 0.1839 1.725 0.0586 81.4 10 B-Stage 10 0.1404 1.554 0.03027 82.7 8.3 Table D.9: New lattice with larger gaps and less solenoid stress. Rectilinear cooling performance in terms of emittance reduction (transverse, longitudinal and 6D) and transmission per stage. VARIANT Cell Stage Pipe Max. BzInt. β⊥DxOn-Axis Wedge Low Stress Length Length Radius On-Axis ByWedge Len. Angle m m cm T Tm cm mm cm deg A-Stage 1 1.9 110.2 28 2.5 0.095 72 -60 30 80 A-Stage 2 1.3 132.6 16 3.6 0.141 47 -56 21.5 100 A-Stage 3 0.9 80.1 10 5.5 0.152 31 -40 15 100 A-Stage 4 0.76 101.08 8 6.9 0.172 23 -35 14 110 B-Stage 1 2.2 50.6 23 3.3 0.118 34 -52 37 110 B-Stage 2 1.8 66.6 19 4 0.144 28 -52 28 120 B-Stage 3 1.5 90 12.5 4.9 0.144 19 -41 24 115 B-Stage 4 1.25 68.75 9.5 5.9 0.151 15 -35 20 120 B-Stage 5 0.85 45.9 6 8.8 0.110 10 -18 12.5 120 B-Stage 6 0.8 43.2 4.5 10.7 0.080 6 -10 11 130 B-Stage 7 0.8 32 3.8 11.5 0.078 5 -9.8 10 130 B-Stage 8 0.78 39 3 12.9 0.064 4 -7.1 7 140 B-Stage 9 0.78 40.56 2.3 13.5 0.059 3.5 -6.1 7.5 140 B-Stage 10 0.78 31.98 2 14.1 0.059 3.1 -5.7 6.8 140 Table D.10: New lattice with larger gaps and less solenoid stress. Rectilinear cooling cell hardware in terms of cell geometry, solenoid fields, dipole fields and wedge geometry 42 Consolidated Parameters Report – October 29, 2025 VARIANT rf Number of rf cell rf gradient rf phase Low Stress frequency rf cells length MHz cm MV/m deg A-Stage 1 352 6 20 25.7 19.9 A-Stage 2 352 4 20 26 23.6 A-Stage 3 704 5 10 31.6 22.2 A-Stage 4 704 4 10 31.6 23.7 B-Stage 1 352 6 22 22.5 32.8 B-Stage 2 352 5 22 23.6 27.1 B-Stage 3 352 4 22 23.2 25.5 B-Stage 4 352 3 22 24.1 27.9 B-Stage 5 704 4 10 27 26.4 B-Stage 6 704 4 8 31.8 25.6 B-Stage 7 704 4 8 31.3 22.7 B-Stage 8 704 4 8 25.9 15.9 B-Stage 9 704 4 8 23.8 15.4 B-Stage 10 704 4 8 24.3 13.6 Table D.11: New lattice with larger gaps and less solenoid stress. Rectilinear cooling cell RF parameters. 0ophase is bunching mode. D.3 Final cooling There are three lattice options for the final cooling in development. Each correspond to the initial conditions of the 6D cooling lattice before it. The first assumes MAP parameters of εT=300 µm,εL=1.5 mm. The second takes the beam from the B8 stage of the IMCC rectilinear cooling εT=260 µm,εL=1.8 mm, and the third takes the beam from the B10 stage of εT=140 µm,εL=1.5 mm. D.3.1 Final Cooling - from MAP initial conditions The final cooling lattice from MAP initial conditions is made of 10 high field solenoids, which alternate in polarity each cell, represented in Figure D.1. 10 matching low-field solenoids are placed between the two high-field solenoids, which have space sufficient to fit RF pillboxes, required to reach the kinetic energies and energy spreads referenced in Table D.12. The absorbers are modelled as a constant pressure of 70.8 kg/m3, which is unrealistic given the beam intensities towards the end of the final cooling lattice [24]. For this reason, the density x length is represented in Table D.12. 43 D. Appendix: Cooling Fig. D.1: Geometric overview of the Final Cooling lattice from MAP parameters, including Bz fieldon-axis. Red for +40 T solenoids, blue for -40 T solenoids, and purple for low-field matching solenoids. Correct relative inner and outer radii. Cell No εTεLKE σKE ρL(H2)Lsol BzT (loss) T (decay) Unit mm mm MeV MeV kg/m2m T % % 0 0.300 1.5 1.00 1 0.247 1.88 123.49 5.42 90.4 1.52 40 100.0 0.99 2 0.203 2.28 123.34 5.82 93.8 1.57 -40 100.0 0.96 3 0.165 2.83 100.41 5.25 78.2 1.35 40 100.0 0.91 4 0.126 3.98 85.49 5.07 80.6 1.38 -40 100.0 0.85 5 0.103 5.13 74.48 5.66 57.8 1.06 40 100.0 0.77 6 0.087 6.73 51.82 4.36 30.9 0.68 -40 100.0 0.67 7 0.060 11.82 32.01 2.40 21.4 0.54 40 95.1 0.55 8 0.045 20.76 18.28 1.30 7.4 0.34 -40 99.7 0.43 9 0.032 39.25 17.94 1.25 8.4 0.36 40 96.4 0.32 10 0.0222 71.72 14.70 1.21 6.4 0.33 -40 89.8 0.20 Table D.12: Overview of final cooling design from MAP initial conditions D.3.2 Final Cooling - from B8 Updated final cooling lattices were designed based on the output beam emittance from the 6D cooling lattices described in Section D.2. The overall cell layout follows the configuration shown in Figure D.1, except that the 0°-phase RF cavities used for phase rotation have been removed. Table D.13 summarizes the output and cumulative emittances at the end of each stage, with the initial emittance taken from BStage 8 in Table D.5. At the end of the cooling channel, the transverse emittance is reduced to 22.4 µm, satisfying the luminosity requirement, while the longitudinal emittance reaches 43 mm, which remains below the current requirement of the acceleration system. The main hardware parameters of the absorber, magnet, and RF system are listed in Tables D.14 and D.15. The peak magnetic field is kept below 42 T, and the RF frequency gradually decreases along the channel to match the increasing bunch length, as shown in Table D.16. 44 Consolidated Parameters Report – October 29, 2025 Stage εTεLε6D Cumulative mm mm mm3transmission % Start 0.26 1.8 0.12 100 Stage 0 0.21 2.5 0.11 99.6 Stage 1 0.16 5.2 0.14 90.1 Stage 2 0.12 8.7 0.13 79.8 Stage 3 0.095 10.3 0.098 72.5 Stage 4 0.063 15.1 0.064 65.5 Stage 5 0.041 22.7 0.039 55.5 Stage 6 0.032 32 0.035 52 Stage 7 0.0224 42.68 0.022 42.7 Table D.13: Short rectilinear final cooling cell performance parameters (latest version) Stage Stage length (m) Peak on-axis Bz (T) LH absorber length (m) ρL(H2)(kg/m2) Stage 0 2.754 33.6 0.692 48.99 Stage 1 5.195 -36 0.397 28.11 Stage 2 5.401 35.5 0.135 9.56 Stage 3 4.268 -41.8 0.053 3.75 Stage 4 5.204 40.9 0.043 3.04 Stage 5 6.836 -41.3 0.018 1.27 Stage6 5.17 38.4 0.012 0.85 Stage 7 5.565 -43.4 0.014 0.99 Table D.14: Short rectilinear final cooling cell magnet lattice parameters (latest version) Stage Frequency Number of RF cells Maximum gradient Phase RF cell length MHz MV/m ◦m stage 0 0 stage 1 142.9 5 9.2 26 1.25 stage 2 67.3 6 5 18.7 1.5 stage 3 52.7 3 4.9 50.2 0.75 stage 4 29.8 10 1.7 15.7 2.5 stage 5 15.3 14 1.5 23 3.5 stage 6 10 10 1.3 28.3 2.5 stage 7 8 11 1.2 40.9 2.75 Table D.15: Short rectilinear final cooling cell RF parameters. 0ophase is bunching mode. (latest version) Stage Final Pz Final energy spread Final cσ_t Units MeV/cMeV c Start 135 3.9 0.04932 Stage 0 95.4 5.3 0.06703 Stage 1 65 3.7 0.2813 Stage 2 53 2.1 0.4926 Stage 3 46.2 2.4 0.6547 Stage 4 36.1 1.8 1.074 Stage 5 31 1.7 1.465 Stage 6 30 1.7 2.492 Stage 7 28 1.6 3.307 Table D.16: Short rectilinear final cooling cell beam longitudinal parameters (latest version) 45 D. Appendix: Cooling D.3.3 Final Cooling - From B10 Another final cooling lattice was also designed based on the output emittance from B-Stage 10. As shown in Table D.17, this design reduces the transverse emittance to 23 µm, while the longitudinal emittance increases to 22 mm, which is nearly a factor of two smaller than that in Table D.13. This improvement results from the smaller initial transverse emittance, which allows for fewer cooling stages (absorbers) and therefore less beam-length growth caused by passage through the absorbers. The main hardware parameters of the absorber, magnet, and RF system are listed in Tables D.18 and D.19, and the corresponding longitudinal beam parameters are given in Table D.20. Stage εTεLε6D Cumulative mm mm mm3transmission % Start 0.14 1.5 0.03 100 Stage 0 0.12 1.9 0.03 99.5 Stage 1 0.08 5.2 0.034 90.6 Stage 2 0.053 7.7 0.023 77.9 Stage 3 0.041 10.9 0.019 71.9 Stage 4 0.029 15.7 0.014 66.8 Stage 5 0.023 22.1 0.012 61.4 Table D.17: Long rectilinear final cooling cell performance parameters (latest version) Stage Stage length (m) Peak on-axis Bz (T) LH absorber length (m) ρL(H2)(kg/m2) Stage 0 2.035 40 0.183 12.96 Stage 1 4.656 -29.3 0.255 18.05 Stage 2 4.628 39.4 0.055 3.89 Stage 3 3.89 -41 0.02 1.42 Stage 4 4.124 39.6 0.015 1.06 Stage 5 5.068 -42.7 0.0092 0.65 Table D.18: Long rectilinear final cooling cell magnet lattice parameters (latest version) Stage Frequency Number of RF cells Maximum gradient Phase RF cell length MHz MV/m ◦m stage 0 0 stage 1 131.8 6 6.6 14.5 1.5 stage 2 56.3 5 4.4 31.4 1.25 stage 3 25.5 6 2.9 17.4 1.5 stage 4 14.8 7 1.7 45.6 1.75 stage 5 11.5 9 1.3 41.3 2.25 Table D.19: Long rectilinear final cooling cell RF parameters. 0ophase is bunching mode. (latest version) 46 Consolidated Parameters Report – October 29, 2025 F.2 Fixed Field Acceleration Milestone 17 [30] outlines the possibility of using vertical-excursion Fixed-Field Accelerator (vFFA) [31] rings as alternatives to one or more of the RCS rings, giving example parameters for RCS1 and RCS4 greenfield equivalents. These would provide the possibility for acceleration unconstrained by magnet ramp rates, removing issues for power conversion and storage, and enabling the construction of rings with full-superconducting magnet technology (thereby enhancing power efficiency). The relative isochronicity of the vFFA concept mitigates the need for frequency cycling in the RF systems, and enables the possibility of on-crest acceleration for an increased acceleration efficiency at a given RF voltage. Table F.5 lists the design parameters of these FFA rings alongside key parameters for comparison to the RCS equivalents. However, the use of FFA arcs implies a closed orbit that moves as a function of energy. This increases requirements for element apertures. Milestone 17 presents a scheme for the implementation of dispersion suppressors to reduce the impact of this upon the RF systems. Depending on the specific execution of these schemes, further optimisation of the parameters in the included table could be possible to reduce peak fields and reduce the size of the machine by separating RF requirements from arc design requirements. Table F.5: FFA alternative tentative parameters Design Parameter Symbol Unit vFFA1 vFFA4 Orbit radius at centre of F-magnet r_0 m 953 5570 F-magnet bending angle θ_Frad. 0.01033 0.00786 Number of cells N_c 790 1000 F-magnet half-opening angle β_Frad. 0.0015640 0.0019700 D-magnet half-opening angle β_Drad. 0.0011800 0.0011660 F-magnet orbit inclination γ_Frad. 0.252 -0.492 vFFA normalised field index m 1/m 31.94 12.13 Comparison Parameter Circumference [m] m 5990 35000 Injection Energy [TeV] TeV 0.06 1.5 Extraction Energy [TeV] TeV 0.3 5 Ramp Rate [T/s] T/s 0 0 Vertical Excursion [m] m 0.048 0.099 Relative path length difference 0 0 Peak Dipole Field On Orbit [T] T 6.93 13.59 Peak Dipole Field (Good Field Region) [T] T 12.52 29.04 Drift length [m] m 1.18 1.03 Tune (0.382, 0.079) (0.460, 0.057) GAppendix: Machine-Detector Interface The beam-induced background arising from muon decay poses a significant challenge for the physics performance of a multi-TeV muon collider. The machine-detector interface relies on massive absorbers in close proximity to the interaction point (IP) to reduce the number of secondary particles reaching the detector. This section describes the geometrical features of the shielding and quantifies the flux of secondary background particles. In addition, the ionizing dose and displacement damage in different 53 G. Appendix: Machine-Detector Interface parts of the detector are presented. G.1 Nozzle geometry and material composition The innermost part of the machine-detector interface consists of a nozzle-like shielding, which defines the inner detector envelope. The nozzle extends from the last magnet (L∗= 6 m) to almost the IP and must be made of a high-Zand high density material to shield efficiently the electromagnetic showers induced by the decay electrons and positrons. All studies carried out so far were based on the slightly modified nozzle geometry than the one developed within the Muon Accelerator Program (MAP) [32, 33]. Although the MAP nozzle was optimized for a center-of-mass energy of 1.5 TeV, it has been used as a starting point for the first 10 TeV studies (see, for example, Refs. [34,35]). Fig. G.1: Left nozzle geometry dimensions. The blue layer is made of INERMET180 (registered trademark), a heavy tungsten alloy, while the green one is composed of borated polyethylene. z [cm] r [cm] Outer surface of nozzle 595 55 100 17.57 6 1 Outer surface of the borated polyethylene layer 595 51 100 13.57 Inner surface of the borated polyethylene layer 595 43 204.49 13.47 100 13.47 Inner aperture of the nozzle 595 1.78 100 0.3 15 0.6 6 1 Table G.1: Nozzle Dimensions Figure G.1 illustrates the modified MAP nozzle geometry in the z−rplane, where zis the beam axis 54 Consolidated Parameters Report – October 29, 2025 and ris the radial coordinate. The nozzle is assumed to have azimuthal symmetry around the z-axis. The figure shows only the nozzle on the left side of the IP; the second nozzle has the same shape but is mirrored with respect to the interaction point. The nozzle is assumed to consist mainly of INERMET180 (registered trademark), a tungsten-based alloy (blue color), with a layer of borated polyethylene on the outer surface (green color) to thermalize and absorb neutrons before they reach the detector. Using a tungsten alloy (instead of pure tungsten) is required to allow the manufacture of such shielding elements, however such a choice reduces slightly the shielding effectiveness of the nozzle due to the lower material density. The beam pipe connecting the two opposite nozzles is made of beryllium, with an internal radius of 2.3 cm and a thickness of 1 mm. The nozzle tip is located at a distance of 6 cm from the IP. The inner aperture of the nozzle features three different angles, with an aperture bottleneck at 100 cm from the IP. In the region between 100 cm and the first magnet at 600 cm, the inner nozzle surface increases and is defined by the required beam clearance to avoid direct halo losses on the aperture. The outer surface of the nozzle follows a conical shape, with two different angles. Near the interaction point, the inclination amounts to 10 degrees, which determines the angular acceptance of the detector. All the space outside the nozzle and the central beam pipe can be occupied by the detector. The present setup is of conceptual nature, without yet considering engineering aspects or a possible support structure for the nozzle. Table G.1 summarizes the coordinates of the inner aperture and outer surface of the nozzle, respectively. Table G.2 provides the material components of the nozzle. Component Density [g/cm3] Element Atomic Fraction (mass fraction if negative) EM Shower Absorber 18 W -0.95 Ni -0.035 Cu -0.015 Neutron Absorber 0.918 H 0.5 C 0.25 B 0.25 Table G.2: Material composition of nozzle G.2 Beam-induced background The number of background particles entering the detector per bunch crossing depends on the nozzle geometry, the nozzle material composition and the interaction region layout. Table 8.2 summarizes the number of secondary electrons, positrons, photons and neutrons reaching the detector in a 10 TeV muon collider. The numbers were obtained with FLUKA Monte Carlo simulations, considering the nozzle introduced in the previous section. The bunch intensity was assumed to be 1.8×1012 muons. Only secondary particles with energies above a given threshold value were considered (see Table G.3). Table G.3: Particle production and transport thresholds assumed in the background simulations. Particle type Threshold Electrons, positrons and photons 100 keV Hadrons and muons 100 keV Neutrons 0.01 meV 55 H. Appendix: Magnets The number of background particles presented in this section includes only the contribution from muon decay, which is expected to be the dominant source of beam-induced background. Other background sources can include muon halo losses on the aperture and incoherent electron-positron pair production. G.3 Ionizing dose and displacement damage in detector To evaluate the cumulative radiation damage in detector equipment, two quantities have been considered: the total ionizing dose and the 1 MeV neutron-equivalent fluence in Silicon. The former is a measure for the radiation damage in organic materials and compounds, while the latter is related to the displacement damage. HAppendix: Magnets Table 9.1 provides a summary of the magnet parameters for the study so far. The short muon lifetime (2.2 µs at rest) and production of bright muon beams results in a unique set of demands for magnet technologies, including large-bore high-field solenoids, dipoles and quadrupoles, compact ultra-high-field solenoids, and very fast-ramping dipoles. Activities within the scope of the IMCC has led to the most advanced set of main magnet conceptual designs and performance parameters. These parameters are an evolution of previous studies, in particular the U.S. Muon Accelerator Program (MAP) [36], extending the performance space by considering recent advances in magnet technology. This section will primarily consider the design challenges of the HTS 6D cooling solenoids, and the aperture-field developments of the collider dipoles and quadrupoles. H.1 Cooling Solenoids The overview of the cooling system parameters are in Section 4, which factors in our evolving understanding of acceptable solenoid parameter limits. We are presently performing analysis and optimization on this latest configuration. The 6D cooling section is crucial for producing a high-brightness muon beam, necessary for achieving the required luminosity at the interaction point. In this section the particles are cooled in the 6D phase space (position and momentum), the beam is focused and the bunch size is manipulated through the ionization cooling process. H.1.1 Baseline 6D Cooling solenoids In the current configuration, a total of 3054 solenoids are spread over a 0.85 km distance. There are 14 unique cell types, and 26 unique solenoid types. During the beam dynamics studies, we integrated a magnet design guide to constrain allowable magnet geometries and current densities based on key solenoid parameters (stresses σ, stored magnetic energy em, critical current density Jc). The limits are evaluated considering tape characteristics based on industrial production (Fujikura FESC-SCH ReBCO tape) [37]. The parameters and limits implemented (considering stand-alone, single solenoid operation) are: hoop stress, σθ<300 MPa; radial tensile stress, σr<20 MPa; and stored magnetic energy density, em<150 MJ/m3. The limits are identified from average single HTS tape characteristics with an adequate safety margin, ensuring a conservative approach given the considered homogenized coil representation. Additionally, a limit on the maximum current density was considered. The JEvalues were compared to the critical current density Jcvalues from the measurements reported in [38], aiming 56 Consolidated Parameters Report – October 29, 2025 Cell EMag eMag Coil JEBpeak σHoop (Max.) σRadial (Min.) σRadial (Max.) (MJ) (MJ/m3) (A/mm2) (T) (MPa) (MPa) (MPa) A1 5.4 21 A1-1 57.6 5.2 42 -8 0 A2 22.1 106.1 A2-1 149.5 11.6 194 -48 0 A3 5.0 49.5 A3-1 131.5 10.1 121 -25 0 A4 8.0 92.3 A4-1 193.2 13.8 225 -51 1 B1 9.1 49.8 B1-1 96.9 7.7 104 -24 0 B2 15.6 64.2 B2-1 102.1 9.2 131 -32 0 B3 36.9 105.9 B3-1 127.9 12.9 208 -57 0 B4 32.2 78.9 B4-1 103.0 10.6 281 -1 24 B4 32.2 78.9 B4-2 110.9 9.9 132 -49 1 B5 17.3 88.9 B5-1 179.6 14.7 295 -2 17 B5 B5-2 154.0 14.7 212 -57 1 B6 8.3 96.6 B6-1 214.4 15.3 339 -5 18 B6 B6-2 211.5 12.0 214 -6 6 B6 B6-3 212.7 12.4 162 -46 0 B7 8.2 87.7 B7-1 183.3 14.7 264 0 25 B7 B7-2 153.9 11.1 175 -4 10 B7 B7-3 210.3 13.2 180 -45 1 B8 8.8 92.1 B8-1 193.7 16.5 270 -6 38 B8 B8-2 202.1 15.4 270 -6 29 B8 B8-3 212.8 13.2 187 -50 0 B9 7.5 76.5 B9-1 256.4 17.2 281 0 37 B9 B9-2 88.4 10.0 95 -2 12 B9 B9-3 204.9 13.2 184 -46 0 B10 5.0 68.6 B10-1 326.8 19.2 378 049 B10 B10-2 146.1 11.1 105 -4 13 B10 B10-3 207.8 12.5 158 -43 1 Table H.1: Table of various parameters for 14 cell types and 26 unique solenoid types in the latest 6D cooling optics [23]. Values correspond to solenoids operating in their respective cells within a lattice. In bold, the parameters exceeding the considered design limits. The reported parameters will vary depending on the solenoid operational conditions (e.g., stand-alone or single cell operation). at 2.5 K margin for HTS operating at 20 K. We report in Tab. H.1 the main parameters of each cooling cell type and unique solenoid type. These values are computed based on the lattice design within Section D.2. Observing Tab. H.1, we find some solenoids exceed allowed design limits, primarily in terms of large hoop stresses (B6-1, B10-1) and tensile radial stresses (B4-1, B7-1, B8-1, B8-2, B9-1, B10-1). The most concerning solenoid is B10-1, with a hoop stress of 378 MPa, tensile radial stress of 49 MPa, and peak field on the coil of 19.2 T, exceeding its Jcby 114%. Critical to the solenoid configuration identified for the latest 6D cooling optics is the gap distance to the beam pipe and to the RF cavities. Following integration studies on the 6D cooling cell demonstrator, we found that larger gaps are needed to integrate the solenoids with RF cavities and absorbers within each cooling cell, making this solution not feasible from the point of view of cell integration. Therefore, another iteration of the design parameters is expected. The proposed solenoid configuration for the latest optic is thus a first step in the definition of 57 H. Appendix: Magnets an integrated design, combining the beam optics requirements with a more comprehensive engineering design of the cooling cell solenoids. Further optimization will be needed, starting from the initial set of solenoids and integrating the inputs from the WP8 cell integration studies. H.1.2 Low Stress 6D Cooling solenoids Cell EMag eMag Coil JEBpeak σHoop (Max.) σRadial (Min.) σRadial (Max.) (MJ) (MJ/m3) (A/mm2) (T) (MPa) (MPa) (MPa) A1 9.8 32.6 A1-1 68.6 6.4 66.1 -16.7 0.2 A2 38 72.7 A2-1 94.7 10.7 149.2 -40 0.7 A3 9.1 87.5 A3-1 168.5 11.9 188.4 -41.3 1.5 A4 13.1 83.9 A4-1 164.6 14 218.5 -49.6 5.6 B1 13.1 13.8 B1-1 32.1 5 33.5 -5.5 0.1 B2 25.4 31.3 B2-1 52.3 7.5 71.3 -14 0.2 B3 32.9 44.1 B3-1 84.6 8.2 154.3 -2.3 5.2 B3 B3-2 67.3 9.3 84.9 -22.3 0.3 B4 47.5 88 B4-1 115.2 9.2 231.5 -3.2 16.4 B4 B4-2 110.1 12.3 176 -52.7 1 B5 11.2 51 B5-1 141.6 12.2 220.1 -7 10.8 B5 B5-2 113.4 12 112.6 -32.9 3.5 B6 14.8 66.7 B6-1 183.4 13.8 276.3 -42.4 14.3 B6 B6-2 132.8 12.2 184.1 -161.3 7.9 B6 B6-3 136.3 10.8 106.5 -43.1 1.1 B7 10.8 47.8 B7-1 220.2 14.5 294.3 -26.4 13.8 B7 B7-2 113 9.4 127.8 -95.3 5.4 B7 B7-3 116.2 10.2 81.5 -26.4 1 B8 6.1 27.1 B8-1 221.6 15.3 293.3 -13.8 23.7 B8 B8-2 115.2 6.1 114.8 -17.4 6.6 B8 B8-3 78.6 6 23.2 -13.8 0.3 B9 15 48.9 B9-1 223 15.7 301.4 -64.4 28.8 B9 B9-2 107.3 7.7 192.3 -20.5 17.4 B9 B9-3 106.6 10.3 74.8 -64.9 0.7 B10 7.2 21.2 B10-1 254.6 16.5 333.6 -19.8 30.9 B10 B10-2 106.7 6.3 117.5 -18.9 8.8 B10 B10-3 65.6 8.3 30.2 -19.9 1.3 Table H.2: New lattice with larger gaps and reduced solenoid stress (low stress variant). In bold, the parameters exceeding the considered design limits. The rectilinear cooling complex has an alternative lattice in Section D.2.1, with the aim of reducing the coil stresses and enlarge the gap distance between the solenoids and the other integrated cell systems (beam pipe, RF cavity, absorbers), in response to the investigation of Section H.1.1. The recalculated stresses are reported in Table H.2. In lattice operation, only three solenoids showed values exceeding the positive radial stress limit (B8-1, B9-1, B10-1), with B9-1 and B10-1 exceeding the hoop stress limit. This is expected, since these three magnets exhibit also the highest peak field values on coils (over 15 T) in a nested coil configuration. An improvement on the feasibility of the 6D cooling magnet configuration has been made in this alternative layout, with higher radial and axial gaps separating the different cell systems. A coil optimization is needed to further increase the gaps, considering the inputs from the 58 Consolidated Parameters Report – October 29, 2025 cooling cell demonstrator study, aiming also to lower the stresses in the last three B-type cells. This variant is not yet considered part of the baseline design due to its lower performance. Hence, further iterations in the design parameters for this lattice version are expected. H.2 Collider Magnets Section 6presents the collider parameters, including the radiation shielding requirements from muon decay. To achieve a compact ring while allowing sufficient shielding, the ARC and Interaction Region (IR) magnets must feature high magnetic fields and large apertures. The main arc magnets are combined-function magnets (dipole/quadrupole and dipole/sextupole) designed for magnetic fields up to 16 T and 160 mm aperture, though this exceeds current technological limits and requires further optimization. The IR quadrupoles are expected to reach magnetic fields up to 20 T and apertures up to 200 mm. Fig. H.1: Performance upper-limit plots for ReBCO-based magnets. Top left: A–B plots for dipoles at 20 K. Top right: A–G plots for quadrupoles at 4.5 K. Bottom: B–G plots for combined-function magnets at 20 K (left) and 4.5 K (right). Analytical evaluations based on sector-coil geometries were used to generate performance limit plots – A–B (aperture vs. field) for dipoles, A–G (aperture vs. gradient) for quadrupoles, and B–G (field vs. gradient) for combined-function magnets—considering NbTi, Nb3Sn, and ReBCO superconductors. –NbTi (1.9 K): inadequate due to low margins and high energy deposition. –Nb3Sn (4.5 K): viable up to 14 T, suitable for ∼3 TeV machines but insufficient for some of the magnet performances required for the 10 TeV. 59 I. Appendix: Radiofrequency Cavities –ReBCO: best-performing option with high fields (10–20 K operation), presently considered as baseline, though R&D is needed to address cost and quench protection challenges. If ReBCO costs are reduced by a factor 3–4, feasible designs could span 14–16 T with 100–140 mm apertures at operating temperature in the range 4.5 K - 20 K. For IR quadrupoles, operation at 4.5 K could enable up to 300 T/m gradients with apertures up to 140 mm. Asemi-analytic design tool has supported fast iteration with beam dynamics, cryogenics, and energy deposition studies. The resulting performance limit plots for dipoles, quadrupoles, and combinedfunction magnets are shown below in Table H.1. IAppendix: Radiofrequency Cavities I.1 RF systems for rectilinear cooling The preliminary RF cavity design for each stage of the rectilinear cooling channel was developed based on the shape presented in [39] following the beam dynamics specification in Table D.7. The other geometrical parameters characterizing the cavity shape are chosen to maximize the shunt impedance (R/Q ·Q0) and reduce surface losses (Pdiss) on the windows and cavity walls. The peak surface electric field (Epeak) is also minimized to avoid RF breakdown risk. The RF cavity frequency (f0), the cavity length (Lcav), and the nominal RF gradient along the cavity axis (Enom) for the studied RF cavities are reported in Table D.7. Table I.1 summarizes the relevant RF figures of merit computed for the operating frequencies of the studied cavities. Most of the power is dissipated in the cavity walls. Q0tfDF R/Q Pdiss Pdiss,Be Pdiss Epeak,Cu Epeak,Be 104µs 10−4ΩMW/cavity - MV/m MV/m Stage A1 3.06 31.203 1.17 171.73 4.25 0.377 11.72 27.383 Stage A2 3.14 32.087 1.21 149.68 4.34 0.085 23.249 26.511 Stage A3 2.20 11.248 0.43 160.36 2.06 0.201 20.802 31.507 Stage A4 2.22 11.345 0.43 150.21 2.21 0.085 27.873 31.829 Stage B1 3.91 39.954 1.51 183.70 2.678 0.23 12.162 21.25 Stage B2 3.56 36.323 1.37 170.47 2.807 0.164 15.251 21.757 Stage B3 3.15 32.148 1.21 141.27 4.07 0.031 26.175 24.429 Stage B4 3.59 36.71 1.38 154.02 3.92 0.009 27.732 22.823 Stage B5 2.23 11.366 0.43 140.85 1.18 0.026 24.116 22.027 Stage B6 2.22 11.36 0.43 137.40 1.89 0.007 33.288 26.514 Stage B7 2.22 11.354 0.43 136.87 1.97 3.08 ×10−335.25 25.981 Stage B8 2.22 11.347 0.43 137.39 1.79 8.32 ×10−434.67 22.885 Stage B9 2.22 11.344 0.43 138.11 2.14 3.16 ×10−438.528 23.268 Stage B10 2.22 11.342 0.43 139.06 1.51 1.56 ×10−432.522 18.341 Table I.1: RF figures of merit for the RF cavities in the rectilinear cooling channel The filling time tf, which is the time required to fill the cavity to the nominal voltage Vnom =EnomLcav, is given by: tf≈2QL ω0 ln 2βc βc−1,(I.1) where QL=Q0/(1 + βc), with Q0being the intrinsic quality factor, βcthe coupling factor, and ω0is 60 Consolidated Parameters Report – October 29, 2025 the angular frequency of the cavity’s operating mode. The beam duty factor (DF ) can be calculated as the ratio between the average power and the peak dissipated power: DF =Pave Pdiss =R∞ 0P(t)dt·fb V2 acc/(R/Q ·Q0),(I.2) where P(t)is the time-dependent power calculated from the cavity voltage profile and Vacc =TTF · Vnom the accelerating cavity voltage, with TTF being the Transit-Time factor, given by: TTF =Rzmax zmin Ezejkz dz Rzmax zmin Ezdz ,(I.3) where k=ω0/(βc)is the wave number with cbeing the speed of light in a vacuum and βthe relativistic velocity factor. The geometric shunt impedance, R/Q, is calculated, considering the TTF as: R Q=|Vz(0,0)|2 ω0U0 TTF2,(I.4) where U=ω0is the energy stored in the cavity. Table I.4 reports the power requirements for each stage of the cooling channel. The peak input RF power is given by: Pg=Pdissβc.(I.5) The duty factor of the RF power source (DFg) is given as the ratio between the average power of the generator and the peak input RF power. DFg=Pave,g Pg =Pgtf·fb Pg ,(I.6) The total plug power for the RF systems was calculated considering the generator (ηG) and modulator (ηM) efficiencies reported in Table I.2 as: Pg,ave,tot =NcavPave,g ηGηM ,(I.7) where Ncav is the total number of cavities for each stage. Parameters Symbol Unit Value Coupling factor βc1.2 Bunch repetition frequency fbHz 5 Generator efficiency ηG0.7 Modulator efficiency ηM0.9 Table I.2: RF parameters for the rectilinear cooling channel For the RF frequency, cavity length and nominal RF gradient of the rectilinear cooling RF system, please refer to Table D.7. Table I.3 displays in addition the RF cavity window radius, window thickness and the relativistic beta of the muon beam at each stage. 61 I. Appendix: Radiofrequency Cavities Window Window Relativistic radius thickness β mm µm - Stage A1 240 120 0.923 Stage A2 160 70 0.894 Stage A3 100 45 0.894 Stage A4 80 40 0.901 Stage B1 210 100 0.886 Stage B2 190 80 0.885 Stage B3 125 50 0.887 Stage B4 95 45 0.886 Stage B5 60 30 0.889 Stage B6 45 20 0.888 Stage B7 38 20 0.887 Stage B8 28 20 0.884 Stage B9 23 10 0.881 Stage B10 20 10 0.884 Table I.3: Beam dynamics specifications for the RF cavities in the rectilinear cooling channel PgDFgNcav Pg,tot Pg,av Pplug,tot MW/cavity 10−4MW kW kW Stage A1 5.094 1.560 348 1772.7 277.09 439.83 Stage A2 5.21 1.610 356 1854.9 297.87 472.82 Stage A3 2.468 0.567 405 999.4 56.70 90.00 Stage A4 2.655 0.573 496 1317.1 75.41 119.70 Stage B1 3.214 2.077 132 424.2 88.1 139.843 Stage B2 3.368 2.097 185 623.1 130.682 207.432 Stage B3 4.882 1.611 240 1171.6 188.801 299.684 Stage B4 4.701 1.843 165 775.673 142.945 226.897 Stage B5 1.419 0.573 275 390.1 22.37 35.51 Stage B6 2.262 0.71 220 497.7 35.35 56.11 Stage B7 2.363 0.613 160 378 23.17 36.783 Stage B8 2.143 0.615 284 608.5 37.449 59.443 Stage B9 2.573 0.571 208 535.1 30.556 48.517 Stage B10 1.806 0.572 188 339.8 19.434 30.848 Table I.4: RF power requirements in the rectilinear cooling channel I.2 RF systems for low-energy acceleration In the low-energy acceleration, only the design of RLA2 is being considered for the computation of RF parameters. The baseline cavity geometry is chosen to be the LEP2 cavity. A summary of the assumed parameters can be found in Table I.5. For the calculation of the losses in the power generation, the parameters of the ILC-powering system were used (Table I.7). The resulting powering parameters for the RLA2 cavities can be found in table I.6. 62 Consolidated Parameters Report – October 29, 2025 Fig. J.2: subdivision of he the total power in series (SPS style) Fig. J.3: resonating circuits: full wave resonance (left), switched resonance (right) An example of transient with the switched resonance circuit is shown in Fig. J.6. 69 J. Appendix: Power Converters Fig. J.4: full wave resonance example Fig. J.5: Switched resonance principle Fig. J.6: Switched resonance example 70 Consolidated Parameters Report – October 29, 2025 J.4 The control problem Tables J.1 and J.2 show some parameters related to the quality of control. In particular they refer to: Pulse-to-pulse repeatability @ ±2σ: This means that on 95% of the pulses, the maximum absolute difference between the current at any time instant of any pulse and the average of them is less than 100 ppm. Control accuracy: This means that if we have two separate circuits and we need the currents to be the same in both of them, the control will not be able to make it more accurately than that. In both cases the tables report a target value rather than a limit. We still don’t know the statistical parameters of the charger and the jitter of the IGBT+driver; therefore it is difficult to say if we can fit in. Simulations with educated guess values, show, nevertheless, that the reported values would represent a limit with respect to what it is possibly achievable. KAppendix: Impedance Transverse HOMs generated by the TESLA cavities would be the main impedance source for the RCS chain. Table K.1 details the shunt impedance, quality factor and resonance frequency of the HOMs considered. Transverse coherent stability simulations were performed to evaluate the impact of the RF cavities and vacuum chambers. To mitigate the instabilities, a transverse damper system can be used to damp the transverse centroid motion of the bunches, and/or chromaticity can be introduced with sextupoles. Parametric scans were performed to find if those are needed and, if necessary, the chromaticity Q′required. The chromaticity was scanned from Q′=−20 to Q′= +20, and the transverse damper from a 4-turn to a 100-turn damping time, with an additional case without damper. Tracking simulations were performed using Xsuite [44] and PyHEADTAIL [45]. The bunch motion is simulated through the complete RCS chain. Muon decay is not included in these simulations, therefore the bunch intensity remains constant through the chain, equal to the intensity of 2.7×1012 muons per bunch at injection in RCS 1. Results showed that a positive chromaticity of Q′= +20 is needed in the accelerators to stabilize the beams and leave enough margin for some initial transverse offset of the bunches, and a 20-turn transverse damper also helps stabilize the beams [46,47]. K.1 Impedance model for the 10 TeV collider ring In the 10 TeV collider ring, the main impedance source would be the resistive-wall contribution from the magnets’ vacuum chamber. To protect the superconducting magnet coils from muon decay induced heating and radiation damage, a tungsten shield is proposed to be the inserted in the magnet cold bore as detailed in Section 12 and described in Ref. [8]. Previous parametric studies performed with Xsuite and PyHEADTAIL showed that a minimum chamber radius of 13 mm, together with a copper coating on the inner diameter are required to ensure coherent transverse beam stability. The current dipole magnet radial build detailed in Table 6.2 foresees a23.5 mm inner radius, with a 10 µmcopper coating. The vacuum chamber properties used for the impedance model computation are summarized in Table 11.3. A particularity of the collider ring is its isochronous operation (i.e. with η≈0) [48], obtained with the flexible momentum compaction cells described in Section 6. This is to avoid the large RF voltage that 71 K. Appendix: Impedance Frequency fres Rs QQ factor Shunt impedance Rs GHz [kΩ/m] [1×104] [MΩ/m] 1.659 0.10 31.432.61 1.705 1.05 1.35 14.16 1.706 1.21 1.34 16.27 1.728 0.97 0.0413 0.4 1.729 0.45 0.0381 0.17 1.736 1.25 0.0516 0.64 1.737 0.95 0.0574 0.54 1.761 0.35 0.583 2.04 1.762 0.28 0.621 1.72 1.788 0.16 0.867 1.43 1.789 0.18 0.890 1.61 1.798 0.11 1.23 1.29 1.799 0.10 1.21 1.27 1.865 0.79 3.91 30.87 1.865 0.83 4.12 34.07 1.874 1.09 3.88 42.32 1.874 1.07 4.39 47.14 1.88 0.22 4.23 9.38 1.88 0.24 5.15 12.21 2.561 0.13 0.0620 0.08 2.561 0.12 0.0527 0.07 2.577 2.05 0.364 7.46 Table K.1: HOMs from TESLA cavity, complete table, for a single cavity. RCS1 RCS2 RCS3 RCS4 Number of cavities 700 380 540 3000 Table K.2: RCS impedance model assumption for number of TESLA cavities would be needed to bunch beams with very short length and large energy spread. However this freezes the synchrotron motion of the particles within the bunch and can lead to beam breakup instabilities such as those encountered in Linacs [49]. Transverse coherent beam stability simulations were performed with Xsuite and PyHEADTAIL, including the effect of muon beam decay [10]. The beam parameters used for these simulations are summarized in Table K.3. With a chromaticity of Q′= 0, the beam becomes unstable over its lifetime in the collider, leading to large transverse emittance growth [10]. A slightly positive chromaticity of Q′= +2 is needed to introduce a betatron frequency spread that helps stabilize the beam. 72 Consolidated Parameters Report – October 29, 2025 Parameter Unit Value Circumference m10 000 Beam energy TeV 5 Bunch intensity at injection muons/bunch 1.80 ×1012 1σbunch length mm 1.5 Longitudinal emittance ϵl=σzσEMeV m 7.5 Transverse normalized emittance µm rad 25 Momentum compaction factor 0 Total RF voltage MV 0 Table K.3: 10 TeV collider machine and beam parameters. LAppendix: Demonstrators L.1 CTF3 Building background and current use The TT7 option has been extensively studied in 2024, the results of which are shown in Table L.1. Civil engineering studies reveal this option to be more expensive and complex than initially expected. for this reason we launched a new study to explore the suitability of reusing the CTF3 building to host the demonstrator facility. The reason not to consider it as a first instance was the fact that at the moment there is not an existing extraction system in the CERN PS that could send beam towards CTF3, in contrast to TT7 where the simple installation of a dipole in a transfer line would have provided an option with less impact on operating machines. The CTF3 building hosted the LIL (Linear Injector of LEP) machine and was later dedicated to the experimental activities around the CLIC study for linear colliders. Although there is no extraction to it, CTF3 has already many characteristics that are needed for the Demonstrator, namely sufficient length that would be sufficient not only for the facility but also for eventual future extensions, a Klystron gallery and all the infrastructure and services necessary to operate such a facility. Moreover, as former building for the injector of LEP, it has a connection to the PS tunnel and therefore no major civil engineering works will be needed to reconnect it to the PS. Only a well-shielded target area shall have to be created, with therefore the hope that costs and efforts can be mostly concentrated on the components of interest. The beamline parameters of a muon cooling demonstrator at the CTF3 facility are displayed in Table L.2. Today CTF3 hosts the CLEAR facility, whose continuation is fully compatible with the new facility. L.2 Proposed demonstrator layout at CTF3: – Extraction. Protons would be extracted from the PS and transported to CTF3 by reopening and adapting the historic link. – Floor usage. Depicted in Figure L.1: – The lower floor hosts the proton transfer line, target station, pion decay channel, magnetic chicane, beam-preparation system, matching section and the cooling-cell gallery. – The upper floor (gallery) hosts klystrons, with waveguide penetrations to the cooling cell gallery—reusing existing infrastructure instead of building a new surface hall. Details of the CTF3 klystrons are in Table L.4. 73 L. Appendix: Demonstrators Area Parameter Name Value Unit Proton Beam Beam Energy 14 GeV Protons/pulse 1×1013 Protons Pulse rep. rate 0.064 Hz (15.6s) Avg beam power 1.5 kW Avg beam power (target assumption) 5 kW RMS pulse length 7.65 ns Proton transfer line Number of dipoles 4 (H), 4 (V) - Number of quadrupoles 7 - Number of correctors 5 - Target Proton Beam Energy 14 GeV Proton Beam RMS size 2 mm Target Material Graphite - Target Length 90 cm Target Radius 0.6 cm Horn Current 220 kA Ltot 200 cm Target Pion Momentum Range 210 – 330 MeV/c Target Pion ϵTacceptance 2 mm rad Simulated Pion Yield per POT 7.90 ×10−4Remote handling YES - Decay channel Decay Channel Lattice 3 quad triplets - & magnetic chicane Decay Channel Length 9.5 m Pion Momentum (Nominal) 270 MeV/c Pion Momentum Acceptance ±50% % Target Muon Momentum Range 190 – 210 MeV/c Target Muon ϵTacceptance 2 mm·rad Chicane Type 3-bend - Dispersion at Chicane En -0.4 m βat BPS Injection 3 m Beam preparation system Number of RF cavities 16 - RF peak gradient 15 MV/m RF phase 0 degrees RF frequency 704 MHz Dipole field 0.67 T Dipole length 1.04 m Table L.1: TT7 Beamline parameters – Target area. Located around the former combiner-ring centre; the layout permits the construction of a target area with limited works and independent access relative to CLEAR. L.2.1 Work underway - Scope of current studies – Beamline & optics. End-to-end lattice from PS extraction to the target; decay channel, momentum-selection chicane and BPS matched to the cooling section (baseline “B5-like” cell). – Integration & access. 3D integration of the tunnel straight and gallery; installation/maintenance scenarios; co-existence planning with CLEAR. 74 Consolidated Parameters Report – October 29, 2025 Area Parameter Name Value Unit Proton Beam Beam Energy 14 GeV Protons/pulse 1×1013 Protons Pulse rep. rate 0.064 Hz (15.6s) Avg beam power 1.5 kW Avg beam power (target assumption) 5 kW RMS pulse length 7.65 ns Extraction Extraction dipole (New, after PS septa) 1 - Bumper magnets 4 - Septa 2 - KFA71 Kicker 1 - Proton transfer line Number of dipoles 1 - Number of quadrupoles 5 - Number of correctors TBD - Target Proton Beam Energy 14 GeV Proton Beam RMS size 2 mm Target Material Graphite - Target Length 90 cm Target Radius 0.6 cm Horn Current 220 kA Ltot 200 cm Target Pion Momentum Range 210 – 330 MeV/c Target Pion ϵTacceptance 2 mm rad Simulated Pion Yield per POT 7.90 ×10−4Remote handling YES - Decay channel Decay Channel Lattice 3 quad triplets - & magnetic chicane Decay Channel Length 9.5 m Pion Momentum (Nominal) 270 MeV/c Pion Momentum Acceptance ±50% % Target Muon Momentum Range 190 – 210 MeV/c Target Muon ϵTacceptance 2 mm·rad Chicane Type 2-bend - Dispersion at Chicane End 0 m βat BPS Injection <1 m Beam preparation system Number of RF cavities 16 RF peak gradient 15 MV/m RF phase 0 degrees RF frequency 704 MHz Dipole field 0.67 T Dipole length 1.04 m Matching section TBD - - Table L.2: CTF3 Beamline parameters – Assembly/disassembly. Removal of remaining CLIC demonstrator hardware where needed; definition of transport paths and lifting means. – Civil engineering. Reopening and adapting the PS link; localized works for the target area, access enlargements and main patio improvement; no enlargement of the main gallery and no new surface building are foreseen. 75 L. Appendix: Demonstrators Fig. L.1: CTF3 Area Definition: Proton extraction (light green), Proton Transfer line (cyan), Target area (red), pion decay channel (magenta), magnetic chicane (peach), proton and pion dump (grey), beam preparation system (orange), matching section (dark green), cooling cell channel (yellow). Area Parameter Name Value Unit Proton transfer line Gallery length 22.3 m Gallery width 5.3 m Gallery height 3 m Target area Gallery length 5 m Gallery width 11 m Gallery height 3 m Pion Decay channel Gallery length 9 m Gallery width 3 m Gallery height 5 m Magnetic chicane Gallery length 11 m Gallery width 3 m Beam Preparation system Gallery length 5 m Gallery width 3 m Matching section Section length 14 m Cooling channel Channel length 36 m Channel width 3 m Channel height 2.5 m Number of cooling cells 30 - Klystron gallery Gallery length 41.5 m Gallery width 6.5 m Gallery height 5 m Number of klystrons 15 - Table L.3: CTF3 Site-specific parameters – Services. Reuse of surrounding power, cooling-water and ventilation with targeted upgrades; RF plant staged in the gallery. – Radiation protection. RP modelling of the target/shielding and an operational zoning scheme that does not interfere with CLEAR. 76 Consolidated Parameters Report – October 29, 2025 Area Parameter Name Value Unit Klystron RF Frequency 704.4 MHz Modulator Scandinova K200 Klystron Voltage 125 kV Klystron Current 242 A Input power 1320 W klystron Efficiency 0.75 Modulator output power 30.25 MW Klystron Output Power 22.69 MW RF system rep. rate 5 Hz RF pulse length 15 us High voltage pulse length 17 us RF power average 1701.56 W Modulator efficiency 0.9 modulator power consumption 2856.94 W klystron solenoid power consumption 5000 W Total average power comsumption 7856.94 W Table L.4: CTF3 Klystron parameters L.2.2 How CTF3 compares to TT7 – What TT7 would need: To host the same demonstrator, TT7 would require tunnel enlargement (≈+3 m width and +1–1.4 m height over tens of meters) and a new surface building (klystrons and services), with access road modifications. – What CTF3 avoids: CTF3 already provides the straight tunnel and the klystron gallery; only local, low impact works (PS link, access improvements, patio/penetrations, target area) are foreseen. Installation can be scheduled outside the accelerator access chain, with no apparent interference with CLEAR. Table L.3 displays the general CTF3 area dimensions. L.3 Net assessment CTF3 is simpler and more cost-efficient in every major aspect except one: the new PS extraction/transfer to CTF3, which is the principal project challenge and integration work. MAppendix: CERN Civil Engineering The Collider Complex is displayed in Figure M.1, presented below. An injector complex has been designed and implemented, initiating at LINAC 4 and ultimately, injecting into a new 10 km Collider Ring from the LHC. The LINAC 4, SPL and ARCR (Accumulator Ring Compressor Ring) are aiming to be equivalent to the Proton Driver as described in Section 2. The entirety of the complex’s surface works would be constructed on CERN land across both the Meyrin and Prévessin sites, minimising territorial and environmental impacts. 77 M. Appendix: CERN Civil Engineering Structure Length (m) Cross Section LINAC 4 SPL SPL to SPS Transfer 650 4m SPS sector Transfers to Prévessin 930 4m & Single Width Tunnel ARCR 628 200m Ring, Double Width Tunnel Target 50 50m x 30m Cooling 1000 Double Width Tunnel w/ Surface Structure Cooling to SC LINAC Transfer 100 Single Width Tunnel SC LINAC 200 Double Width Tunnel w/ Surface Structure SC LINAC to RLA 1 Transfer 110 Single Width Tunnel Racetrack (RLA 1) 700 Single Width Tunnel w/ Surface Structure RLA 1 to RLA 2 Transfer 600 Single Width Tunnel Racetrack (RLA 2) 2300 Single Width Tunnel w/ Surface Structure RLA 2 to SPS Transfer Lines (2: µ+, µ−) 1010 4m SPS SPS to LHC Transfer Lines (TI12) 536 3.5m SPS to LHC Transfer Lines (TI18) 258 3.5m LHC LHC to Collider Ring Transfer 4012 4m MUON Collider Ring 10000 5.5m Table M.1: Muon Collider Sequence at CERN. (Italics shows existing tunnels). "Single Width" refers to a (5m x 4m) tunnel, whereas "Double width" refers to a (8m x 4m) tunnel. Fig. M.1: Muon Collider Complex. 78