Abstract: Hadrontherapy with protons and carbon ions is a fast developing methodology in radiation oncology. The accelerators used and planned for this purpose are reviewed starting from the cyclotrons used in the thirties. As discussed in the first part of this paper, normal and superconducting cyclotrons are still employed, together with synchrotrons, for proton therapy while for carbon ion therapy synchrotrons have been till now the only option. The latest developments concern a superconducting cyclotron for carbon ion therapy, fast-cycling high frequency linacs and 'single room' proton therapy facilities. These issues are discussed in the second part of the paper by underlining the present challenges, in particular the treatment of moving organs.

Abstract: A multi-TeV muon collider offers a spectacular opportunity in the direct exploration of the energy frontier. Offering a combination of unprecedented energy collisions in a comparatively clean leptonic environment, a high energy muon collider has the unique potential to provide both precision measurements and the highest energy reach in one machine that cannot be paralleled by any currently available technology. The topic generated a lot of excitement in Snowmass meetings and continues to attract a large number of supporters, including many from the early career community. In light of this very strong interest within the US particle physics community, Snowmass Energy, Theory and Accelerator Frontiers created a cross-frontier Muon Collider Forum in November of 2020. The Forum has been meeting on a monthly basis and organized several topical workshops dedicated to physics, accelerator technology, and detector R&D. Findings of the Forum are summarized in this report.

Abstract: The objective of this work is the evaluation of the risk of suffering a multipactor discharge in an S-band dielectric-assist accelerating (DAA) structure for a compact low-energy linear particle accelerator dedicated to hadrontherapy treatments. A DAA structure consists of ultra-low loss dielectric cylinders and disks with irises which are periodically arranged in a metallic enclosure, with the advantage of having an extremely high quality factor and very high shunt impedance at room temperature, and it is therefore proposed as a potential alternative to conventional disk-loaded copper structures. However, it has been observed that these structures suffer from multipactor discharges. In fact, multipactor is one of the main problems of these devices, as it limits the maximum accelerating gradient. Because of this, the analysis of multipactor risk in the early design steps of DAA cavities is crucial to ensure the correct performance of the device after fabrication. In this paper, we present a comprehensive and detailed study of multipactor in our DAA design through numerical simulations performed with an in-house developed code based on the Monte-Carlo method. The phenomenology of the multipactor (resonant electron trajectories, electron flight time between impacts, etc.) is described in detail for different values of the accelerating gradient. It has been found that in these structures an ultra-fast non-resonant multipactor appears, which is different from the types of multipactor theoretically studied in the scientific literature. In addition, the effect of several low electron emission coatings on the multipactor threshold is investigated. Furthermore, a novel design based on the modification of the DAA cell geometry for multipactor mitigation is introduced, which shows a significant increase in the accelerating gradient handling capabilities of our prototype.