A muon collider would enable the big jump ahead in energy reach that is needed for a fruitful exploration of fundamental interactions. The challenges of producing muon collisions at high luminosity and 10 TeV centre of mass energy are being investigated by the recently-formed International Muon Collider Collaboration. This Review summarises the status and the recent advances on muon colliders design, physics and detector studies. The aim is to provide a global perspective of the field and to outline directions for future work.

We present a model which describes proton scattering data from ISR to Tevatron energies, and which can be applied to collimation in high energy accelerator

In this paper we present a new lattice design for a 30–350 MeV scaling fixed-field alternating gradient accelerator for proton therapy and tomography—NORMA (NOrmal-conducting Racetrack Medical Accelerator). The energy range allows the realization of proton computed tomography and utilizes normal conducting magnets in both a conventional circular ring option and a novel racetrack configuration, both designed using advanced optimization algorithms we have developed in pyzgoubi. Both configurations consist of ten focusing-defocusing-focusing triplet cells and operate in the second stability region of Hills equation. The ring configuration has a circumference of 60 m, a peak magnetic field seen by the beam of $<1.6\mathrm{T}$, a maximum horizontal orbit excursion of 44 cm and a dynamic aperture of 68 mm mrad—determined using a novel dynamic aperture (DA) calculation technique. The racetrack alternative is realized by adding magnet-free drift space in between cells at two opposing points in the ring, to facilitate injection and extraction. Our racetrack design has a total magnet-free straight lengths of 4.9 m, a circumference of 71 m, a peak magnetic field seen by the beam of $<1.74\mathrm{T}$, a maximum horizontal orbit excursion of 50 cm and a DA of 58 mm mrad. A transverse magnet misalignment model is also presented for the ring and racetrack configurations where the DA remains above 40 mm mrad for randomly misaligned error distributions with a standard deviation up to $100\mu \mathrm{m}$.

We investigate the use of tapered rectangular dielectric-lined waveguides (DLWs) for the acceleration of low-energy, subrelativistic, electron bunches by the interaction with multicycle narrowband terahertz (THz) pulses. A key challenge exists in this subrelativistic regime; the electron velocity changes significantly as energy is gained. To keep electrons in the accelerating phase, the phase velocity must also be increased to match. We present simulations which demonstrate that the dielectric thickness can be kept constant and the width of the dielectric lining can be tapered along the direction of travel to vary the phase velocity, an approach only possible by the use of a rectangular waveguide geometry. The properties of tapered DLWs are discussed and following this, a design process is presented to demonstrate that the way this tapering can be optimized for different pulse and beam parameters. The minimum accelerating gradient for electron bunch capture is derived and compared to simulations. As examples of this design process, designs are considered based on considerations of the THz source, incoming electron beam, and manufacturing tolerances. A maximum THz pulse energy of $22.5\mathrm{\mu }\mathrm{J}$ in the DLW was considered, which represents what is readily achievable using mJ-level regenerative amplifier laser systems together with optical-to-terahertz conversion in lithium niobate crystals. This will be more than double the energy of a 100 keV electron beam, increasing it to 205 keV. We describe the optimization process and present a detailed exploration of the beam dynamics, discussing how the performance will further improve with compressed bunches.