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.

The use of low-dimensional dynamical systems as reduced models for plasma dynamics is useful as solving an initial value problem requires much less computational resources than fluid simulations. We utilize a data-driven modeling approach to identify a reduced model from simulation data of a convection problem. A convection model with a pressure source centered at the inner boundary models the edge dynamics of a magnetically confined plasma. The convection problem undergoes a sequence of bifurcations as the strength of the pressure source increases. The time evolution of the energies of the pressure profile, the turbulent flow, and the zonal flow capture the fundamental dynamic behavior of the full system. By applying the sparse identification of nonlinear dynamics (SINDy) method, we identify a predator-prey type dynamical system that approximates the underlying dynamics of the three energy state variables. A bifurcation analysis of the system reveals consistency between the bifurcation structures, observed for the simulation data, and the identified underlying system.

A new generation magnetic spectrometer in space will open the opportunity to investigate the frontiers in direct high-energy cosmic ray measurements and to precisely measure the amount of the rare antimatter component in cosmic rays beyond the reach of current missions. We propose the concept for an Antimatter Large Acceptance Detector In Orbit (ALADInO), designed to take over the legacy of direct measurements of cosmic rays in space performed by PAMELA and AMS-02. ALADInO features technological solutions conceived to overcome the current limitations of magnetic spectrometers in space with a layout that provides an acceptance larger than 10 m${}^2$ sr. A superconducting magnet coupled to precision tracking and time-of-flight systems can provide the required matter–antimatter separation capabilities and rigidity measurement resolution with a Maximum Detectable Rigidity better than 20 TV. The inner 3D-imaging deep calorimeter, designed to maximize the isotropic acceptance of particles, allows for the measurement of cosmic rays up to PeV energies with accurate energy resolution to precisely measure features in the cosmic ray spectra. The operations of ALADInO in the Sun–Earth L2 Lagrangian point for at least 5 years would enable unique revolutionary observations with groundbreaking discovery potentials in the field of astroparticle physics by precision measurements of electrons, positrons, and antiprotons up to 10 TeV and of nuclear cosmic rays up to PeV energies, and by the possible unambiguous detection and measurement of low-energy antideuteron and antihelium components in cosmic rays.

The L-H transition denotes a shift to an improved confinement state of a toroidal plasma in a fusion reactor. A model of the L-H transition is required to simulate the time dependence of tokamak discharges that include the L-H transition. A 3-ODE predator-prey type model of the L-H transition is investigated with bifurcation theory of dynamical systems. The analysis shows that the model contains three types of transitions: an oscillating transition, a sharp transition with hysteresis, and a smooth transition. The model is recognized as a slow-fast system. A reduced 2-ODE model consisting of the full model restricted to the flow on the critical manifold is found to contain all the same dynamics as the full model. This means that all the dynamics in the system is essentially 2-dimensional, and a minimal model of the L-H transition could be a 2-ODE model.

In the frame of a collaboration between CERN, ASI, University of Trento, and TIFPA, the HTS demonstrator magnet for space project has started to define methods and procedures for manufacturing high temperature superconducting magnets for space applications. To this purpose, we developed a conceptual design of a superconducting magnetic spectrometer for a physics experiment in space. The configuration is a toroid with twelve superconducting coils based on ReBCO tape. By using ReBCO tape with an engineering critical current density, J _e, exceeding 1000 A mm⁻² at 4.2 K and 20 T , as reached in the H2020-ARIES program, the magnet system provides an average bending strength of 3 T m . This is sufficient to measure charged particles with rigidities up to 100 TV , more than two orders of magnitude higher than the present state-of-the-art space spectrometer. The magnet system requires about 62 km of 12 mm ReBCO tape and produces a peak magnetic field of 11.9 T at an operating temperature of 20 K . A small scale single coil, which is about one third in size of a coil from the toroidal magnet system, will be manufactured and tested as demonstrator of the magnet technology. The mechanical structure and performance of the toroidal magnet system and demonstrator coil are described.