Beam merging techniques assisted by curved crystals

• Davide Annucci

The installation of the UA9 experiment is located in the H8 beamline of the CERN SPS North Area, which can provide a narrow-spot and low-divergence proton beam with energy ranging from 200 to 400 GeV and \(1.2\times10^6\) particles per spill. The UA9 Collaboration is currently investigating an innovative beam merging scheme based on bent crystal coherent processes, such as Channeling and Volume Reflection. To test the possibility of the two-beams merging with one crystal, it would be necessary to have two beams coming from different directions but in perfect synchronism. Since this type of line is not available, the collaboration planned and managed to put into operation a one-beam, three-crystal line. The first two crystals, placed in the primary beam, produce two channeled beamlets that converge towards the third crystal where the merging process takes place. The simulations of the experimental setup show that the recombined beamlet can be well separated and distinguished from all the other background sources. The UA9 roadmap consisted in two part. In the first part of the experimental program, the beam-time available until June 2024 allowed the precise measurement and characterisation of various crystals, in order to assess their characteristics such as the bending angle and the Channeling efficiency. The second part of the program, in October 2024, instead consisted in the assessment of the two converging beamlets extraction, as well as the double-Channeling. In order to achieve this goal, precise optical and beam-based alignments are necessary, especially for the crystal in which the merging takes place. After these two preparatory stages, the final experiment was set-up and operated from June 2025 onwards and the experimental results are in excellent agreements with the simulations.

Dicussion

Non-inertial physics of action-angle variables​

• Francesco Vergari

Action–angle (AA) variables play a central role in the description of integrable Hamiltonian systems, where they transpose the dynamics onto invariant tori in AA phase space. Here we review the physical and geometric meaning of these variables, starting from Hamiltonian systems and canonical transformations and recalling their historical introduction in the old quantum theory by Arnold Sommerfeld. We emphasize that the conventional multi-dimensional AA choice does not correspond directly to actual trajectories in real space, suggesting an intrinsic connection with non-inertial reference frames. Finally, we introduce a new formulation of these variables, where the invariant torus arises naturally from principles of symmetry related to the phase space structure (circle inversion).

Discussion