Three-dimensional crystalline beams in a storage ring
In plain words
Cooled enough, a circulating ion beam should freeze into an ordered crystal moving as one; real rings have shown only ions lined up in a single file.
Precise statement
Molecular-dynamics theory predicts that a beam in a ring operated below transition ($\gamma < \gamma_t$), with lattice superperiodicity above $2\sqrt{2}$ times the betatron tune, can form a 3D crystalline state when cooled below its Coulomb-coupling threshold, while shear from bending dispersion heats it. One-dimensional ordering was observed for electron-cooled heavy ions at the GSI ESR (1996) and for protons at the Kyoto S-LSR ring (2007), and 3D crystals were stored in the circular RF trap PALLAS (2001). Determine whether laser or electron cooling acting on all three degrees of freedom in a ring with dispersion can reach and maintain a 2D or 3D crystalline beam.
What would settle it
Beam-profile or Schottky-noise measurements showing a 2D or 3D ordered state persisting over many turns in a ring with bending dispersion.
Status in the literature
Unverified note
Records checked through 2026 show only 1D ordering in rings (Steck et al., https://doi.org/10.1103/PhysRevLett.77.3803; Shirai et al., https://doi.org/10.1103/PhysRevLett.98.204801); 3D crystals only in the PALLAS trap (https://doi.org/10.1038/35089045).