{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"0f1e54af489b39b54e2b89ed890490c7536927c4f05f3cccaf531ff5cffb5998","created":"2026-10-03T07:17:56Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"88143fa404d8e09ad4754fa5fb64857a39d4a713b4641ddb74071a27a414a165","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"beams.beam-cooling.crystalline-beam-ring","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"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.","posed_since":"","precise":"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.","problem_ref":null,"references":"","settled_by":"Beam-profile or Schottky-noise measurements showing a 2D or 3D ordered state persisting over many turns in a ring with bending dispersion.","status_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).","title":"Three-dimensional crystalline beams in a storage ring","topic_ref":"e4bb53556b8c7d13b4b819a20298552b24074d3ba33b0f60982a9bfdd1aa5461"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"916960d1a46816f7a1db2132e0b725d2367cb0684165b1e3be6506f94af70913","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"80ded170d40444659c26e2427a35056ae0949ea77d8abf899bebc9ef82c8efa9","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"YFPXFkIw4sC6GeI99-7Z_EeTwF1UP5qVq4Ht_HA9AoQRUK2G5n5nCrkztghyeDddfjYctabla7wRSs3Rv-r-Cg"},"schema":"pubphys.envelope/1"},"record_hash":"916960d1a46816f7a1db2132e0b725d2367cb0684165b1e3be6506f94af70913","leaf_index":650}