{"schema":"pubphys.bundle/1","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"},"content_withheld":"false","files":[],"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"916960d1a46816f7a1db2132e0b725d2367cb0684165b1e3be6506f94af70913","schema":"pubphys.attested/1"},"id_token":null,"id_token_withheld":"false","envelope":{"attested_hash":"80ded170d40444659c26e2427a35056ae0949ea77d8abf899bebc9ef82c8efa9","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"YFPXFkIw4sC6GeI99-7Z_EeTwF1UP5qVq4Ht_HA9AoQRUK2G5n5nCrkztghyeDddfjYctabla7wRSs3Rv-r-Cg"},"schema":"pubphys.envelope/1"},"ots":{"attested":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEIgN7RcNQERGWcJuJCejUFauCUnqd9ir-Jm-vJ74LI76nxIIDOD8ZLyjXl4gIYPfi9Fd8F7eEyeRFQElEleERzrM8uCPAgPs4TOKvP2HFZaqfbOcDdVYoDMt4JostgFMlc547An_EI8SBQeNsZKIrw9L16hkpLsRLd41URk0C2uxxaun7p206lRAjxIKq6V__w_nP_d9VREP1nZj3Fp1_9x05bPoWmSqPmO-I5CPAgAzMjJMJCuYZyhXrcnUKsibyUAfJ5hSHXuqgAjjJNT8kI8CDV-VrDeBU4Rd2bdiIF8sD3kaoaI1e591WQPNBrVmYJsAjxILgyucegs6Hj0k-Cn4WCqTsz35fOCSyIA5vaVrSM5ConCPAgIc68cJ-EOb_p9fBzMx1sIuwuI-BGalPIOj3vrhU7YtUI8CBxK_WraVEkFPQAC7yAevXyyf-CupxAva0AtHIOkj6nkwjwIIhzmnVeFxVHRiBmi7SsQd_gIBRvsrzzZf-fzyEkp8wnCPAgy6DmLQtIuWm-zrDRmaSy95vcFWsjvWyppQO7wIWrfC4I8SAQuuTPkAGyvS_wKMy9BtKvnki2puESdY2vXem8hT1uIQjwIBGYo5Vxy-d7U5zKv5vp3Ii7hJPH_BDLCzA13c47p9q7CP_wCHbghVgOFMuNCPAQPZK2lHbTMqcCYUotzOQcmQjwIJ7ruRIs6HnufKxCpmLUgeUl0aUu0ov4_3PqcppS-bddCPEgI530vHzdwz_3o9jYQ3WablSaV64Wfn7Pmby5WLyI-A0I8QRqwKw78AhITF7Tr3a1xP8Ag9_jDS75DI4sK2h0dHBzOi8vYm9iLmJ0Yy5jYWxlbmRhci5vcGVudGltZXN0YW1wcy5vcmcI8CBXWeNiWFWltfHE0nkDXsVKIykUUwuObhsnN-2fvBt98gjwIM5Vf7j68sOFgVysYMc5S09Hho-fqxYW3oQ4oKUX7JpPCPAgaKHHQB3sdd9w1hu4NMh7vmb-p0X2r4uyVKKCj1G7S28I8SAW2Mg6Bzi9ygjrrjIYB7w90fwMcxH24SsqLmzPyAMGfwjwIMQ863zlveYIpNKWVrZaDOa4vowwoOg2CcTW8gXtxK3dCPEgrZxGGAf-t8jhz_eLMUyBN1IhNrdYDRcNHWvQcwNG9woI8CCVOUHG1YXudbaFIgUYvrCIevRWvb2ubhQAo-z0duD0rQjxIDBeKerVGkO3J2eXDwdraSioXbIWsdIPEN1s8pIwJIS2CPAgV2kB3n3JZ5HwBQjpRL1CWKnqvdCjZk3RcALk6N2wHigI8CB-wbljNlfqElD25uZkNg6taS81YDRU2vfMqGVQ420O9AjxWQEAAAABJM43UU6MLMRrPlCUqossvu1q_knons5yylyWTgxZzWUAAAAAAP7___8CLgABAAAAAAAWABQrYt3E7OllKRCEmL3FL589l78_5wAAAAAAAAAAImog8ATiyw4ACAjxILmbcIO7ixv3pCtwUMZ1VQGKus54F9lZ8-w5ECD5ZuiICAjwIG6ynCyFTLPE7Rgk-0ZGCtBDyqNQx8YvaSZNHy8D8p8jCAjwIMX8zoD2Be1YWvcx_bexVPRmBX0hK-do8b8t9SarimQVCAjxIG6XtpqIEclLlhzcK1LVjqoPGrjjmLnyno8tcETMzECECAjwIF6mlfXOFY51JhrK4eze8zQlKV75OYZYqbtyi8BWxmAsCAjwIKKUcJmVoz-u-geiRV_-ZHdF0VEPXaEPFWf_JX_0e7G2CAjxIGMeD0Z5QWNKBcAEpHht007FFIILW6aSJ8f3CMkKNsneCAjwIBFr6Je8rkB7kwhPGbq0yRgFwZsvW9JhY5sXDRtrq0QwCAjwIAHAwXaus-yUgKICJB5mVvx8VZuJgjwnpb0qWPg1pi6DCAjxIAJhb8cefkVHTAMymdsxa-_i-tUua62LcpALQnPG7R9_CAjwIDvsFqBhPfAL6TCtXZd7gBWmMpx6iiZ-Ug0Jf_LlcstgCAjwIDJRBX6Q0Vge-ra-k1_g76yJWTEp6WWF13I3JpTnsZPJCAjwILykZCbkC9VQgl5gytPKKir6T9nTvKR6y05iWSHBTQgzCAgABYiWDXPXGQED45c78Ah-sGbmQAwfZwjwEAYqxtHnZiPZnJEGPx_JvKsI8SDXkqDg17YsZIrEz5acRx7mBXCKW5mKNgRYnw_-U2cpDgjxBGrArDrwCEfK6Mono428_wCD3-MNLvkMji4taHR0cHM6Ly9hbGljZS5idGMuY2FsZW5kYXIub3BlbnRpbWVzdGFtcHMub3JnCPAg10nyJ6Jn4kshQQQCKE0Lvj3hBC6nLRBVIzaPV4eh8VwI8CCQaAqWlxEbac_XOq1MOlf9iOKHEsxXspzbjK0vLpy8BwjwII3iRbRXUcDxrhAdkZmFlI15nySCSEZ7g922tF1Xln5DCPEgYYvZ1L4v4rPu_UqLfcHPtwSb2OH2GhPgVcVhhH6DpkQI8CDZCIoR20sC-uchP40oAmcLm9EJFV7xzwplj54AeVadXQjxILvLBjPFpCoz29m9Yf2qRnV7PI9GqxE8ozVQfk9QwCqrCPEgZXcMudvEoB_MJ8tqOW2PLTKAIeQBnE-1bfzptRc2gR8I8VkBAAAAAfXq-bmxWqOz7B5wKkwjzHGv2R4s7Y0Z76LqXWYNhmz0AAAAAAD-____Av0cAAAAAAAAFgAUl-skmdZDtn7Hnub6mF4HP2uVn7oAAAAAAAAAACJqIPAE4MsOAAgI8CBDmQsbEXc46Hu8DivhCBM1LGExa4TTM-wo7HpoCVjBTQgI8CCty5vkQtPHzzs8xqArOYhVSjgaDoG1ou3cojv5_P7wQQgI8SDQWB0kdXCTwbk-TqTt0QfRMyzDNLOtU1XXFgvGSRlW8wgI8CC2PKa_QCIBZtrXodq1GdEzppISMsMRDOnzr2gFjLKOAAgI8CCwQ_QF67bcFk_uJ2s0VCZmf5PGIjTmTCpt_qnVY5p_8AgI8SAbzyx7z-oxPMju6PvtQhzrJIQyH2ZAc9oyLuYemzbmZQgI8CC5bh7J74uUk91r8LwybHQFCNBC3PWeuwtMCCNFKWj19AgI8SAf4R2TUNPjaX_PWDUImpoITK0JoW89zaMKnD1wlEEi8AgI8SC2vNmdm7eyP5Ytl1yTzT0njliMdALl1ViKG-s3bG2zswgI8CCpbIVNz1GFVXdJk2zd82hBUoNFFemUPBt7IJdWEOciPwgI8CBtYdRQcrtX1FtCm1SxF7sx-5cO04U8KzbJh8fqBkyReAgI8CBHs2LGmX6gI-lV7yp1RrV7_tGfdiBAwnEFF6B6yXHzAQgI8CATotVmbXBMAixhZ-QKy5Q4lR0FusdA_wcIC1TbB7GmxAgIAAWIlg1z1xkBA-KXOw"],"envelope":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEInVReO9lOsveT8R_ml60G8o9mdEXdF_InJGjPKvYU1D_xIJ1I6zUbhK5KlaFjrUISb2ssawbbjBhDUguwzJJMPO8rCPAgKMP_rVV6xkkXFM-peshv0vR6eOHSEz_CvNY1cb90ivwI8CDpH-x_xu6Sstwl9ui53aPJC6k8FR96-yNSQ_jbhw4gRAjxIEmxjGxPtfcK-IhNQ5LTlIlzuBVqkVT18bpfaJNZXp1DCPEgeHKtZSiYPKt0rXC3_mBt9NFt_g-f5pZmBTAK4LzlT1cI8CD_ab8vg7MnrBEEUcQB6M41xDYF6_4JNgbVYyFfbJEdxAjwIFOuMtkA1LNDpwHC6veKLJYyL459iDJzE8koE8xHbrjhCPAgwmK3CUEOY-5QE2iSOuU3W3YgTzeiLK0zofehysSfjssI8CB0Pk63gwyd_u5K2K1drJW3UxU3mXTBkDKQdutj6_nnEgjxIFf8EhaVa-ubjpYx3wEAcKGxkzfUQq6B-8jimpRd8IqnCPAgy6DmLQtIuWm-zrDRmaSy95vcFWsjvWyppQO7wIWrfC4I8SAQuuTPkAGyvS_wKMy9BtKvnki2puESdY2vXem8hT1uIQjwIBGYo5Vxy-d7U5zKv5vp3Ii7hJPH_BDLCzA13c47p9q7CP_wCHbghVgOFMuNCPAQPZK2lHbTMqcCYUotzOQcmQjwIJ7ruRIs6HnufKxCpmLUgeUl0aUu0ov4_3PqcppS-bddCPEgI530vHzdwz_3o9jYQ3WablSaV64Wfn7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