{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"219aa54684f1fee70ebd2582bd311833f91627210dca1d19b84dffd38ee409ca","created":"2026-10-03T07:17:56Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"89782f1426b9b6d91feba916cdd8a5b3ee3669a121f71047d33501216f92cbe7","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"beams.superheating-field.defect-barrier","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"Small bumps and impurities on the metal can let vortices enter early. The question is how much each kind of imperfection lowers the limit.","posed_since":"","precise":"For a type-II superconductor with surface topography of rms height $h$ and lateral scale $l$, and with local suppression of the order parameter over a region of size comparable to the coherence length $\\xi$, compute the reduction of the vortex penetration field relative to $H_{\\mathrm{sh}}$ of a flat surface. An answer is a formula or computed map $H_p(h/\\xi, l/\\xi, \\kappa)$ usable to set surface specifications.","problem_ref":null,"references":"","settled_by":"Ginzburg-Landau simulations of realistic measured surfaces whose predicted $H_p$ matches cavity quench fields.","status_note":"Ginzburg-Landau simulations of idealized defects and roughness exist (2015 to 2020); predictions from measured cavity surfaces that match quench fields are lacking.","title":"How surface roughness and defects reduce the vortex-entry field","topic_ref":"8435c3a546282d17b0eb844e640d9eefc95ff411015bd07858913254362d02e5"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"beb1a8e952d99e25c79ffd1c295c73591633a95cc0ed55ccc59c598f0047d371","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"c12c36218bbce92c026b6519e97f14b60842efc885f650e971462fc0d48dd3d9","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"tGQosBHzjgQpTcWOLx-OnYrZivpIYtioVFdjKEEVMBwOKyzWpNPcorWEg5HUM8-REeu1Pvm3rN-X97JtrvAZDQ"},"schema":"pubphys.envelope/1"},"record_hash":"beb1a8e952d99e25c79ffd1c295c73591633a95cc0ed55ccc59c598f0047d371","leaf_index":711}