{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"d2d3609e3322581b24a16fe27b41a3507199fac0c0091b35b19ceb00a0519a6d","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["9bb2bffc99216f832c166ac67f451bc71d37afa38db78a3487414d0e58383667","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"ba3d38e2b306b7a93d0b3569df06d90bc792694012123fccb5853731236d44cc","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"beams.rf-breakdown.bdr-field-scaling","kind":"well-posed","literature_status":"open","n":"2","parents":[],"plain":"The chance of a spark per pulse grows roughly as the 30th power of the field and the 5th power of the pulse length; this empirical rule has no derivation.","posed_since":"","precise":"Measured breakdown rate per pulse per unit length in conditioned Cu structures follows $\\mathrm{BDR} \\sim E^{n} \\tau_{p}^{m}$ with n approximately 30 and m approximately 5 (CLIC test-stand data), and BDR at fixed field decreases slowly with accumulated pulse number (conditioning). Derive n, m and the conditioning curve from a microscopic model, and state whether the power law persists at BDR below $10^{-7}$ per pulse per meter of structure.","problem_ref":"9bb2bffc99216f832c166ac67f451bc71d37afa38db78a3487414d0e58383667","references":"","settled_by":"A model whose predicted n, m and conditioning curve match test-stand data at two or more frequencies without refitting.","status_note":"","title":"Origin of the steep power-law scaling of breakdown rate","topic_ref":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"9e6a45bed70c6fd5bc32d8ad2961129f10cfaea00dda304b56c0948b4d12aec3","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"68895d8af6bbee0f42ec334bc4d5bb07b3eee7f7203b087b87ddeab101616b52","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"zvByJV_iFulZ1rpEtomQ1KDxmWQMu4kycJ1DIinbf0fAq1cI7ILFCU4VFfy7tgscu5zCskQx7bAjqXLlxI4-BA"},"schema":"pubphys.envelope/1"},"record_hash":"9e6a45bed70c6fd5bc32d8ad2961129f10cfaea00dda304b56c0948b4d12aec3","leaf_index":2516}