{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"12bf576def8984cb067826eeeeeaaa697be314598ecdadd6801c7c36e5127124","created":"2026-10-03T07:17:56Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["010d2ae9b6af71dc96488853d420978ccd8287facc6333282924bcb157f63c4f","5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"178b24285abfff1194950024a58aeabfbc3f19c3f7dfea75d4f45f4ddd0cab9c","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":"1","parents":[{"note":"","parent_revision":"010d2ae9b6af71dc96488853d420978ccd8287facc6333282924bcb157f63c4f","relation":"special_case"}],"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 1e-7 per pulse per meter of structure.","problem_ref":null,"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":"29c52025bad0f3bb40505db955939f35befc6ea9256f5e4972142fac9de7c602"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"9bb2bffc99216f832c166ac67f451bc71d37afa38db78a3487414d0e58383667","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"1f81f85717237cc67de20cecb83393b93d0c1c4bd839e234274b86e97cb3c946","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"-vDt0mVmI83_t-zxIESUPfCCkK_E8jMsNnYXKjMt2E3bhc-T3cfFgZUwCizjYbVOTsPtvadR5xpaWzwivRb7Dw"},"schema":"pubphys.envelope/1"},"record_hash":"9bb2bffc99216f832c166ac67f451bc71d37afa38db78a3487414d0e58383667","leaf_index":691}