{"schema":"pubphys.bundle/1","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},"content_withheld":"false","files":[],"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"9e6a45bed70c6fd5bc32d8ad2961129f10cfaea00dda304b56c0948b4d12aec3","schema":"pubphys.attested/1"},"id_token":null,"id_token_withheld":"false","envelope":{"attested_hash":"68895d8af6bbee0f42ec334bc4d5bb07b3eee7f7203b087b87ddeab101616b52","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"zvByJV_iFulZ1rpEtomQ1KDxmWQMu4kycJ1DIinbf0fAq1cI7ILFCU4VFfy7tgscu5zCskQx7bAjqXLlxI4-BA"},"schema":"pubphys.envelope/1"},"ots":{"attested":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEIaIldiva77g9C7DNLxNW7B7Pu5_cgOwh7h93qsQFha1LxIGh_rMwGOGipUI2Bi4L-2vyrBrHhaUvBZop64SrN8fRzCPEg7g3LxPTvebtseN1HYCufh02E27zmw1oXo3BxtCC81eAI8SAG54j2u5JhccLfU9LSity9uKr5iHv7cX6bSdI6FHaaDgjwIGT-SCjPsRxOvWSTfjkK-BHe6p3UgOnIW_jJJsEkzA-4CPAgifAC04JEf7t_zUawinVeIYMxbJ7rKE_SEp1_wd5cqK0I8SBcMw2pvf8wrDaCCWJ15laJajPIG2V10Awj6MCOsyTJQQjxIJ6xxSFbP5yKvGDsivHs5WdfqkpRl9d-xpUzY-9mzCvLCPAgNWsj73C-FdBKnM-YIq56Rzi4rZw0zXjVnprUdC52gz4I8SBcP9hQb3hxUiLf8dFx-DuqZHA2xkmG-c_qCFt8QfQHCAjwIOv_x0B6HyZ6WMHKeIf_d_EUIvwPGdZeVY-hXN3RLDM5CPEgHd9u6OIGCvUV12A1B1xdiOprSJ-4w0cqwfe7CzVX5HsI8CDQo_sIWZiWXaTGRSQBLmU-lHJKskYKqsjO1r02DhB8LAj_8Ajn9YmozHwo9QjwEJ46aM9ZDv3TdtqV3ZbRsNgI8SBOF8pILGf1kodr5MKmQs6Cd93joraGn3g6UPt_-kewPwjwIOG-gmM7bd_eR4AiDMNfluS3xvr7vicLR-sCBr5qtG2cCPAgrVNFrCoeQcCxhlmnE0BzHgR8HQpZAlfqzDDFzfWb8GUI8QRq0WWT8AjZJ2cF_c7k8ACD3-MNLvkMjiwraHR0cHM6Ly9ib2IuYnRjLmNhbGVuZGFyLm9wZW50aW1lc3RhbXBzLm9yZ_AI9ZMS1zxd7IEI8BDd00WgJZ0RncsC1Fyai_4aCPEgvxMFrnu7F05IW5INiraQ3OVEYMjNx6JfBxw1Q4jPLi4I8QRq0WWS8Ag2zxPAtI5JsP8Ag9_jDS75DI4uLWh0dHBzOi8vYWxpY2UuYnRjLmNhbGVuZGFyLm9wZW50aW1lc3RhbXBzLm9yZwjxIHAnv4KFFf4uiYEFJvLxiMxSyz8VowJP4roTfDD9h7bICPAgj5tgvbNF7mxSP4jGGE66ezUFRLnI4g1VTkvuV4VtCPAI8CCxlc1HuKORuHgn7DYIYcDhc4oo99OkTWBEvddBypoa7AjwIFcjjaF8kDNDYCZGaNISlRjvX-I7in-QNwsr4JYQbFJvCPAgnl0k4gs7LuY5i1umiHO-J7My3uBThLJUWQoY9LdVSrQI8SA6-Ft11_K_GqMNWYhkVsVqCFvXSYbp4S8JoLsLBnUzvgjxIBC8_mAE7JBP35SNxDBcG7joLJwURpMxdV2vSO64_jEOCPEge04Coj1xSi7CE8UwqiBGNhPyZ5QdD_YZwn-heSdObU4I8SBgdDSgr3VUx1j8m_pK7-OzMwwFgXeLy43ujffCv-hf5AjwIMl-PnAt4xjoBEVU4-nkyN0NKRa9AvX4kEMfllFyIJS9CPFZAQAAAAHz4rV-uwQFg02bVnEMUFgpIdGKjM4tWuID1kTVnrjisAAAAAAA_v___wJURAIAAAAAABYAFBFys2oc0-U-bYrC3VulGLzND5fbAAAAAAAAAAAiaiDwBHLTDgAICPEgMJIBYi46xOIuFDwzJ9nOx14ngW5HbglUf65ORpkoIYcICPAgHgGWEGCDHWgscwT92NOoJ7s-ezbPkyiWr2RnYZDC_dwICPAgtffMyyLu-MscJsDc0dzwGspwSrrmvVAnMNgsgWhHClgICPAgMUl1OfBDUwhp5VZjHwVA0nuz1F5HZTUJCHAnM1L1F3MICPAgStK7UWpnrUueV5EaE7uE0y6BLMp6EANmrbhrTqEBZu8ICPAg5LVW7IHtUL5mNOvPx1hOTfLMmqlQ7t9EFW-KDtrISIQICPAgABgXZ6upFU8qiDQKFtQFpqkjKwl0PsxM4JUjVLlDKbkICPAgEwb96FiOhjlbwI8GFZQ4a5GXwxs4bUdqVOMKrtBWV30ICPEgqBg-wp0c8CAPV9k6J7wIa9_GtQfpWmhpE1zqFZyi2pQICPAg2pZLTVPGJbriiz0UhMytYDVYAXOgQnWDcrMOewK9O8cICPEgxm3QwzbvT4siJzubQGnST67bWv-exYwSPP1KDi7CaUwICPEgm6udUudfjUaM0gUFTylKGDMypj7ptMTG0zmxd_T5yTcICPAgMpOInkjFCVp1pOZhfZnyPAl8hdWGmHzQcrGLgLwSKLgICAAFiJYNc9cZAQPzpjs"],"envelope":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEIHqLCQHXnpOZGbWk87U_2JN19j0TRp2bF08XtXsl-ULfxIB6e7MvaKvMn0eaO6-bmzBEkR4kwOwfYIcchw_yTLLrWCPAgEXiCL1MbA_SKXWdq50RYX_TG5GwJUW9TCloYORtETMwI8CCEZCj4MphPaXEeG-iJMHIC66QuOTETMIngcECvaRdiDAjwIOsiVt4YY2iAOCYxMCmq3CKfP3En6hhmHSY1iVzGHcAdCPAg8aiAkI9kiPFO5PvggiASOMuX2uDnMJ8iyK5XaFbRuboI8SAZIDk3wUg4WayPyB9DLo9yIiAvTaNjz407qHzoLnLnuAjwIKbu5o-ZXluaLmNjUVgppzdGWJansJj-PZdQ12hYr-l8CPEgbfsqNEiKd31vqHmWLbVpOwfRJ_Z2YUckwYh0fQRhz9sI8SCHI26f1bMr-H5VtXG_HgMHDd8PPImPLhsWPB8PPaY3jwjwIKD8mGRUgbk2Dt1xG-4OxMpCuw1ya5UEUQXsqASURGCtCPAgkPXX-naXR0fRIdS-sEDlzYmtMvSCNH42ESUF0QXb6NUI8CDQo_sIWZiWXaTGRSQBLmU-lHJKskYKqsjO1r02DhB8LAj_8Ajn9YmozHwo9QjwEJ46aM9ZDv3TdtqV3ZbRsNgI8SBOF8pILGf1kodr5MKmQs6Cd93joraGn3g6UPt_-kewPwjwIOG-gmM7bd_eR4AiDMNfluS3xvr7vicLR-sCBr5qtG2cCPAgrVNFrCoeQcCxhlmnE0BzHgR8HQpZAlfqzDDFzfWb8GUI8QRq0WWT8AjZJ2cF_c7k8ACD3-MNLvkMjiwraHR0cHM6Ly9ib2IuYnRjLmNhbGVuZGFyLm9wZW50aW1lc3RhbXBzLm9yZ_AI9ZMS1zxd7IEI8BDd00WgJZ0RncsC1Fyai_4aCPEgvxMFrnu7F05IW5INiraQ3OVEYMjNx6JfBxw1Q4jPLi4I8QRq0WWS8Ag2zxPAtI5JsP8Ag9_jDS75DI4uLWh0dHBzOi8vYWxpY2UuYnRjLmNhbGVuZGFyLm9wZW50aW1lc3RhbXBzLm9yZwjxIHAnv4KFFf4uiYEFJvLxiMxSyz8VowJP4roTfDD9h7bICPAgj5tgvbNF7mxSP4jGGE66ezUFRLnI4g1VTkvuV4VtCPAI8CCxlc1HuKORuHgn7DYIYcDhc4oo99OkTWBEvddBypoa7AjwIFcjjaF8kDNDYCZGaNISlRjvX-I7in-QNwsr4JYQbFJvCPAgnl0k4gs7LuY5i1umiHO-J7My3uBThLJUWQoY9LdVSrQI8SA6-Ft11_K_GqMNWYhkVsVqCFvXSYbp4S8JoLsLBnUzvgjxIBC8_mAE7JBP35SNxDBcG7joLJwURpMxdV2vSO64_jEOCPEge04Coj1xSi7CE8UwqiBGNhPyZ5QdD_YZwn-heSdObU4I8SBgdDSgr3VUx1j8m_pK7-OzMwwFgXeLy43ujffCv-hf5AjwIMl-PnAt4xjoBEVU4-nkyN0NKRa9AvX4kEMfllFyIJS9CPFZAQAAAAHz4rV-uwQFg02bVnEMUFgpIdGKjM4tWuID1kTVnrjisAAAAAAA_v___wJURAIAAAAAABYAFBFys2oc0-U-bYrC3VulGLzND5fbAAAAAAAAAAAiaiDwBHLTDgAICPEgMJIBYi46xOIuFDwzJ9nOx14ngW5HbglUf65ORpkoIYcICPAgHgGWEGCDHWgscwT92NOoJ7s-ezbPkyiWr2RnYZDC_dwICPAgtffMyyLu-MscJsDc0dzwGspwSrrmvVAnMNgsgWhHClgICPAgMUl1OfBDUwhp5VZjHwVA0nuz1F5HZTUJCHAnM1L1F3MICPAgStK7UWpnrUueV5EaE7uE0y6BLMp6EANmrbhrTqEBZu8ICPAg5LVW7IHtUL5mNOvPx1hOTfLMmqlQ7t9EFW-KDtrISIQICPAgABgXZ6upFU8qiDQKFtQFpqkjKwl0PsxM4JUjVLlDKbkICPAgEwb96FiOhjlbwI8GFZQ4a5GXwxs4bUdqVOMKrtBWV30ICPEgqBg-wp0c8CAPV9k6J7wIa9_GtQfpWmhpE1zqFZyi2pQICPAg2pZLTVPGJbriiz0UhMytYDVYAXOgQnWDcrMOewK9O8cICPEgxm3QwzbvT4siJzubQGnST67bWv-exYwSPP1KDi7CaUwICPEgm6udUudfjUaM0gUFTylKGDMypj7ptMTG0zmxd_T5yTcICPAgMpOInkjFCVp1pOZhfZnyPAl8hdWGmHzQcrGLgLwSKLgICAAFiJYNc9cZAQPzpjs"]},"log":{"leaf_index":"2516","tree_size":"3804","proof":["a05d7e2d0c51fe36d6401b100559774e2621f34161a991583c336751257d87ef","9911362350b615245f5a6a6545b6cade4efc20f0b3bdd6ba742eb8237cb0f00a","79ce75a6249c342bd188874fbb722894b91adbba1a8609fdbc903cc5f9fe753e","6e51aa026db2941b723eadf29cc8547f84dcc6322f8eef270cfb03355824706a","7b27cf6b310fe2f4e92f993be1e629e5f5474dcdb7e016a90cb35c4d42a7ad51","93e989eb5afccf6bd159e36aa811aa8ef30289d271f3d15eb59667f4267f8193","7c0747095d37385fe6f4d152c1a4f15f2c176d36931329cf6ad82b081e9f63f6","193f7e120934503cd45d11622182f80d8b1635765c3becdc1c2cab15bb00bcc2","ad2bf8922b230304eb5887f66a1631d0d013048aef3d1e5c2bce55da65e76cef","453fe2db8b5276d732edac85634e8be036b4709a91a2584f32a4b9edcc8ca9de","325287f5a43e4f3ad4072ec4bd53d43c50c1393021a056122e9cb0fad83b868f","3c578dccc15502c5f3efe228cadc99fee76ab536ed01f66b14d316fdcc157429"],"checkpoint":"pubphys.com/log/v1\n3804\nAK6t4qgu96+M9wScTrIlsJ10d/zhKVEtYguyM3aeJvo=\n\n— pubphys.com/log/v1 JFPwIPP8EtoxgcsQg7V7CwIdL4UKPqJtpv+eB8sFNJjyQHIdyA1VabmBsPyLqq2bLxJPn57rA6fQi8y0QDDjRXHvlQg=\n","promise":"pubphys.com/log/v1 promise\n01dbb6c793fb777424477bb6d132492f2b268f10d8a8a0fe4c4d56e5baebd0ac\n2516\n2026-10-15T23:43:57Z\n2026-10-16T01:43:57Z\n\n— pubphys.com/log/v1 JFPwIJm15OAeSXWjejdZ9hzbOTyA8hsXgCgmPGZGn1z8C3TWz50reIlEoixc/bEJbw3dkaBqJWTzZsg824GlZieTIQA=\n"},"orcid_key_evidence":[],"attesting":null}