{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"27e53b21ecf0781f9f2aa55c88771381ecedecb72cfc54de8102ac72fd5d84de","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["92481a57e681bdbeb0e4ffcdd84b3a204ae4300ad00eca7869e464aa0b57a224","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"008c1ec116944a9c13bb725b441de34b999896bca3411dcccbdd0b364ec4cabb","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"beams.rf-breakdown.magnetic-field-breakdown","kind":"well-posed","literature_status":"partially-resolved","n":"2","parents":[],"plain":"A muon collider needs accelerating cavities placed inside very strong magnets, and such cavities spark at lower fields than without the magnet.","posed_since":"","precise":"Vacuum normal-conducting cavities at $\\sim 200\\text{-}800\\,\\mathrm{MHz}$ in axial magnetic fields $B \\sim 3 \\times 10^{4}\\,\\mathrm{G}$ show reduced maximum gradient, attributed to field-emitted electrons focused by B onto the walls, causing local heating. Establish the scaling of the safe gradient with B, frequency and wall material up to $B \\sim 10^{5}\\,\\mathrm{G}$ and above, as required for 6D muon ionization cooling channels.","problem_ref":"92481a57e681bdbeb0e4ffcdd84b3a204ae4300ad00eca7869e464aa0b57a224","references":"","settled_by":"Gradient-limit measurements versus B up to the cooling-channel field for at least two wall materials and frequencies, compared with an electron-focusing heating model.","status_note":"Beryllium-walled and high-pressure gas-filled cavities reached approximately $0.5\\,\\mathrm{MeV}/\\mathrm{cm}$ in fields near $3 \\times 10^{4}\\,\\mathrm{G}$ at the Fermilab MuCool Test Area (reported around 2020); higher fields remain untested.","title":"Breakdown limit of RF cavities inside strong solenoid fields","topic_ref":null},"content_withheld":"false","files":[],"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"33483c883593db903c75ad06709c85ec9efbce09ea57330fc4f272c937fb32ea","schema":"pubphys.attested/1"},"id_token":null,"id_token_withheld":"false","envelope":{"attested_hash":"6d28c5d39bd43e85f9b7d0af4ec272a22d032814dfca3e84b2611a91e085f4c8","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"B_9edJl2F5sw6q_RFNIiIci3dZAYJ5rCaU7k6VshhOidC4HsAKy13d7mfdc-SN3Fqi2JG1M1jlM0zAo94lAnAQ"},"schema":"pubphys.envelope/1"},"ots":{"attested":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEIbSjF05vUPoX5t9CvTsJyoi0DKBTfyj6EsmEakeCF9MjwIG06-9Yvod0SrDkwaqMW6bmdckTRJ-aYDsF0wtfk7UgTCPAgnCnusIDUPTJy4ky8565VS-HvbF70hpvDRgFUIq9YpoMI8SBadXb7MtqvBQ2rCJtxtjxauzEdTXUVlWv_tVSID847WwjxIA_dKXFv8PO7sDfgqE8wC8crjSv4joxRsze1rQK82IKbCPAgUmBzncrixG7TDnwHURz5xiwPIz2OdAbrkUa9jXf9DaEI8SD_5zFJHCmnJMVG3y8g48CODsGJwzCSeSjMybN-JiGepwjwICRMULf4Qk7B4Ixs-w5_AnqKLFYrm25Y_JDm1-0Q4j1tCPEgV483a5w_VdTK7my82rqJCPIXOvGhZNeRkwqfWifoP4MI8SBcP9hQb3hxUiLf8dFx-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_ieLohOiSlAEI06Tqf64FyAp2yOfUtQjDgDG7Vsp8jTFNNq0VcGqQInHxINN_HeHp0GOv6jx6Azxa7_c0xXsoPXkH51fKinZz8UDkCPEgFTZhyvMb0mwiHcWW1s6Q5VibHVoi_bfS85L6ZX_ZsgsI8CCAmPzgNgMzF8RbwSQHsmYDJvN4T6pPvcqU3jO87leQAAjwIPCUh4vjMmXF2n1UeVz1r2AdY26DU-QQJLAdZf2dRCi_CPEgksUwW9OcIn32QixCJNiZqXrHWrDEdVxwOPYnuNedlfAI8CChmsHBwNW1viG09L2LhDEmTnRyQDCn4wsXrYS9lbqKNwjxII-HQyDbfySaSfEBkdNEhf9eJgFGPux1xPs8ZdzzMWpACPEgA7tb_tb_4KngwMf2GSJCpmxJdfmzdO37wjFC3fvNh0wI8CCSqAf0sn_1-kk9EDPXEZvjRff_ciLViVfMVybjDX1OsQjxID89HsXrUag9eRv04qSQX18D2ak5pxDN4H8m3_0Qkp84CPAg3mczMYDKOd7Nhf3ojA9ZvuTsN66Y1NnyYTp9j8GKQNwI8SCvAiiN-Hrv7IEejd8wdUihoozu5KOvpoBFJ0vg3UnGAQj_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":"2520","tree_size":"3804","proof":["99707993d29db01b1dfc1ed309b16e3b41c287f9acc3177d2f3db469777a7cf1","63560d76d1ddf4a0a228999b330705f0eaee7e2fc59d254dc08e27ef9c1c3553","a56a751c7b0bf573dad2a0e4ccab525424b79d29f4143200be842148716c29d8","a1d6bf2518ee8e25c243cb47ebe74ab5442ce557f2574accb0f714e558f69101","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\n0565e731199bd4cc7db8212aaf1cda525b7bd6edb9b0d50f7ce98135e9933d2c\n2520\n2026-10-15T23:43:57Z\n2026-10-16T01:43:57Z\n\n— pubphys.com/log/v1 JFPwIJNHRK66PuzmSjjd14HXIwUcIbNc0rXdjIkWe+Cw2GUcoksRGB/ojvpYEasih6Ndahua/jaLiD2DtSP6BynbSwM=\n"},"orcid_key_evidence":[],"attesting":null}