{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"394e2906b7257d0789d649035e68a413b2adec685547d18cfa2f5b275e82c2b0","created":"2026-10-03T07:17:56Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"97a89ef11db1ed84b37b5114c6f13784c795f3ecbcce67596a9211bad66c00b8","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"beams.collective-instabilities.tmci-space-charge","kind":"well-posed","literature_status":"contested","n":"1","parents":[],"plain":"The beam's own repulsion shifts its oscillation frequencies, and theories disagree on whether this raises or lowers the intensity at which bunches start to shake apart.","posed_since":"1998","precise":"For a single proton bunch with transverse impedance $Z$ and incoherent space-charge tune shift $\\Delta Q_{\\mathrm{sc}}$ comparable to or larger than the synchrotron tune $Q_s$, compute the transverse mode-coupling instability threshold intensity as a function of $\\Delta Q_{\\mathrm{sc}}/Q_s$, wake shape (broadband, resonator, resistive wall) and longitudinal profile. Reconcile with CERN SPS measurements in which TMCI is suppressed but other instabilities appear at high space charge.","problem_ref":null,"references":"","settled_by":"A self-consistent theory or converged simulation that reproduces the measured SPS thresholds versus space-charge strength without free parameters.","status_note":"Models published 2016-2018 give thresholds rising or falling with space charge depending on wake sign and phase advance; SPS experiments reported in 2022 saw TMCI replaced by other instabilities at high space charge.","title":"Effect of space charge on the transverse mode-coupling instability threshold","topic_ref":"dd60e631adb08b9b18495c7a3ab1cfd2ffd7375b33108ba5cf5ec6cce7af2868"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"48947250de8b007e42ecd73ed08abd6f433986b07e5101782a251dc330e2fe1a","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"4406ee789c4c04fa13a583582b21513c9cc2fdd8d23372953a054d8ae827d626","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"2gt0NF9McdtfaWccvF6jtrRYjd8UquJQFQ9hJf-GE6hjCJ0O91ToCsgb55fwqevs7nx2dDroumwXIhFxTt7QAQ"},"schema":"pubphys.envelope/1"},"record_hash":"48947250de8b007e42ecd73ed08abd6f433986b07e5101782a251dc330e2fe1a","leaf_index":660}