{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"0bd9998a9b153208239abc28eb4cdc5be19a20a6318963fbc4e14d1201256d03","created":"2026-10-03T07:17:56Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"330374d2d5b88394f7b22c589713109738dfce4ea5641b9ad9e2fb10f5fd4ef2","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"beams.nonlinear-dynamics.diffusion-rate-4d-maps","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"Inside the region that looks stable, particles can still drift outward extremely slowly through thin chaotic layers; how fast is not known.","posed_since":"","precise":"For a 4D symplectic map of linear rotation with tunes $(Q_x, Q_y)$ plus thin sextupole and octupole kicks of strength $\\epsilon$, with tune modulation $\\Delta Q \\sim 1e-5 \\text{ to } 1e-4$ at frequencies $50\\,\\mathrm{Hz} \\text{ to } 10\\,\\mathrm{kHz}$ from power-supply ripple, compute the rate of chaotic transport in action (Arnold and modulational diffusion) at amplitudes below the short-term dynamic aperture as a function of $\\epsilon$ and $\\Delta Q$. Test against direct tracking to 1e9 turns.","problem_ref":null,"references":"","settled_by":"Analytic or semi-analytic diffusion coefficients matching tracked action distributions over at least three decades of turn number.","status_note":"","title":"Rate of chaotic action diffusion in weakly nonlinear 4D maps","topic_ref":"7c02bc0932cd39db40c654c1af162e4d605ebff51574000fcd91aa1d4d9677ff"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"9f669373e2f90d33b37b83507ca0bfafb024b22d2d8753c8fd773a10023fe5b0","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"247767009e368bdf20019b061a76fe44d2ac1652a281a3075bb7b0ddfb7b827a","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"TyODZ3x60clXXwL1iYl4Mabi-Qbg91vmJgLws-RaKsly60Juhsd2csoa8AKqCvNllcs6l68QPyYYAVAiubcABQ"},"schema":"pubphys.envelope/1"},"record_hash":"9f669373e2f90d33b37b83507ca0bfafb024b22d2d8753c8fd773a10023fe5b0","leaf_index":678}