{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"5a16e52db7cdf7f7b9f587ec6bfbb1e65fc16c284865a37a3aab3e681390eb1c","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["9f669373e2f90d33b37b83507ca0bfafb024b22d2d8753c8fd773a10023fe5b0","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"1b7b84d0065039728153376510303d2723d8d80c4b68680ec2409ff7a8e81f1b","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":"2","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 $\\Delta Q \\sim 10^{-5} \\text{ to } 10^{-4}$ 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 $10^{9}$ turns.","problem_ref":"9f669373e2f90d33b37b83507ca0bfafb024b22d2d8753c8fd773a10023fe5b0","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":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"4f663bc2b1c3e09737bd9ec0ef2b77a8e25ab7dca86a70967666793ab6d57c26","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"640bd68b4b771b3daeed1337d2711fa62c245b11d279ec8e1ea0dd453cf52439","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"LMdcAaIakpK_iKDPG4zIg9MQ4Bxn3cL4Dog15fNDnz3X2G_jUSuPliyW3Ab5dVg1p3UCwXq61ZUBLNKErVs-AA"},"schema":"pubphys.envelope/1"},"record_hash":"4f663bc2b1c3e09737bd9ec0ef2b77a8e25ab7dca86a70967666793ab6d57c26","leaf_index":2496}