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For magnetic bunch compressors where this inequality fails ($\\sigma_z \\sim 1e-4$ to 1e-3 cm, 1e8 to 1e10 electrons per bunch), compute projected and slice emittance growth including the transverse variation of the radiation field, transient fields at magnet entrance and exit, and vacuum-chamber shielding, and state the parameter region in which the 1D model errs by more than a factor 2.","problem_ref":null,"references":"","settled_by":"Self-consistent 3D field calculations benchmarked against slice-emittance measurements downstream of a chicane scanned across $\\sigma_x \\sim (\\sigma_z^2 R)^{1/3}$.","status_note":"3D CSR codes have been developed since the 2000s, but measured benchmarks in the regime where the 1D model fails remain few (2024-2026 literature not checked in detail).","title":"Emittance growth from three-dimensional coherent synchrotron radiation in 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