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For magnetic bunch compressors where this inequality fails ($\\sigma_z \\sim 10^{-4}$ to $10^{-3}$ cm, $10^{8}$ to $10^{10}$ 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":"40a081cf1906d471195856c9495a422a86b867e04a1598cded570923fcdc6577","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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