Emittance growth from three-dimensional coherent synchrotron radiation in compressors
In plain words
Standard models treat the bunch as a thin line, which fails for bunches that are wide compared with their length; the blow-up of such wide, compressed bunches is not reliably predicted.
Precise statement
The 1D steady-state CSR wake for a bunch of rms length $\sigma_z$ on a bend of radius $R$ is valid when the transverse size satisfies $\sigma_x << (\sigma_z^2 R)^{1/3}$. 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.
What would settle it
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 in the literature
Unverified 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).