Emittance growth from three-dimensional coherent synchrotron radiation in compressors

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 ($\sigma_z \sim 10^{-4}$ 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.

Self-consistent 3D field calculations benchmarked against slice-emittance measurements downstream of a chicane scanned across $\sigma_x \sim (\sigma_z^2 R)^{1/3}$.