Three-dimensional effects of coherent synchrotron radiation by electrons in a bunch compressor

Abstract

We develop a three-dimensional theory of coherent synchrotron radiation in steady-state. Starting from the Hamiltonian in the Courant-Synder theory in a curvilinear coordinate system, we find that the transverse force is essentially the Lorentz force with an additional term: -eϕ/ρ in the bending plane, where ϕ is the potential and ρ the bending radius. The potential term partially cancels the centrifugal force, resulting in a residual wakefield: -Λδ(z)/ρ, where, 2≤Λ≤4 and z is the longitudinal coordinate. The measurement in the bunch compressor supports the sign predicted by the theory but with a smaller value.