Coherent synchrotron radiation by electrons moving on circular orbits

Abstract

We study coherent synchrotron radiation by electrons in the Frenet-Serret coordinate system with a constant curvature 1/ρ. Based on the Hamiltonian in the Courant-Synder theory of particle accelerators, we find in general that the transverse force is essentially the Lorentz force but with a substitution of the transverse magnetic field B_{x,y}→(1+x/ρ)B_{x,y}, where x and y are the transverse positions. The curvature term provides us a key to derive the point-charge wakefield explicitly in terms of the incomplete elliptic integrals of the first and second kind, resulting in a steady-state theory of the coherent synchrotron radiation in two-dimensional free space.