Coherent synchrotron radiation extraction from a bent beam pipe

Coherent synchrotron radiation generated in a bending magnet can propagate far downstream and heat the beam pipe. We investigate a beam-free side outlet that diverts part of this radiation into a separate guide. We use a paraxial equation to calculate radiation generation in the bend and its division between the two guides. Modal and finite-difference solutions are used in the bend, and quadratic finite elements on a changing transverse mesh in the branching region. We check the paraxial approximation against full-wave solutions at selected frequencies. Separately, we calculate radiation attenuation in a conducting pipe without an outlet using complex modes that satisfy impedance boundary conditions. For this example, independently damped perfectly conducting modes underestimate the high-frequency transmitted power. For a $70\times 25$ mm rectangular chamber with a ${30}^{\circ }$ bend of radius 2.2 m and Gaussian bunches of rms length $10\mu$m, the selected outlet diverts about 53% of the total outgoing radiation power into the beam-free channel.