A theory is developed to model diffraction and bremsstrahlung radiation in the transverse magnetic mode from a loop of charge in a cylindrical pipe with a discontinuous change in wall radius. The beam kinetics is assumed a priori. A consistent definition of the longitudinal coupling resistance is developed. Scattering effects peak at the cutoff frequencies of the modes of the larger pipe. When kinetic losses are sufficiently large, a change in loop charge radius may alter the propagation of the dominant mode when the charge moves from a larger to smaller diameter pipe. This effect is not present if the charge motion is in the reverse direction.