A theory is developed to model diffraction and Bremsstrahlung radiation from a loop and a disk of charge in a cylindrical pipe with multiple step changes in wall radius supporting all azimuthally symmetric transverse magnetic modes. The beam kinetics are assumedapriori. A correction in phase due to the abrupt change in beam velocity is incorporated at each step change in wall radius. A longitudinal coupling impedance based on energy and power considerations is employed. Loop charge radiation from cavity and collimator geometries is examined. By suitably choosing the loop charge radius, the energy backscattered in the beam tunnel problem can be minimized. The loading effects of the cavity onto the beam is sensitive to its length.