Excitation of a Closed Cylindrical Cavity by a Charged Ring Moving along the Axis at Constant Velocity

An important aspect of the design of high-current devices is the beam loading of the accelerating structure. The phenomenon is sensitive to the charge distribution of the beam and to the geometry of the structure. Calculations for realistic geometry are difficult; to gain insight, a number of authors have studied the simplified problem of beam interaction with a closed, right cylindrical cavity. A formal solution, for arbitrary charge distribution, has been give as a (double) sum over the modes of the cavity. It has been emphasized by all previous workers that the simplified problem approximates reality only for those modes having wavelengths large compared to the holes in an actual structure. We have developed a computational program aimed at evaluating the energy transfer to the cavity when the geometry of the beam is characterized by inner and outer radii as well as an axial length. Sums over selected sets of (or all) modes are available. Parametric studies are presented of the total cavity excitation by a charged ring.