Speaker
Description
We present a theoretical framework for calculating the time-dependent electromagnetic space-charge fields generated by an accelerating charged-particle bunch in a finite cylindrical radio-frequency cavity with a flat cathode and an axial aperture. The beam-induced scalar and vector potentials are formulated in the Lorenz gauge using retarded Green's functions and cylindrical eigenmode expansions that satisfy the conducting-wall boundary conditions. Exact modal expressions are derived for the radial and longitudinal electric fields and the azimuthal magnetic field without numerical differentiation of the potentials. The downstream aperture is treated by matching the cavity fields to propagating and evanescent modes in the adjoining circular beam pipe. For apertures that are electrically and geometrically small, Bethe-type electric and magnetic polarizabilities are considered as an asymptotic approximation and benchmark for the mode-matching solution. Particular attention is given to causality, image fields, accelerating beam trajectories, convergence of the modal expansions, and the correct field symmetries for electron beams. The resulting formulation provides a basis for self-consistent beam-dynamics simulations in photoinjectors, high-gradient accelerating cavities, and beam-driven high-power microwave sources.