Design of 118 MHz twelfth harmonic cavity of APS PAR

Two radio frequency (RF) cavities are needed in the Positron Accumulator Ring (PAR) of the Advanced Photon Source. One is for the first harmonic frequency at 9.8 MHz, and the other is for the twelfth harmonic frequency at 118 MHz. This note reports on the design of the 118 MHz RF cavity. Computer models are used to find the mode frequencies, impedances, Q-factors, and field distributions in the cavity. The computer codes MAFIA, URMEL, and URMEL-T are useful tools which model and simulate the resonance characteristics of a cavity. These codes employ the finite difference method to solve Maxwell`s equations. MAFIA is a three-dimensional problem solver and uses square patches to approximate the inner surface of a cavity. URMEL and URMEL-T are two-dimensional problem solvers and use rectangular and triangular meshes, respectively. URMEL-T and MAFIA can handle problems with arbitrary dielectric materials located inside the boundary. The cavity employs a circularly cylindrical ceramic window to limit the vacuum to the beam pipe. The ceramic window used in the modeling will have a wall thickness of 0.9 cm. This wall thickness is not negligible in determining the resonant frequencies of the cavity. In the following, results of two- and three-dimensional modeling of the cavities using the URMEL-T and MAFIA codes are reported.