| Electromagnetic, thermal and structural analyses of radio-frequency (RF) cavities were performed as part of a developmental RF cavity program for muon cooling. RF cavities are necessary to provide longitudinal focusing of the muons and to compensate for their energy loss. Closing the cavity ends by electrically conducting windows reduces the power requirement and increases the on-axis electric field for a given maximum surface electric field. Many factors must be considered in the design of RF cavity windows. RF heating can cause the windows to deform in the axial direction of the cavity. The resulting thermal stresses in the window must be maintained below the yield stress of the window material. The out-of-plane deflection must be small enough so that the consequent frequency shift is tolerable. For example, for an 805 MHz cavity, the out-of-plane deflection must be kept below 25 microns to prevent the frequency of the cavity from shifting more than 10 kHz. In addition, the window design should yield smooth electric and magnetic fields, terminate field leakage beyond the window, and minimize beam scattering. In the present thesis, gridded-tube window designs were considered because of their high structural integrity.; As a starting point in the analysis, a cylindrical pillbox cavity was considered as a benchmark problem. Analytical and finite element solutions were obtained for the electric and magnetic fields, power loss density, and temperature profile. Excellent agreement was obtained between the analytical and finite element results. The finite element method was then used to study a variety of gridded-tube windows. It was found that cooling of the gridded-tube windows by passing helium gas inside the tubes significantly reduces the out-of-plane deflection and the thermal stresses. Certain tube geometries and grid patterns were found to satisfy all of the design requirements. |
