Finite element analysis of thin beryllium windows for a muon cooling channel

The cooling channel for a muon collider or neutrino factory may utilize thin beryllium windows to separate RF cells and enhance on-axis accelerating fields. The nominal windows for an 805 MHz design are composed of 16 cm diameter circular foils, 127 microns thick. These windows undergo significant ohmic heating from RF power, and displace out of plane, causing the cavities to detune. In order to understand how to control this effect and to evaluate different window designs, a Finite Element Analysis (FEA) model was created in ANSYS, and this model was correlated to windows tested in the laboratory. The prototype windows are actually brazed assemblies, and the thin foils in these assemblies become pre-stressed during cool down from braze temperature, complicating the analysis. Using empirically validated models, several other window designs are analyzed, such as windows of different thicknesses, non-constant thickness windows ("stepped" designs), and windows of diameters much larger than 16 cm.