Thin beryllium windows (foils) may be utilized to increase shunt impedance of closed-cell RF cavities. These windows are subject to ohmic heating from RF currents. The resulting temperature gradients in the windows can produce out of plane displacements that detune the cavity frequency. The window displacement can be reduced or eliminated by pre-stressing the foils in tension. Because of possible variations during manufacture, it is important to quantify the actual prestress of a Be window before it is put into service. We present the thermal and mechanical analyses of such windows under typical operating conditions and describe a simple non-destructive means to quantify the pre-stress using the acoustic signature of a window. Using finite element analysis, thin plate theory and physical measurements of the vibration modes of a window we attempted to characterize the actual Be window pre-stress in a small number of commercially sourced windows (30% of yield strength is typical). This method can be used for any window material and size, but this study focused on 16 cm diameter Be Windows ranging in thickness from 125 microns to 508 microns and with varying pre-stresses. The method can be used to nondestructively test future Be windows for the desired prestress. the desired fundamental frequency was identified. It was found that the higher order mode shapes were more difficult to discriminate, but may not be necessary to measure pre-stress.
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