Windows grid design2/23/2023 ![]() ![]() This led to the production of larger pieces. With the Industrial Revolution, glass production became easier and less expensive. Certain tube geometries and grid patterns were found to satisfy all of the design requirements.Glass Production Becomes Easier and Larger 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. The finite element method was then used to study a variety of gridded-tube windows. Excellent agreement was obtained between the analytical and finite element results. Analytical and finite element solutions were obtained for the electric and magnetic fields, power loss density, and temperature profile. As a starting point in the analysis, a cylindrical pillbox cavity was considered as a benchmark problem. In the present thesis, gridded-tube window designs were considered because of their high structural integrity. In addition, the window design should yield smooth electric and magnetic fields, terminate field leakage beyond the window, and minimize beam scattering. 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. The out-of-plane deflection must be small enough so that the consequent frequency shift is tolerable. The resulting thermal stresses in the window must more » be maintained below the yield stress of the window material. RF heating can cause the windows to deform in the axial direction of the cavity. Many factors must be considered in the design of RF cavity windows. 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. RF cavities are necessary to provide longitudinal focusing of the muons and to compensate for their energy loss. The cavit « lessĮlectromagnetic, thermal and structural analyses of radio-frequency (RF) cavities were performed as part of a developmental RF cavity program for muon cooling. ![]() High-power RF tests of the 805 MHz cavity are in progress at Lab G in Fermilab. The design and performance of this cavity are reported here. ![]() Many of the RF-related issues for muon cooling channels are being studied both theoretically and experimentally using an 805 MHz cavity that has a pillbox-like geometry with thin Be windows to terminate the cavity aperture. The possibility of using grids of thin-walled metallic tubes for the termination is also being more » explored. To achieve a high shunt impedance while maintaining a large enough aperture to accommodate a large transverse emittance muon beam, the cavity design adopted is a pillbox-like geometry with thin Be foils to terminate the electromagnetic field at the cavity iris. The RF structures have to be operated in a strong magnetic field and thus the use of superconducting RF cavities is excluded. « lessĪ muon cooling channel calls for very high accelerating gradient RF structures to restore the energy lost by muons in the absorbers. The method can be used to nondestructively test future Be windows for the desired prestress. 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. 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). We present the thermal and mechanical analyses of such windows under typical operating conditions and describe a simple non-destructive more » means to quantify the pre-stress using the acoustic signature of a window. Because of possible variations during manufacture, it is important to quantify the actual prestress of a Be window before it is put into service. The window displacement can be reduced or eliminated by pre-stressing the foils in tension. The resulting temperature gradients in the windows can produce out of plane displacements that detune the cavity frequency. These windows are subject to ohmic heating from RF currents. ![]() Thin beryllium windows (foils) may be utilized to increase shunt impedance of closed-cell RF cavities. ![]()
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