A 201 Mhz Rf Cavity Design with Non-stressed Pre-curved Be Windows for Muon Cooling Channels*

We present a 201-MHz RF cavity design for muon cooling channels with non-stressed and pre-curved Be foils to terminate the beam apertures. The Be foils are necessary to improve the cavity shunt impedance with large beam apertures needed for accommodating large transverse size muon beams. Be is a low-Z material with good electrical and thermal properties. It presents an almost transparent window to muon beams, but terminates the RF cavity electro-magnetically. Previous designs use pre-stressed flat Be foils in order to keep cavity from detuning resulting from RF heating on the window surface. Be foils are expensive, and difficult to make under pre-stress to accommodate thermal expansion. An alternative design is to use pre-curved and non-stressed Be foils where the buckling direction is known, and frequency shifts can be properly predicted. We will present mechanical simulations of the Be window designs. INTRODUCTION High gradient RF cavities at 201 MHz are required for muon cooling channels in a neutrino factory or a muon collider, and also for a recently proposed muon cooling demonstration experiment at RAL (Rutherford Appleton Laboratory) MICE (An International Muon Ionization Cooling Experiment). As high as 16 MV/m at frequency of 201 MHz is required, or 1.07 Kilpatrick. Eight 201 MHz cavities are needed for the MICE cooling channels, but the accelerating gradient for MICE will have to be limited to ~ 8 MV/m restricted by budget for RF power sources, not by cavity design. The cavity design supports a gradient of 16+ MV/m. In order to achieve such a high gradient for naturally large dimension muon beams, using conventional open iris structures would inevitably introduce very high peak surface fields, a limiting factor of achievable accelerating gradient. A closed-cell (pillbox like) cavity design was proposed and reported [1] where the beam apertures are electro-magnetically terminated by low Z and thin Be foils. To keep the cavity from detuning by RF heating power, these Be foils are under tension which is introduced by small CTE (coefficient of thermal expansion) difference between the thin Be foils and thick Be window frame during the brazing process. The pre-stressed windows should stay flat up to a certain temperature gradient limit where the pre-tension becomes zero. This temperature gradient limit determines how much heating power it can take for a given window thickness. Manufacturing of the pre-stressed Be windows is expensive, and predicting the temperature limit is difficult. Predictions on the temperature gradient limit are difficult. Previous Be window designs for the 201 MHz cavity were scaled from the pre-stressed Be windows for an 805 MHz cavity. Recent experimental tests on the 805 MHz cavity found that the cavity frequency started to shift at a lower than predicted temperature gradient on the windows (the frequency shift was quite small and well within the klystron bandwidth). By taking advantage of the pillbox-like profile, non-stressed and pre-curved Be windows should result in smaller frequency shifts with both windows are installed oriented to the same direction in a cavity.