Thermal and Lorentz Force Analysis of Beryllium Windows for a Rectilinear Muon Cooling Channel

Reduction of the 6-dimensional phase-space of a muon beam by several orders of magnitude is a key requirement for a Muon Collider. Recently, a 12-stage rectilinear ionization cooling channel has been proposed to achieve that goal. The channel consists of a series of low frequency (325 MHz-650 MHz) normal conducting pillbox cavities, which are enclosed with thin beryllium windows (foils) to increase shunt impedance and give a higher field on-axis for a given amount of power. These windows are subject to ohmic heating from RF currents and Lorentz force from the EM field in the cavity, both of which will produce out of the plane displacements that can detune the cavity frequency. In this study, using the TEM3P code, we report on a detailed thermal and mechanical analysis for the actual Be windows used on a 325 MHz cavity in a vacuum ionization cooling rectilinear channel for a Muon Collider.