Lawrence Berkeley National Laboratory

High-gradient normal-conducting radio-frequency (rf) cavities are crucial components of the rectilinear cooling channel in a muon collider, providing the accelerating field necessary to sustain the rapid six-dimensional ionization cooling essential to achieve high luminosity. To reach this goal, a muon collider requires approximately 10 12 muons per bunch. At such high beam intensities, beam loading induced by bunch-driven wakefields can significantly reduce the cavity accelerating gradient and compromise beam stability. This paper focuses on the conceptual rf design and beam-induced-effect analysis of copper cavities with so-called beam windows developed to meet the beam dynamics requirements of the rectilinear muon cooling channel. We first present the design and optimization of the cavities, evaluating their rf performance and power requirements. Thereafter, we analyze cavity wakefields and beam loading effects, proposing a new numerical method for their compensation, which takes the transverse distribution of the beam into account.