Muon accelerators have the potential to open new paths for advancing particle physics, in both the intensity and energy frontiers. The short lifetime of muons and strict limitations on the muon beam emittance require the implementation of ionization cooling. Most contemporary designs of muon ionization cooling channels require high-gradient, normal-conducting RF accelerating cavities in multi-tesla solenoidal magnetic fields. One of the limitations of cavities' performance is RF breakdown. It was experimentally shown that the presence of an external magnetic field increases breakdown rate at a given gradient. The pulsed heating model that describes the role of the magnetic field during breakdown was developed. The model proposes that cyclic fatigue leads to the degradation of metal surfaces and, eventually, breakdown. The cyclic fatigue is caused by the periodic bombardment of cavity surfaces by dark current electrons, which are emitted from local surface imperfections and focused by the external magnetic field.
An 805 MHz pillbox cavity was designed to study the effect of external magnetic field on RF breakdown. The "modular" design of the cavity allowed for control over sources of systematic error and frequent surface inspections. Frequent inner surface inspections are essential for tracking breakdown damage and understanding the effect of different materials on RF breakdown. I will discuss the results of high power tests of the Modular Cavity with copper and beryllium walls in the range of magnetic fields. Measured gradient performance is tested against the predictions of the pulsed heating model.