  Ionization cooling is the preferred method for producing bright muon beams.
This cooling technique requires the operation of normal conducting,
radio-frequency (RF) accelerating cavities within the multi-tesla fields of DC
solenoid magnets. Under these conditions, cavities exhibit increased
susceptibility to RF breakdown, which can damage channel components and imposes
limits on channel length and transmission efficiency. We present a solution to
the problem of breakdown in strong magnetic fields. We report, for the first
time, stable high-vacuum, copper cavity operation at gradients above 50 MV/m
and in an external magnetic field of three tesla. This eliminates a significant
technical risk that has previously been inherent in ionization cooling channel
designs.
