  In halo dark matter axion search experiments, cylindrical microwave cavities
are typically employed to detect signals from the axion-photon conversion. To
enhance the conversion power and reduce the noise level, cavities are placed in
strong solenoid magnetic fields at sufficiently low temperatures. Exploring
high mass regions in cavity-based axion search experiments requires high
frequency microwave cavities and thus understanding cavity properties at high
frequencies in extreme conditions is deemed necessary. We present a study of
the magnetoresistance of copper using a cavity with a resonant frequency of
12.9 GHz at the liquid helium temperature in magnetic fields up to 15 T
utilizing a second generation high temperature superconducting magnet. The
observations are interpreted to be consistent with the anomalous skin effect
and size effect. This is the first measurement of magnetoresistance at a high
frequency (> 10 GHz) in high magnetic fields (> 10 T).
