  A high Q-factor microwave resonator in a high magnetic field could be of
great use in a wide range of fields, from accelerator design to axion dark
matter search. The natural choice of material for the superconducting cavity to
be placed in a high field is a high temperature superconductor (HTS) with a
high critical field. The deposition, however, of a high-quality, grain-aligned
HTS film on a three-dimensional surface is technically challenging. We have
fabricated a polygon-shaped resonant cavity with commercial
YBa$_2$Cu$_3$O$_{7-x}$ (YBCO) tapes covering the entire inner wall and measured
the Q-factor at 4 K at 6.93 GHz as a function of an external DC magnetic field.
We demonstrated that the high Q-factor of the superconducting YBCO cavity
showed no significant degradation from 1 T up to 8 T. This is the first
indication of the possible applications of HTS technology to the research areas
requiring a strong magnetic field at high radio frequencies.
