  This paper reports on a surface impedance measurement of a niobium titanium
superconducting radio frequency (SRF) cavity in a magnetic field (up to
$10\,{\rm T}$). A novel method is employed to decompose the surface resistance
contributions of the cylindrical cavity end caps and walls using measurements
from multiple $TM$ cavity modes. The results confirm that quality factor
degradation of a NbTi SRF cavity in a high magnetic field is primarily from
surfaces perpendicular to the field (the cavity end caps), while parallel
surface resistances (the walls) remain relatively constant. This result is
encouraging for applications needing high Q cavities in strong magnetic fields,
such as the Axion Dark Matter eXperiment (ADMX), because it opens the
possibility of hybrid SRF cavity construction to replace conventional copper
cavities.
