  A method for determining the internal DC magnetic field inside a
superconducting cavity is presented. The method relies on the relationship
between magnetic field and frequency of the Kittel mode of a ferrimagnetic
sphere, hybridised in the dispersive regime of the superconducting cavity.
Results were used to experimentally determine the level of screening a
superconducting Nb cavity provides as it changes from perfect diamagnetism to
no screening. Two cavity geometries were tested, a cylinder and single post
re-entrant cavity. Both demonstrated a consistent value of field that enters
the cavity, expected to be the superheating critical field. Hysteresis in the
screened field during ramp up and ramp down of the external magnetic field due
to trapped vortices was also observed. Some abnormal behaviour was observed in
the cylindrical cavity in the form of plateaus in the internal field above the
first critical field, and we discuss the potential origin of this behaviour.
The measurement approach would be a useful diagnostic for axion dark matter
searches, which plan on using superconducting materials but need to know
precisely the internal magnetic field.
