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Bulk superconductors, in their capacity as trapped field magnets, offer a practical means of generating high magnetic fields in small volumes. This is desirable for applications in which portability is of primary concern. In particular, superconducting materials are seen as enablers leading towards light-weight, high power density electric motors to be used in future hybrid-electric passenger aircraft. One of the issues that needs to be addressed before this can become a reality, however, is the instability of trapped magnetic field in these materials, when exposed to external time-varying magnetic fields. In this work a comprehensive study of the effect of AC magnetic fields on the trapped magnetic field in bulk superconductors is presented. Two distinct geometries are studied; the crossed-field and the parallel configuration, in which the AC magnetic field is applied perpendicular or parallel to the direction of trapped magnetic field, respectively. An analytical empirical model is derived, with which the decay of trapped magnetic field in the crossed-field configuration can be predicted accurately, provided the value of the critical current density in the material is known. The model is found to be in excellent agreement with the observed experimental data, as well as with finite-element numerical simulations. In the parallel configuration the time dependence of trapped magnetic field is studied as a function of the AC magnetic field amplitude, its frequency and the operating temperature of the superconductor. Subsequently, the data are compared with their equivalent in the crossed-field configuration. It is found that, while the crossed-field configuration leads to a greater rate of decay of trapped field, in both configurations reducing the operating temperature proves an effective mitigation measure against it. Lastly, the limits of the well established Bean critical state model are studied within the scope of the Campbell penetration depth of magnetic field, which is, itself, a direct consequence of the reversible and elastic movement of flux vortices within the pinning potential. I derive a convenient way of measuring the Campbell penetration depth using a pick-up method, and present measurements of its value in a bulk superconductor at different applied magnetic fields.