Critical-state model for harmonic generation in high-temperature superconductors

High-temperature superconductors exhibit harmonic generation when immersed in an ac magnetic field. To explain this phenomenon, we propose a macroscopic critical-state model as an alternative to the loop model used by Jeffries et al. While the original Bean model of the critical state only predicts odd harmonics, our extended model also predicts even harmonics by taking into account the dependence of the critical current upon magnetic field. The results of our measurements of harmonic signals as a function of ac magnetic field, dc magnetic field, temperature, and harmonic number are consistent with the proposed model. In particular, we find that, as the magnetic field is increased, the critical current crosses over from the Bean regime, where $J_c$ is independent of field, to the Anderson-Kim regime, where $J_c$ is approximately inversely proportional to the field.