This research has two major components. The first is the development of a new theory that extends the critical state model of the quasi-static magnetization of type-II superconductors to rapidly changing fields where viscous retardation of the motion of flux cannot be ignored. Secondly we have designed and used a system to automatically measure losses and third harmonic generation in oriented samples of {dollar}rm YBasb2Cusb3Osb7 and DyBasb2Cusb3Osb7{dollar} at audio frequencies and beyond.; The theory indicates that the dynamics of flux penetration into a superconducting specimen is seen to proceed as a front whose velocity decreases rapidly with time and approaches the critical state model as a limit. A diffusion relaxation time, in a medium of resistivity {dollar}psb{lcub}f{rcub}{dollar} over a distance of full penetration length, is introduced to characterize this flux motion. This time constant is defined by {dollar}tau = 10sp{lcub}-7{rcub}Hsbsp{lcub}0{rcub}{lcub}2{rcub}/4pi Jsbsp{lcub}c{rcub}{lcub}2{rcub}psb{lcub}f{rcub},{dollar} where {dollar}Hsb0{dollar} is the driving magnetic field amplitude and {dollar}Jsb{lcub}c{rcub}{dollar} the critical current density.; The theory, when extrapolated to infinitely small driving fields, predicts that surface losses per cycle are proportional to the cube of the amplitude of the applied field while the amplitude of the third harmonic in the non-linear response is proportional to the square of the field. These dependences are confirmed by the experiments.; At high driving fields, the extended critical state model predicts that the loss per cycle decreases with increasing frequency after an increase at low frequencies. The peak occurs at around {dollar}nusb{lcub}m{rcub} = 0.15tausp{lcub}-1{rcub}.{dollar} The theory also predicts that the amplitude of the third harmonic decreases monotonically with increasing frequency. All these effects are observed in the experiments.; The effect of thermally assisted flux flow is observed at 77K where there is a sharp increase of loss at low frequencies. This effect is seen to be somewhat less evident at a lower temperature. In addition, critical currents can be inferred from either the losses or the generation of the third harmonics. Both calculations yield the same value which warrants the validity of the theory.; Furthermore, two experimental methods have been employed in determining the losses. The first is by measuring the phase angle and the amplitude of the first harmonic of dB/dt. The second technique involves the use of a phase-sensitive detector to construct hysteresis loops by taking the output voltage as a function of the phase angle between applied field and detector setting. The two methods give, within experimental error, identical results over the frequency range we have covered.
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