The magnetic response of a type II superconductor lo an applied magnetic field is described by solving the Bean model and viscous flux flow equations simultaneously. Two analytical solutions are presented, which detail the flux distribution within the superconductor induced by a sawtooth-like applied magnetic field. The resultant hysteresis loops show features which depend strongly on the 'sharpness' of the sawtooth waveform. A s expected the magnetic hysteresis losses increase with frequency, reflecting t h e viscous nature of t h e flux flow. In the zero frequency limit. as the velocity of flux flow approaches zero. the usual Bean result is obtained.

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Propagation properties of quasi-longitudinal leaky surface acoustic wave (QLL-SAW) on rotated-Y cut quartz are described. It is found that by reducing the relative thickness of quartz substrate, i.e. the ratio of the substrate thickness to the SAW wavelength, Q-value of QLL-SAW resonator can be improved. Its phase velocity is about 5704 m/s, which is close to the velocity of longitudinal BAW (5750m/s) and about 1.8 times that of Rayleigh SAW. Propagation characteristics are simulated using finite element method. The results indicate that many guided wave modes exist near the velocity of the longitudinal BAW and strongly couple to QLL-SAW modes. Experimental results show these guided wave modes affect QLL-SAW propagation and deteriorate the resonator Q-values. By reducing the relative thickness of quartz substrate, frequency difference between QLL-SAW and the guided wave modes increases, which weakens the coupling. As a result, 700 MHz SAW resonators having a Q-value of over 8000 are realized.