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.

Using a K-cut quartz SAW resonator, which is significantly less sensitive to thermalshock than an ST-cut quartz SAW resonator, we studied their design and made prototype SAW resonators w i t h cylindrical capsules.They have zero temperature coefficient of frequency at room temperature and have good properties for practical use.

A new type of quartz SAW resonator for use as a stable frequency source has been developed. It was studied from the point of view of frequency instability caused by transient thermal behavior, and a new angle of cut named the K-cut for quartz SAW resonators was found. The static and dynamic frequency temperature coefficients are both zero at a room temperature. Taking into consideration the influence of the electrode-film thickness, the width modes of the waves, and power-flow angles, optimized resonators and oscillators were designed. These devices had frequency stability of 2x10(-10) for the mean time of 0.01 s.