Ultra-stable sapphire resonator-oscillator

Preliminary measurements of the properties of cryogenic sapphire resonators with various concentrations of paramagnetic impurities are reported. These resonators are mounted in both copper and niobium shields. It is found that one can achieve extrema in the frequency-temperature function in the temperature range 5-18 K due to the compensating effects of the dielectric constant temperature dependence and the Curie law dependence on the susceptibility of the paramagnetic impurities. In samples where dominant paramagnetic impurity has a high ESR (electron spin resonance) unloaded resonator Q factors as high as 4×10⁹ are observed. The increased Q factors coupled with reduced shield interactions should result in an improvement in frequency stability for an oscillator based around this resonator as compared to the best results achieved to date as the authors´ laboratory (an Allan variance of 9×10^-15). The preliminary measurement of the tilt sensitivity of the oscillator is reported to be a fractional frequency shift of 6.5×10^-12 per degree