Improved sapphire dielectric resonators for ultrastable oscillators

It is shown that, in 5 cm Crystal Systems "HEMEX" resonators, unloaded Q values, not limited by wall losses, of 5-8 × 10⁹ at 2 K and 3 × 10⁹ at 6 K are possible. Frequency-temperature self-compensation, in which the temperature dependence of the real part of the AC susceptibility of paramagnetic impurities balances that due to the dielectric constant of the sapphire, can be achieved in H modes at convenient operating temperatures. Because chromium and iron concentrations are very small, ions with very high frequency ESRs provide essentially frequency-independent self-compensation, allowing freedom of choice of operating frequency. The dominant paramagnetic ion has been identified as Mo³⁺. Since the Mo³⁺ concentration is essentially fixed by the crystal growth process, and one desires the lowest possible frequency-temperature coefficient and dielectric loss, the H_m11 modes are the best candidates for high-stability HEMEX resonators. The observed power dependence of mode frequency, ~10^-8 W^-1, will require that resonator power fluctuations be maintained at less than 100 nW if a frequency stability of 1 × 10 ^-15 is to be achieved