The frequency fluctuations of an electronically cooled rotor

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Abstract
Calculations show that even a modest-sized laboratory rotor can exhibit stability comparable to that of good frequency standards if it is sufficiently undisturbed and if its moment of inertia is constant enough. Further, they show that electronic cooling, by derivative feedback, can cause these properties to be exhibited in much more useful regimes of time and frequency. This paper describes theoretical and experimental efforts to evaluate the effects of such feedback on a practical rotor, presently far from ideal. The stability measurements are presented in the context of averaging or observing times and are given as Allan variances. Representative results for a small (few centimeters) rotor with a magnetic suspension bearing show noise 4–5 orders of magnitude above the ideal, i.e., noise caused only by molecular bombardment. These analyses are in the region of averaging times from 10 to 100 000 s, and the measurements were in a laboratory in which the temperature fluctuates a few degrees Centigrade. Measured and calculated transfer functions from temperature variations show that a significant part of the excess noise is caused by these variations. Electronic cooling by feedback behaves as expected in modifying the noise spectrum. The changes in the excess noise are the same as those calculated for molecular bombardment noise, thus indicating that the excess noise comes from frequency-independent driving torques.