水晶振動子を用いた摩擦真空計の理論

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The theory of a friction vacuum gauge using a tuning-fork-shaped quartz oscillator is presented. The dependences of electric impedance and resonance frequency of the quartz oscillator on gas pressure are theoretically analyzed on the basis of “a string-of-beads” model for the quartz oscillator. It is shown that the impedance change results from the velocity term of the drag acting on an oscillator, while the resonance frequency shift results from the acceleration term of the drag. The drag is calculated by means of the kinetic theory of gases in lower pressure (molecular flow) region, and by means of fluid mechanics in higher pressure (viscous flow) region. These theoretical results are found to be in quantitative agreement with experimental results. In particular, it is shown that the increase of impedance in the neighborhood of atmospheric pressure results from the small vibration of fluid (surrounding gas) rather than turbulent flow or the emission of sound. Also, theoretical predictions about the dependences of impedance and resonance frequency on gas species are experimentally verified.<BR>Furthermore, the pressure dependence of the impedance in intermediate pressure region is formulated by taking into account a “slip” effect of gas molecules at the surface of an object. By the formal extension of this formula to molecular flow region, a single formula describing the pressure dependence of the impedance over the whole pressure region is obtained. This formula is found to be in numerical agreement with experimental data.
日本真空協会の論文

水晶振動子を用いた摩擦真空計の理論

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