Waveguide effects on quasispherical microwave cavity resonators

Underwood, Robin; Mehl, James B.; Pitre, Laurent; Edwards, G. J.; Sutton, Gavin; Podesta, Michael de

doi:10.1088/0957-0233/21/7/075103

Cited by 39 publications

(70 citation statements)

References 17 publications

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“…For such geometry, a theoretical calculation of the second-order corrections of microwave eigenvalues has only recently been completed [21], and found to be in outstanding agreement with the results of experiments [22].…”

Section: Introductionmentioning

confidence: 83%

“…In 1986, Mehl and Moldover [12] used first-order perturbation theory to prove that the mean eigenfrequency of a multiplet is independent of volume-preserving deformations, and suggested that the volume of an imperfect spherical resonator could thus be determined from its microwave spectrum. Several of our earlier papers have set the groundwork for this determination [2,3,16,20,22].…”

Section: Measurement Of the Volume Of The Resonatormentioning

confidence: 99%

“…-the microwave penetration depth using measured half-widths of the resonances, as described in [2]; -the inlet and outlet gas ducts and the two microwave antennas using the extensive study of the effects of probes and holes in a QSR performed by Underwood et al [22]; -the shape of the QSR, using Mehl's second-order theory [21] and our measurements of the frequency splitting of the microwave triplets.…”

Section: Measurement Of the Volume Of The Resonatormentioning

confidence: 99%

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Measurement of the Boltzmann Constant k B Using a Quasi-Spherical Acoustic Resonator

et al. 2011

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There is currently great interest in the international metrological community for new accurate determinations of the Boltzmann constant k B , with the prospect of a new definition of the unit of thermodynamic temperature, the kelvin. In fact, k B relates the unit of energy (the joule) to the unit of the thermodynamic temperature (the kelvin). One of the most accurate ways to access the value of the Boltzmann constant is from measurements of the velocity of the sound in a noble gas. In the method described here, the experimental determination has been performed in a closed quasi-spherical cavity. To improve the accuracy, all the parameters in the experiment (purity of the gas, static pressure, temperature, exact shape of the cavity monitored by EM microwaves, etc.) have to be carefully controlled. Correction terms have been computed using carefully validated theoretical models, and applied to the acoustic and microwave signals. We report on two sets of isothermal acoustic measurements yielding the value k B = 1.380 647 74(171) × 10 −23 J · K −1 with a relative standard uncertainty of 1.24 parts in 10 6 . This value lies 1.9 parts in 10 6 below the 2006 CODATA value (Mohr et al., Rev. Mod. Phys. 80, 633 (2008)), but, according to the uncertainties, remains consistent with it.

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Section: Introductionmentioning

confidence: 83%

Section: Measurement Of the Volume Of The Resonatormentioning

confidence: 99%

Section: Measurement Of the Volume Of The Resonatormentioning

confidence: 99%

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Measurement of the Boltzmann Constant k B Using a Quasi-Spherical Acoustic Resonator

et al. 2011

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“…In this work, the average radius of BCU3 has been determined from measurements of the frequencies and half-widths of nine microwave triplets, corrected to take into account three effects: (i) the microwave penetration depth using measured half-widths of the resonances, as described by Sutton et al [2], (ii) the inlet and outlet gas ducts and the two microwave antennas using the extensive study of the effects of probes and holes in a quasi-spherical resonator (QSR) performed by Underwood et al [22], and (iii) the shape of the QSR, using second-order theory [21] and our measurements of the frequency splitting of the microwave triplets. The determination of the equivalent radius and its uncertainty budget was accomplished in four steps.…”

Section: Precise Measurement Of the Volume Of The Resonatormentioning

confidence: 99%

“…We corrected these frequencies to account for shape and probe perturbations using the models and the results in Underwood et al [22]. -With loop antennas, we determined the electrical conductivity of the copper surface and established a bound on any dielectric layer on the surface, in the same experimental conditions (20 • C and flowing argon) as those specified for the previous step.…”

Section: Precise Measurement Of the Volume Of The Resonatormentioning

confidence: 99%

Determination of the Boltzmann constant using a quasi-spherical acoustic resonator

Pitre

Sparasci

Truong

et al. 2011

Phil. Trans. R. Soc. A.

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The paper reports a new experiment to determine the value of the Boltzmann constant, k B = 1.3806477(17) × 10 −23 J K −1 , with a relative standard uncertainty of 1.2 parts in 10 6 . k B was deduced from measurements of the velocity of sound in argon, inside a closed quasispherical cavity at a temperature of the triple point of water. The shape of the cavity was achieved using an extremely accurate diamond turning process. The traceability of temperature measurements was ensured at the highest level of accuracy. The volume of the resonator was calculated from measurements of the resonance frequencies of microwave modes. The molar mass of the gas was determined by chemical and isotopic composition measurements with a mass spectrometer. Within combined uncertainties, our new value of k B is consistent with the 2006 Committee on Data for Science and Technology (CODATA) value: (k new B /k B_CODATA − 1) = −1.96 × 10 −6 , where the relative uncertainties are u r (k new B ) = 1.2 × 10 −6 and u r (k B_CODATA ) = 1.7 × 10 −6 . The new relative uncertainty approaches the target value of 1 × 10 −6 set by the Consultative Committee on Thermometry as a precondition for redefining the unit of the thermodynamic temperature, the kelvin.

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Acoustic Resonator Experiments at the Triple Point of Water: First Results for the Boltzmann Constant and Remaining Challenges

et al. 2010

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We report on two sets of isothermal acoustic measurements made with argon close to the triple point of water using a 50 mm radius, thin-walled, diamondturned quasisphere. Our two isotherms yielded values for the Boltzmann constant, k B , which differ by 0.9 parts in 10 6 , and have an average value of k B = (1.380 649 6 ± 0.000 004 3) × 10 −23 J · K −1 . The relative uncertainty is 3.1 parts in 10 6 , and the average value is 0.58 parts in 10 6 below the 2006 CODATA value (Mohr et al. Rev Mod Phys 80:633, 2008), and so the values are consistent within their combined (k = 1) uncertainties.

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Waveguide effects on quasispherical microwave cavity resonators

Cited by 39 publications

References 17 publications

Measurement of the Boltzmann Constant k B Using a Quasi-Spherical Acoustic Resonator

Measurement of the Boltzmann Constant k B Using a Quasi-Spherical Acoustic Resonator

Determination of the Boltzmann constant using a quasi-spherical acoustic resonator

Acoustic Resonator Experiments at the Triple Point of Water: First Results for the Boltzmann Constant and Remaining Challenges

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