Multimode dielectric resonator for accurate determination of frequency and temperature dependence of complex permittivity in small, high-permittivity cylinders

Abstract

We present a technique to measure permittivity and loss tangent in high-permittivity cylinders. This method utilizes a resonator to conduct concurrent measurements at the three lowest quasi-TE01p modes across various temperatures, combined with an algorithm to fit the loss tangent dependence on frequency and temperature. Our technique serves as a preliminary step to characterize dielectrics used in Hakki–Coleman resonators for surface resistance measurements. Consequently, parameters for dielectric characterization—such as sample size and modes used—are determined by the requirements of subsequent surface resistance measurements, rather than optimizing the determination of the material’s intrinsic dielectric properties. Despite this focus, our measurements on rutile align well with existing literature. We conducted measurements on three rutile samples from the same production batch, covering a frequency range from 6.0 to 9.4 GHz, with uncertainties of less than 0.7% for permittivity and 13% for loss tangent. These measurements revealed sample-to-sample differences that cannot be attributed to measurement uncertainty alone. Our findings suggest that the previous approach of using multiple rutile crystals with varying sizes to assess the frequency dependence of dielectric loss may lead to significant uncertainty in predicting loss tangents due to variations in sample properties. We describe the possible extension of this technique to characterize other dielectrics beyond rutile, including commercial dielectrics, across frequency and temperature. We also discuss its potential widespread application in the use of Hakki–Coleman resonators for quality control of materials used in particle accelerators, such as the future circular collider hadron-hadron (FCC-h).

This work was supported by CERN under Grant FCC-GOV-CC-0210 (KE4945/ATS) and Grant FCC-GOV-CC-0209 (KE4946/ATS). The work of Nikki Tagdulang was supported for the Ph.D. Scholarship under Grant MSCA-COFUND-2016-754397.

Peer Reviewed

Postprint (published version)