A Scanned Perturbation Technique For Imaging Electromagnetic Standing Wave Patterns of Microwave Cavities

We have developed a method to measure the electric field standing wave distributions in a microwave resonator using a scanned perturbation technique. Fast and reliable solutions to the Helmholtz equation (and to the Schrodinger equation for two dimensional systems) with arbitrarily-shaped boundaries are obtained. We use a pin perturbation to image primarily the microwave electric field amplitude, and we demonstrate the ability to image broken time-reversal symmetry standing wave patterns produced with a magnetized ferrite in the cavity. The whole cavity, including areas very close to the walls, can be imaged using this technique with high spatial resolution over a broad range of frequencies.Comment: To be published in Review of Scientific Instruments,September, 199

Complex microwave conductivity of Na-DNA powders

We report the complex microwave conductivity, $\sigma=\sigma_1-i\sigma_2$, of Na-DNA powders, which was measured from 80 K to 300 K by using a microwave cavity perturbation technique. We found that the magnitude of $\sigma_1$ near room temperature was much larger than the contribution of the surrounding water molecules, and that the decrease of $\sigma_1$ with decreasing temperature was sufficiently stronger than that of the conduction of counterions. These results clearly suggest that the electrical conduction of Na-DNA is intrinsically semiconductive.Comment: 16 pages, 7 figure

Electron density and collision frequency of microwave‐resonant‐cavity‐produced discharges

A review of perturbation diagnostics applied to microwave resonant cavity discharges is presented. The classical microwave perturbation technique examines the shift in the resonant frequency and cavity quality factor of the resonant cavity caused by low‐electron density discharges. However, the modifications presented allow the analysis to be applied to discharges with electron densities beyond the limit predicted by perturbation theory. An ‘‘exact’’ perturbation analysis is presented which models the discharge as a separate dielectric, thereby removing the restrictions on electron density imposed by the classical technique. The ‘‘exact’’ method also uses measurements of the shifts in the resonant conditions of the cavity. Third, an electromagnetic analysis is presented which uses a characteristic equation, based upon Maxwell’s laws, and predicts the discharge conductivity based upon measurements of a complex axial wave number. By allowing the axial wave number of the electromagnetic fields to be complex, the fields are experimentally and theoretically shown to be spatially attenuated. The diagnostics are applied to continuous‐wave microwave (2.45 GHz) discharges produced in an Asmussen resonant cavity. Double Langmuir probes, placed directly in the discharge at the point where the radial electric field is zero, act as a comparison with the analytic diagnostics. Microwave powers ranging from 30 to 100 W produce helium and nitrogen discharges with pressures ranging from 0.5 to 6 Torr. Analysis of the data predicts electron temperatures from 5 to 20 eV, electron densities from 1011 to 3×1012 cm−3, and collision frequencies from 109 to 1011 s−1.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69731/2/JAPIAU-74-6-3724-1.pd

Precision microwave dielectric and magnetic susceptibility measurements of correlated electronic materials using superconducting cavities

We analyze microwave cavity perturbation methods, and show that the technique is an excellent, precision method to study the dynamic magnetic and dielectric response in the $GHz$ frequency range. Using superconducting cavities, we obtain exceptionally high precision and sensitivity for measurements of relative changes. A dynamic electromagnetic susceptibility $\tilde{\zeta}(T)=\zeta ^{\prime}+i\zeta ^{\prime \prime}$ is introduced, which is obtained from the measured parameters: the shift of cavity resonant frequency $\delta f$ and quality factor $Q$. We focus on the case of a spherical sample placed at the center of a cylindrical cavity resonant in the $TE_{011}$ mode. Depending on the sample characteristics, the magnetic permeability $\tilde{\mu}$, the dielectric permittivity $\tilde{\epsilon}$ and the complex conductivity $\tilde{\sigma}$ can be extracted from $\tilde{\zeta}_{H}$. A full spherical wave analysis of the cavity perturbation is given. This analysis has led to the observation of new phenomena in novel low dimensional materials.Comment: 16 pages, 5 figure

Application of the Bead Perturbation Technique to a Study of a Tunable 5 GHz Annular Cavity

Microwave cavities for a Sikivie-type axion search are subject to several constraints. In the fabrication and operation of such cavities, often used at frequencies where the resonator is highly overmoded, it is important to be able to reliably identify several properties of the cavity. Those include identifying the symmetry of the mode of interest, confirming its form factor, and determining the frequency ranges where mode crossings with intruder levels cause unacceptable admixture, thus leading to the loss of purity of the mode of interest. A simple and powerful diagnostic for mapping out the electric field of a cavity is the bead perturbation technique. While a standard tool in accelerator physics, we have, for the first time, applied this technique to cavities used in the axion search. We report initial results from an extensive study for the initial cavity used in the HAYSTAC experiment. Two effects have been investigated: the role of rod misalignment in mode localization, and mode-mixing at avoided crossings of TM/TE modes. Future work will extend these results by incorporating precision metrology and high-fidelity simulations.Comment: 6 pages, 4 figures, submitted to the 2nd Workshop on Microwave Cavities and Detectors for Axion Researc

Complex microwave conductivity of Pr1.85_{1.85}Ce0.15_{0.15}CuO4−δ_{4-\delta} thin films using a cavity perturbation method

We report a study of the microwave conductivity of electron-doped Pr$_{1.85}$Ce$_{0.15}$CuO$_{4-\delta}$ superconducting thin films using a cavity perturbation technique. The relative frequency shifts obtained for the samples placed at a maximum electric field location in the cavity are treated using the high conductivity limit presented recently by Peligrad $\textit{et}$ $\textit{al.}$ Using two resonance modes, TE$_{102}$ (16.5 GHz) and TE$_{101}$ (13 GHz) of the same cavity, only one adjustable parameter $\Gamma$ is needed to link the frequency shifts of an empty cavity to the ones of a cavity loaded with a perfect conductor. Moreover, by studying different sample configurations, we can relate the substrate effects on the frequency shifts to a scaling factor. These procedures allow us to extract the temperature dependence of the complex penetration depth and the complex microwave conductivity of two films with different quality. Our data confirm that all the physical properties of the superconducting state are consistent with an order parameter with lines of nodes. Moreover, we demonstrate the high sensitivity of these properties on the quality of the films

Rapid, non-invasive characterization of the dispersity of emulsions via microwaves

A rapid and non-invasive method to determine the dispersity of emulsions is developed based on the interrelationship between the droplet size distribution and the dielectric properties of emulsions. A range of water-in-oil emulsions with different water contents and droplet size distributions were analysed using a microwave cavity perturbation technique together with dynamic light scattering. The results demonstrate that the dielectric properties, as measured by non-invasive microwave cavity analysis, can be used to characterise the dispersity of emulsions, and is also capable of characterizing heavy oil emulsions. This technique has great potential for industrial applications to examine the sedimentation, creaming and hence the stability of emulsions

Temperature correction for cylindrical cavity perturbation measurements

The need for accurate material property measurements using microwave cavities requires a form of compensation to correct for changes in temperature and other external influences. This paper details a method for temperature correcting microwave cavity perturbation measurements by monitoring two modes; one which is perturbed by the sample and one which is not (referred to as a nodal mode). The nodal modes used (TM310 and TE311 for an axial sample in a cylindrical cavity) are subject only to sample-independent influences. To demonstrate this technique, the bulk permittivity of a PTFE rod has been measured under varying temperature conditions. The results show that without correction, the measured temperature-dependent dielectric constant has large variations associated with the stepped and linear temperature ramping procedures. The corrected response mitigates systematic errors in the real part. However, the correction of the imaginary part requires careful consideration of the mode coupling strength. This paper demonstrates the importance of temperature correction in dynamic cavity perturbation experiments

Apparatus for high resolution microwave spectroscopy in strong magnetic fields

We have developed a low temperature, high-resolution microwave surface impedance probe that is able to operate in high static magnetic fields. Surface impedance is measured by cavity perturbation of dielectric resonators, with sufficient sensitivity to resolve the microwave absorption of sub-mm-sized superconducting samples. The resonators are constructed from high permittivity single-crystal rutile (TiO2) and have quality factors in excess of 10^6. Resonators with such high performance have traditionally required the use of superconducting materials, making them incompatible with large magnetic fields and subject to problems associated with aging and power-dependent response. Rutile resonators avoid these problems while retaining comparable sensitivity to surface impedance. Our cylindrical rutile resonators have a hollow bore and are excited in TE_01(n-d) modes, providing homogeneous microwave fields at the center of the resonator where the sample is positioned. Using a sapphire hot-finger technique, measurements can be made at sample temperatures in the range 1.1 K to 200 K, while the probe itself remains immersed in a liquid helium bath at 4.2 K. The novel apparatus described in this article is an extremely robust and versatile system for microwave spectroscopy, integrating several important features into a single system. These include: operation at high magnetic fields; multiple measurement frequencies between 2.64 GHz and 14.0 GHz in a single resonator; excellent frequency stability, with typical drifts < 1 Hz per hour; the ability to withdraw the sample from the resonator for background calibration; and a small pot of liquid helium separate from the external bath that provides a sample base temperature of 1.1 K.Comment: 10 pages, 5 figure