Gordon Coupler with Inductive or Capacitive Iris for Small EPR Resonators for Aqueous Samples.

The Gordon coupler was introduced for use in EPR experiments at liquid helium temperatures. It provides an evanescent wave incident on the iris of a microwave resonator. Match of power incident on the coupler to the resonator is obtained by variation of the amplitude of an evanescent wave that arises from displacement of a dielectric wedge in a tapered waveguide. Reduced microphonics from helium bubbling was reported. The Gordon coupler was subsequently extended from cavity resonators to loop-gap resonators, initially at helium temperatures but later for aqueous samples. Plastics with low dielectric constants, usually Teflon, were used. Here, we extend the Gordon coupler for application in X-band five-loop-four-gap resonators using fused quartz, sapphire, or rutile dielectrics, noting that the size of the coupler can then be commensurate with dimensions of dielectric loop-gap resonators as well as dielectric tube resonators. Finite element modeling of electromagnetic fields has been carried out, and use of a capacitive iris that interfaces with the Gordon coupler reduces pulling of the resonant frequency when matching the resonator.

EPR UNIFORM FIELD SIGNAL ENHANCEMENT BY DIELECTRIC TUBES IN CAVITIES.

The dielectric tube resonator (DTR) for EPR spectroscopy is introduced. It is defined as a metallic cylindrical TE011 microwave cavity that contains a dielectric tube centered on the axis of the cylinder. Contour plots of dimensions of the metallic cylinder to achieve resonance at 9.5 GHz are shown for quartz, sapphire, and rutile tubes as a function of wall thickness and average radius. These contour plots were developed using analytical equations and confirmed by finite element modeling. They can be used in two ways: design of the metallic cylinder for use at 9.5 GHz that incorporates a readily available tube such as a sapphire tube intended for NMR, or design of a custom procured tube for optimized performance for specific sample-size constraints. The charts extend to the limiting condition where the dielectric fills the tube. However, the structure at this limit is not a dielectric resonator due to the metal wall and does not radiate. In addition, the uniform field (UF) DTR is introduced. Development of the UF resonator starting with a dielectric tube resonator is shown. The diameter of the tube remains constant along the cavity axis, and the diameter of the cylindrical metallic enclosure increases at the ends of the cavity to satisfy the uniform field condition. This structure has advantages over the previously developed UF TE011 resonators: higher resonator efficiency parameter Λ, convenient overall size when using sapphire tubes, and higher quality data for small samples. The DTR and UF DTR structures fill the gap between free space and dielectric resonator limits in a continuous manner.

A pressure-jump EPR system to monitor millisecond conformational exchange rates of spin-labeled proteins.

Site-directed spin labeling electron paramagnetic resonance (SDSL-EPR) using nitroxide spin labels is a well-established technology for mapping site-specific secondary and tertiary structure and for monitoring conformational changes in proteins of any degree of complexity, including membrane proteins, with high sensitivity. SDSL-EPR also provides information on protein dynamics in the time scale of ps-µs using continuous wave lineshape analysis and spin lattice relaxation time methods. However, the functionally important time domain of µs-ms, corresponding to large-scale protein motions, is inaccessible to those methods. To extend SDSL-EPR to the longer time domain, the perturbation method of pressure-jump relaxation is implemented. Here, we describe a complete high-pressure EPR system at Q-band for both static pressure and millisecond-timescale pressure-jump measurements on spin-labeled proteins. The instrument enables pressure jumps both up and down from any holding pressure, ranging from atmospheric pressure to the maximum pressure capacity of the system components (~3500 bar). To demonstrate the utility of the system, we characterize a local folding-unfolding equilibrium of T4 lysozyme. The results illustrate the ability of the system to measure thermodynamic and kinetic parameters of protein conformational exchange on the millisecond timescale.

Uniform Field Resonators for EPR Spectroscopy: A Review.

Cavity resonators are often used for electron paramagnetic resonance (EPR). Rectangular TE102 and cylindrical TE011 are common modes at X-band even though the field varies cosinusoidally along the Z-axis. The authors found a way to create a uniform field (UF) in these modes. A length of waveguide at cut-off was introduced for the sample region, and tailored end sections were developed that supported the microwave resonant mode. This work is reviewed here. The radio frequency (RF) magnetic field in loop-gap resonators (LGR) at X-band is uniform along the Z-axis of the sample, which is a benefit of LGR technology. The LGR is a preferred structure for EPR of small samples. At Q-band and W-band, the LGR often exhibits nonuniformity along the Z-axis. Methods to trim out this nonuniformity, which are closely related to the methods used for UF cavity resonators, are reviewed. In addition, two transmission lines that are new to EPR, dielectric tube waveguide and circular ridge waveguide, were recently used in UF cavity designs that are reviewed. A further benefit of UF resonators is that cuvettes for aqueous samples can be optimum in cross section along the full sample axis, which improves quantification in EPR spectroscopy of biological samples.

Rutile dielectric loop-gap resonator for X-band EPR spectroscopy of small aqueous samples.

The performance of a metallic microwave resonator that contains a dielectric depends on the separation between metallic and dielectric surfaces, which affects radio frequency currents, evanescent waves, and polarization charges. The problem has previously been discussed for an X-band TE011 cylindrical cavity resonator that contains an axial dielectric tube (Hyde and Mett, 2017). Here, a short rutile dielectric tube inserted into a loop-gap resonator (LGR) at X-band, which is called a dielectric LGR (dLGR), is considered. The theory is developed and experimental results are presented. It was found that a central sample loop surrounded by four "flux-return" loops (i.e., 5-loop-4-gap) is preferable to a 3-loop-2-gap configuration. For sufficiently small samples (less than 1 µL), a rutile dLGR is preferred relative to an LGR both at constant Λ (B1/Pl) and at constant incident power. Introduction of LGR technology to X-band EPR was a significant advance for site-directed spin labeling because of small sample size and high Λ. The rutile dLGR introduced in this work offers further extension to samples that can be as small as 50  nL when using typical EPR acquisition times.

Multipurpose EPR loop-gap resonator and cylindrical TE011 cavity for aqueous samples at 94 GHz.

A loop-gap resonator (LGR) and a cylindrical TE(011) cavity resonator for use at W band, 94 GHz, have been designed and characterized using the Ansoft (Pittsburgh, PA) high frequency structure simulator (HFSS; Version 10.0). Field modulation penetration was analyzed using Ansoft MAXWELL 3D (Version 11.0). Optimizing both resonators to the same sample sizes shows that EPR signal intensities of the LGR and TE(011) are similar. The 3 dB bandwidth of the LGR, on the order of 1 GHz, is a new advantage for high frequency experiments. Ultraprecision electric discharge machining (EDM) was used to fabricate the resonators from silver. The TE(011) cavity has slots that are cut into the body to allow penetration of 100 kHz field modulation. The resonator body is embedded in graphite, also cut by EDM techniques, for a combination of reasons that include (i) reduced microwave leakage and improved TE(011) mode purity, (ii) field modulation penetration, (iii) structural support for the cavity body, and (iv) machinability by EDM. Both resonators use a slotted iris. Variable coupling is provided by a three-stub tuning element. A collet system designed to hold sample tubes has been implemented, increasing repeatability of sample placement and reducing sample vibration noise. Initial results include multiquantum experiments up to 9Q using the LGR to examine 1 mM 2,2,6,6-tetramethylpiperidine-1-oxyl (TEMPO) in aqueous solution at room temperature and field modulation experiments using the TE(011) cavity to obtain an EPR spectrum of 1 microM TEMPO.

Extruded dielectric sample tubes of complex cross section for EPR signal enhancement of aqueous samples.

This paper builds on the work of Mett and Hyde (2003) and Sidabras et al. (2005) where multiple flat aqueous sample cells placed perpendicular to electric fields in microwave cavities were used to reduce the RF losses and increase the EPR signal. In this work, we present three novel sample holders for loop-gap resonators (LGRs) and cylindrical cavity geometries. Two sample holders have been commissioned and built by polytetrafluoroethylene (PTFE) extrusion techniques: a 1mm O.D. capillary with a septum down the middle, named DoubleDee, and a 3.5mm O.D. star shaped sample holder, named AquaStar. Simulations and experimental results at X-band show that the EPR signal intensity increases by factors of 1.43 and 3.87 in the DoubleDee and AquaStar respectively, over the current TPX 0.9mm O.D. sample tube in a two-loop-one-gap LGR. Finally, combining the insight gained from the constructed sample holders and finite-element solutions, a third multi-lumen sample holder for a cylindrical TE011 cavity is optimized, named AquaSun, where simulations show an EPR signal intensity increase by a factor of 8.2 over a standard 1mm capillary.

Uniform field loop-gap resonator and rectangular TEU02 for aqueous sample EPR at 94GHz.

In this work we present the design and implementation of two uniform-field resonators: a seven-loop-six-gap loop-gap resonator (LGR) and a rectangular TEU02 cavity resonator. Each resonator has uniform-field-producing end-sections. These resonators have been designed for electron paramagnetic resonance (EPR) of aqueous samples at 94GHz. The LGR geometry employs low-loss Rexolite end-sections to improve the field homogeneity over a 3mm sample region-of-interest from near-cosine distribution to 90% uniform. The LGR was designed to accommodate large degassable Polytetrafluorethylen (PTFE) tubes (0.81mm O.D.; 0.25mm I.D.) for aqueous samples. Additionally, field modulation slots are designed for uniform 100kHz field modulation incident at the sample. Experiments using a point sample of lithium phthalocyanine (LiPC) were performed to measure both the uniformity of the microwave magnetic field and 100kHz field modulation, and confirm simulations. The rectangular TEU02 cavity resonator employs over-sized end-sections with sample shielding to provide an 87% uniform field for a 0.1×2×6mm3 sample geometry. An evanescent slotted window was designed for light access to irradiate 90% of the sample volume. A novel dual-slot iris was used to minimize microwave magnetic field perturbations and maintain cross-sectional uniformity. Practical EPR experiments using the application of light irradiated rose bengal (4,5,6,7-tetrachloro-2',4',5',7'-tetraiodofluorescein) were performed in the TEU02 cavity. The implementation of these geometries providing a practical designs for uniform field resonators that continue resonator advancements towards quantitative EPR spectroscopy.

Broadband W-band Rapid Frequency Sweep Considerations for Fourier Transform EPR.

A multi-arm W-band (94 GHz) electron paramagnetic resonance spectrometer that incorporates a loop-gap resonator with high bandwidth is described. A goal of the instrumental development is detection of free induction decay following rapid sweep of the microwave frequency across the spectrum of a nitroxide radical at physiological temperature, which is expected to lead to a capability for Fourier transform electron paramagnetic resonance. Progress toward this goal is a theme of the paper. Because of the low Q-value of the loop-gap resonator, it was found necessary to develop a new type of automatic frequency control, which is described in an appendix. Path-length equalization, which is accomplished at the intermediate frequency of 59 GHz, is analyzed. A directional coupler is favored for separation of incident and reflected power between the bridge and the loop-gap resonator. Microwave leakage of this coupler is analyzed. An oversize waveguide with hyperbolic-cosine tapers couples the bridge to the loop-gap resonator, which results in reduced microwave power and signal loss. Benchmark sensitivity data are provided. The most extensive application of the instrument to date has been the measurement of T1 values using pulse saturation recovery. An overview of that work is provided.

MRI surface-coil pair with strong inductive coupling.

A novel inductively coupled coil pair was used to obtain magnetic resonance phantom images. Rationale for using such a structure is described in R. R. Mett et al. [Rev. Sci. Instrum. 87, 084703 (2016)]. The original rationale was to increase the Q-value of a small diameter surface coil in order to achieve dominant loading by the sample. A significant improvement in the vector reception field (VRF) is also seen. The coil assembly consists of a 3-turn 10 mm tall meta-metallic self-resonant spiral (SRS) of inner diameter 10.4 mm and outer diameter 15.1 mm and a single-loop equalization coil of 25 mm diameter and 2 mm tall. The low-frequency parallel mode was used in which the rf currents on each coil produce magnetic fields that add constructively. The SRS coil assembly was fabricated and data were collected using a tissue-equivalent 30% polyacrylamide phantom. The large inductive coupling of the coils produces phase-coherency of the rf currents and magnetic fields. Finite-element simulations indicate that the VRF of the coil pair is about 4.4 times larger than for a single-loop coil of 15 mm diameter. The mutual coupling between coils influences the current ratio between the coils, which in turn influences the VRF and the signal-to-noise ratio (SNR). Data on a tissue-equivalent phantom at 9.4 T show a total SNR increase of 8.8 over the 15 mm loop averaged over a 25 mm depth and diameter. The experimental results are shown to be consistent with the magnetic resonance theory of the emf induced by spins in a coil, the theory of inductively coupled resonant circuits, and the superposition principle. The methods are general for magnetic resonance and other types of signal detection and can be used over a wide range of operating frequencies.

Hyperbolic-cosine waveguide tapers and oversize rectangular waveguide for reduced broadband insertion loss in W-band electron paramagnetic resonance spectroscopy. II. Broadband characterization.

Experimental results have been reported on an oversize rectangular waveguide assembly operating nominally at 94 GHz. It was formed using commercially available WR28 waveguide as well as a pair of specially designed tapers with a hyperbolic-cosine shape from WR28 to WR10 waveguide [R. R. Mett et al., Rev. Sci. Instrum. 82, 074704 (2011)]. The oversize section reduces broadband insertion loss for an Electron Paramagnetic Resonance (EPR) probe placed in a 3.36 T magnet. Hyperbolic-cosine tapers minimize reflection of the main mode and the excitation of unwanted propagating waveguide modes. Oversize waveguide is distinguished from corrugated waveguide, overmoded waveguide, or quasi-optic techniques by minimal coupling to higher-order modes. Only the TE10 mode of the parent WR10 waveguide is propagated. In the present work, a new oversize assembly with a gradual 90° twist was implemented. Microwave power measurements show that the twisted oversize waveguide assembly reduces the power loss in the observe and pump arms of a W-band bridge by an average of 2.35 dB and 2.41 dB, respectively, over a measured 1.25 GHz bandwidth relative to a straight length of WR10 waveguide. Network analyzer measurements confirm a decrease in insertion loss of 2.37 dB over a 4 GHz bandwidth and show minimal amplitude distortion of approximately 0.15 dB. Continuous wave EPR experiments confirm these results. The measured phase variations of the twisted oversize waveguide assembly, relative to an ideal distortionless transmission line, are reduced by a factor of two compared to a straight length of WR10 waveguide. Oversize waveguide with proper transitions is demonstrated as an effective way to increase incident power and the return signal for broadband EPR experiments. Detailed performance characteristics, including continuous wave experiment using 1 µM 2,2,6,6-tetramethylpiperidine-1-oxyl in aqueous solution, provided here serve as a benchmark for other broadband low-loss probes in millimeter-wave EPR bridges.

Aqueous flat-cells perpendicular to the electric field for use in electron paramagnetic resonance spectroscopy, II: design.

This paper builds on the work of Mett and Hyde [J. Magn. Reson. 165 (2003) 137]. Various aqueous flat-cell geometries in the perpendicular orientation have been studied using Ansoft High Frequency Structure Simulator (version 9.0, Pittsburgh, PA) and Computer Simulation Technology Microwave Studio (version 5.0, Wellesley Hills, MA). The analytic theory of Mett and Hyde has been refined to predict optimum dimensions of multiple sample cell structures including the effect of the sample holder dielectric properties and the interaction of the cells with each other on EPR signal strength. From these calculations and simulations we propose a practical multiple cell sample structure for use in commercial rectangular TE102 cavities that yields 2.0-2.3 times higher sensitivity relative to a single flat-cell in the nodal orientation. We also describe a modified TE102 resonator design with square rather than cylindrical sample-access stacks that is predicted to give a factor of 2.2-2.7 enhancement in EPR signal strength of a single flat-cell in the nodal orientation. These signal enhancements are predicted with sample holders fabricated from polytetrafluoroethylene. Additional improvement in EPR signal of up to 75% can be achieved by using sample holder materials with lower dielectric constants.

Aqueous flat cells perpendicular to the electric field for use in electron paramagnetic resonance spectroscopy.

An analytic solution of the Maxwell equations for aqueous flat cells in rectangular TE(102) cavities has led to the prediction of significant (3-6 times) X-band EPR signal improvement over the standard flat cell for a new sample configuration consisting of many flat cells oriented perpendicular to the electric field nodal plane. Analytic full wave solutions in the presence of sample and wall losses have been obtained and numerically evaluated. Observation of the predicted fields led to a classification of three distinct types of sample loss mechanisms, which, in turn inspired sample designs that minimize each loss type. The resulting EPR signal enhancement is due to the presence and centering of a tangential electric field node within each individual sample region. Samples that saturate with the available RF magnetic field and those that do not are considered. Signal enhancement appears in both types. These observations, done for the TE(102) mode, carry over to the uniform field (UF) modes, a relatively new class of microwave cavities for use in EPR spectroscopy developed in this laboratory. Rectangular UF modes have an RF magnetic field magnitude that is uniform in a plane. Based on this analysis, a practical multiple flat-cell design is proposed.

A microwave resonator for limiting depth sensitivity for electron paramagnetic resonance spectroscopy of surfaces.

A microwave Surface Resonator Array (SRA) structure is described for use in Electron Paramagnetic Resonance (EPR) spectroscopy. The SRA has a series of anti-parallel transmission line modes that provides a region of sensitivity equal to the cross-sectional area times its depth sensitivity, which is approximately half the distance between the transmission line centers. It is shown that the quarter-wave twin-lead transmission line can be a useful element for design of microwave resonators at frequencies as high as 10 GHz. The SRA geometry is presented as a novel resonator for use in surface spectroscopy where the region of interest is either surrounded by lossy material, or the spectroscopist wishes to minimize signal from surrounding materials. One such application is in vivo spectroscopy of human finger-nails at X-band (9.5 GHz) to measure ionizing radiation dosages. In order to reduce losses associated with tissues beneath the nail that yield no EPR signal, the SRA structure is designed to limit depth sensitivity to the thickness of the fingernail. Another application, due to the resonator geometry and limited depth penetration, is surface spectroscopy in coating or material science. To test this application, a spectrum of 1.44 µM of Mg(2+) doped polystyrene 1.1 mm thick on an aluminum surface is obtained. Modeling, design, and simulations were performed using Wolfram Mathematica (Champaign, IL; v. 9.0) and Ansys High Frequency Structure Simulator (HFSS; Canonsburg, PA; v. 15.0). A micro-strip coupling circuit is designed to suppress unwanted modes and provide a balanced impedance transformation to a 50 Ω coaxial input. Agreement between simulated and experimental results is shown.

Dielectric microwave resonators in TE(011) cavities for electron paramagnetic resonance spectroscopy.

The coupled system of the microwave cylindrical TE(011) cavity and the TE(01delta) dielectric modes has been analyzed in order to determine the maximum achievable resonator efficiency parameter of a dielectric inserted into a cavity, and whether this value can exceed that of a dedicated TE(01delta) mode dielectric resonator. The frequency, Q value, and resonator efficiency parameter Lambda for each mode of the coupled system were calculated as the size of the dielectric was varied. Other output parameters include the relative field magnitudes and phases. Two modes are found: one with fields in the dielectric parallel to the fields in the cavity center and the other with antiparallel fields. Results closely match those from a computer program that solves Maxwell's equations by finite element methods. Depending on the relative natural resonance frequencies of the cavity and dielectric, one mode has a higher Q value and correspondingly lower Lambda than the other. The mode with the higher Q value is preferentially excited by a coupling iris or loop in or near the cavity wall. However, depending on the frequency separation between modes, either can be excited in this way. A relatively narrow optimum is found for the size of the insert that produces maximum signal for both modes simultaneously. It occurs when the self-resonance frequencies of the two resonators are nearly equal. The maximum signal is almost the same as that of the dedicated TE(01delta) mode dielectric resonator alone, Lambda congruent with40 G/W(1/2) at X-band for a KTaO(3) crystal. The cavity is analogous to the second stage of a two-stage coupler. In general, there is no electron paramagnetic resonance (EPR) signal benefit by use of a second stage. However, there is a benefit of convenience. A properly designed sample-mounted resonator inserted into a cavity can give EPR signals as large as what one would expect from the dielectric resonator alone.