Search

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.

Cavity resonators are often used for electron paramagnetic resonance (EPR). Rectangular TE(102) and cylindrical TE(011) 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- and W-bands, 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.

The dielectric tube resonator (DTR) for electron paramagnetic resonance 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 and 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 DTR 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.

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.

This paper builds on the work of Mett and Hyde [J. Magn. Reson. 165 (2003) p.137] and Sidabras, Mett, and Hyde [J. Magn. Reson. 172 (2005) p.333] 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 1 mm O.D. capillary with a septum down the middle, named DoubleDee, and a 3.5 mm 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 0.9 mm 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 1 mm capillary.

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 94 GHz. The LGR geometry employs low-loss Rexolite end-sections to improve the field homogeneity over a 3 mm sample region-of-interest from near-cosine distribution to 90% uniform. The LGR was designed to accommodate large degassable Polytetrafluorethylen (PTFE) tubes (0.81 mm O.D.; 0.25 mm I.D.) for aqueous samples. Additionally, field modulation slots are designed for uniform 100 kHz 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 100 kHz 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 × 6 mm3 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.

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 TE(011) cylindrical cavity resonator that contains an axial dielectric tube [J. S. Hyde and R. R. Mett, Appl. Magn. Reson. 48, 1185–1204 (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 ([Formula: see text]) 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 nLwhen using typical EPR acquisition times.

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.

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.

At high frequencies, e.g., Q- and W-bands, it is advantageous to make the axial length of loop-gap resonators (LGRs) at least as long as a free-space wavelength. The opposite scaling of capacitance and inductance with LGR length suggests that the length of an LGR can be increased without limit, with the axial radio frequency (rf) field profiles and resonance frequency independent of length. This scaling is accurate for resonator dimensions much less than one free-space wavelength. When the resonator length approaches one-tenth of a free-space wavelength, the rf field uniformity degrades. From one-tenth to one free-space wavelength, computer simulations and experimental measurements show that the axial magnetic field energy density profile is peaked in the center of the LGR, gradually decreases from 25 to 50% at a distance one radius from the end, and rapidly there-after. The nonuniformity is of two types. One type, in the vicinity of one radius of the end, is caused by the flaring of the field as it curves from the central loop to the end region, into the larger return loop(s). The other type, in the central part of the resonator, is caused by impedance mismatch at the ends of the LGR. The LGR may be viewed as a strongly reentrant (ridge) waveguide nearly open at both ends and supporting a standing wave. A transmission line model relates the central nonuniformity to the fringing capacitance and inductance at the ends of the resonator. This nonuniformity can be eliminated in several ways including modifying the ends of the LGR by adding a small metal bridge or a dielectric ring. These uniformity trimming elements increase the fringing capacitance and/or decrease the fringing inductance. With trimmed ends, LGRs can be made many free-space wavelengths long. The maximum resonator length is determined by the proximity in frequency of the fundamental LGR mode to the next highest frequency mode as well as the quality factor. Results of this theory are compared and conformed with finite-element simulations. This theory connects the uniform LGR with the uniform field cavity resonators previously introduced by this laboratory.

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.

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.

Uniform field (UF) microwave cavities consist of three sections: the center with transverse dimensions set to the cutoff condition for a selected propagation mode, and two end sections. In the first article on UF modes, [R. R. Mett, W. Froncisz, and J. S. Hyde, Rev. Sci. Instrum. 72, 4188 (2001)] end sections were filled with dielectric 1/4 wavelength thick. In a second UF article, [J. R. Anderson, R. R. Mett, and J. S. Hyde, Rev. Sci. Instrum. 73, 3027 (2002)] the cross-sectional dimensions of the end sections were increased again setting the length to 1/4 wavelength. We describe here a third approach to end-section design in UF resonators: maintaining the cross section constant and introducing re-entrant conducting rods parallel to the electric field. Electromagnetic field distributions were simulated using the Ansoft high frequency structure simulator (HFSS) (Ansoft Corporation, Pittsburgh, PA) three-dimensional finite-element modal frequency (eigenmode) solution method. Simulation procedures are described. Re-entrant end-section UF resonators are compared with other UF types. The transition zone between sections is narrow and similar to that of the dielectric UF design. The Q value is high and similar to that in the second article.

The radio frequency (rf) magnetic field in a microwave cavity ought to be uniform along a line sample in electron paramagnetic resonance (EPR) spectroscopy so that all portions respond uniformly. Mett, Froncisz, and Hyde discovered a way to achieve this objective [Rev. Sci. Instrum. 72, 4188 (2001)]. Their resonators consisted of three regions, a central section for the sample with dimensions at the cutoff condition, and two end sections that had the same cross section as the central section but were made electrically larger by filling them with a low-loss dielectric. The end sections were each one-quarter wavelength long. We have found that the dielectric in the end sections can be omitted and the dimensions made correspondingly larger. Effects of the resulting discontinuities in cavity cross sections perpendicular to the cavity axis have been analyzed using finite element high frequency structure simulator calculations. Closed form expressions for Q values and relative rf field values have been obtained. The length of the uniform field region is decreased somewhat by the discontinuities (∼1 cm at X band). This disadvantage is outweighed by the benefits of higher Q values and elimination of impurity EPR signals from the dielectric materials. End sections may be cylindrical or hemispherical for cylindrical modes and rectangular or hemicircular for rectangular modes.

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.

The effect of magnetic field on plasma uniformity was investigated for a capacitively coupled plasma in a dielectric etch chamber and a tool to measure the dc bias uniformity across the high-powered cathode (e.g., 1200 W) was developed. At that power, the dc bias can be as high as 1500 V at 50 mT. A 5% variation in the dc bias across the cathode corresponds to a 75 V potential drop across the wafer, which may in turn cause degradation or breakdown of gate oxide structures. Therefore control of the instantaneous plasma uniformity is important to minimize device damage. The primary effect of the magnetic field on instantaneous plasma uniformity is through the E×B drift force which, because of the strong electric field at the cathode surface at high powers, dominates the other magnetic field effects on the plasma. dc bias measurements show that the plasma nonuniformity can be optimized by adjusting the gradient of the magnetic field, and thus the E×B drift force, across the cathode over a wide range of magne...

A novel method of decreasing ohmic losses and increasing Q-value in metallic resonators at high frequencies is presented. The method overcomes the skin-depth limitation of rf current flow cross section. The method uses layers of conductive foil of thickness less than a skin depth and capacitive gaps between layers. The capacitive gaps can substantially equalize the rf current flowing in each layer, resulting in a total cross-sectional dimension for rf current flow many times larger than a skin depth. Analytic theory and finite-element simulations indicate that, for a variety of structures, the Q-value enhancement over a single thick conductor approaches the ratio of total conductor thickness to skin depth if the total number of layers is greater than one-third the square of the ratio of total conductor thickness to skin depth. The layer number requirement is due to counter-currents in each foil layer caused by the surrounding rf magnetic fields. We call structures that exhibit this type of Q-enhancement "meta-metallic." In addition, end effects due to rf magnetic fields wrapping around the ends of the foils can substantially reduce the Q-value for some classes of structures. Foil structures with Q-values that are substantially influenced by such end effects are discussed as are five classes of structures that are not. We focus particularly on 400 MHz, which is the resonant frequency of protons at 9.4 T. Simulations at 400 MHz are shown with comparison to measurements on fabricated structures. The methods and geometries described here are general for magnetic resonance and can be used at frequencies much higher than 400 MHz.

The two-way insertion loss of a 1 m length of waveguide was reduced by nearly 5 dB over a 4% bandwidth at W-band (94 GHz) for an electron paramagnetic resonance (EPR) spectrometer relative to WR10 waveguide. The waveguide has an oversize section of commercially available rectangular WR28 and a novel pair of tapers that vary in cross section with axial position according to a hyperbolic-cosine (HC) function. The tapers connect conventional rectangular WR10 waveguide to the WR28. For minimum loss, the main mode electric field is parallel to the long side of the WR28. Using mode coupling theory, the position of maximum flare (inflection point) in the taper was optimized with respect to the coupling to higher order modes and the reflection of the main mode. The optimum inflection point position is about one-tenth of the taper length from the small end of the taper. Reflection and coupling were reduced by about 20 dB relative to a pyramidal (linear) taper of the same length. Comb-like dips in the transmission coefficient produced by resonances of the higher order modes in the oversize section were about 0.03 dB. Specially designed high-precision, adjustable WR28 flanges with alignment to about 5 μm were required to keep higher order mode amplitudes arising from the flanges comparable to those from the HC tapers. Minimum return loss was about 30 dB. This paper provides a foundation for further optimization, if needed. Methods are not specific to EPR or the microwave frequency band.

The theory of toroidicity‐induced Alfven eigenmodes (TAE) and kinetic TAE (KTAE) is generalized to arbitrary mode numbers for a large aspect ratio low‐beta circular tokamak. The interaction between nearest neighbors is described by a three‐term recursion relation that combines elements from an outer region, described by the ideal magnetohydrodynamic equations of a cylinder, and an inner region, which includes the toroidicity and the nonideal effects of finite ion Larmor radius, electron inertia, and collisions. By the use of quadratic forms, it is proven that the roots of the recursion relation are stable and it is shown how perturbation theory can be applied to include frequency shifts due to other kinetic effects. Analytic forms are derived which display the competition between the resistive and radiative damping, where the radiation is carried by kinetic Alfven waves. When the nonideal parameter is small, the KTAE modes appear in pairs. When this parameter is large, previously found scaling for the single gap case is reproduced analytically.

An analytic kinetic description of the toroidicity‐induced Alfven eigenmode (TAE) is presented. The theory includes electron parallel dynamics nonperturbatively, an effect that is found to strongly influence the character, and damping of the TAE−contrary to previous theoretical predictions. A parallel conductivity model that includes collisionless (Landau) damping on the passing electrons and collisional damping on both trapped and passing electrons is used. Together, these mechanisms damp the TAE more strongly than previously expected. This is because the TAE couples (or merges) with the kinetic Alfven wave (KAW) within the gap region under conditions that depend on the gap size, the shear, the magnitude of the conductivity, and the mode numbers. The high damping could be relevant to recent experimental measurements of the TAE damping coefficient. In addition, the theory predicts a ‘‘kinetic’’ TAE, whose eigenfreqeuency lies just above the gap, whose existence depends on finite conductivity, and that is formed by the coupling of two KAW’s

Current drive due to helicity injection and the dynamo effect are examined in an inhomogeneous bounded plasma. Averaged over a magnetic surface, there is, in general, no dynamo effect independent of resistivity—contrary to the results found previously for an unbounded plasma. The dynamo field is calculated explicitly for an incompressible viscoresistive fluid in the plane‐slab model. In accord with the authors’ general conclusion, outside the Alfven resonant layer it is proportional to the resistivity. Within the resonant layer there is a contribution which is increased, relative to its value outside the layer, by a factor [ωa2/(η+ν)], where ω is the wave frequency, a is the plasma radius, η is the magnetic diffusivity, and ν is the kinematic viscosity. However, this contribution vanishes when integrated across the layer. The average field in the layer is resonance enhanced by a factor [ωa2/(η+ν)]2/3 and is proportional to the shear in the magnetic field and the cube root of the gradient of the Alfven spe...

Current drive and helicity injection by plasma waves are examined with the use of kinetic theory. The Vlasov equation yields a general current drive formula that contains resonant and nonresonant (ponderomotivelike) contributions. Standard quasilinear current drive is described by the former, while helicity current drive may be contained in the latter. Since direct analytical comparison of the sizes of the two terms is, in general, difficult, a new approach is taken. Solution of the drift‐kinetic equation shows that the standard Landau damping/transit time magnetic pumping quasilinear diffusion coefficient is the only contribution to steady‐state current drive to leading order in e=ρL/l, where ρL is the Larmor radius and l is the inhomogeneity scale length. All nonresonant contributions, including the helicity, appear at higher order, after averages are taken over a flux surface, over azimuth, and over time. Consequently, at wave frequencies well below the electron cyclotron frequency, a wave helicity flu...

An analytic circuit model for slot coupling from a waveguide to a loop-gap resonator (LGR) in a context of electron paramagnetic resonance (EPR) spectroscopy is presented. The physical dimensions of the waveguide, iris, LGR, and aqueous sample are transformed into circuit values of inductance, capacitance, and resistance. These values are used in a solution of circuit equations that results in a prediction of the radio frequency (rf) currents, magnitude and phase, frequency, and magnetic and electric stored energies near the critical coupling. The circuit geometry reflects magnetic flux conservation between the iris and LGR as well as modification of the outer loop LGR currents by the iris. Unlike conventional models, coupling is not explicitly based on a mutual inductance between the iris and LGR. Instead, the conducting wall high-frequency rf boundary condition is used to define surface currents, regions, and circuit topology with lumped-circuit values of self-inductance, capacitance, and resistance. Match is produced by a combination of self-inductive and capacitive circuit coupling. Two conditions must be met to achieve match. First, the equivalent resistance of the LGR as seen by the iris must be transformed into the waveguide characteristic impedance. This transformation is met at a particular frequency relative to the natural LGR resonance frequency. The frequency shift magnitude is largely determined by the LGR properties, weakly dependent on the iris length and placement, and independent of other iris dimensions. The second condition for match is that the iris reactance at this frequency shift must cancel the residual reactance of the LGR. This second condition is sensitive to the iris dimensions. If both conditions are not simultaneously satisfied, overcoupling or undercoupling results. A slotted iris with a length equal to the size of the large dimension of the waveguide is found to have many properties opposite to a conventional iris with shorter length. Notably, the magnetic field near the iris tends to reinforce rather than oppose the magnetic field in the resonator. The long iris improves the LGR EPR performance by providing increased rf magnetic field homogeneity at the sample, higher signal, and reduced total frequency shift since the shifts due to sample and iris tend to cancel. Investigations reveal that the first match condition can be adjusted by LGR dimensional changes and such adjustment can eliminate the frequency shift. Results are consistent with Ansoft High Frequency Structure Simulator (Version 10.1, Ansoft Corporation, Pittsburgh, PA) simulations and can be extended to cavity resonators.

Fundamentals of low‐frequency current drive produced by a packet of arbitrarily polarized nonlinear Alfven waves in an incompressible plasma with an inhomogeneous equilibrium magnetic field and aligned fluid velocity are explored. Analysis of the equations of magnetohydrodynamics with electrical conductivity and kinematic viscosity using an eikonal formulation yields coupled nonlinear equations for the Alfven wave amplitude and an induced magnetic field and fluid velocity. Introduction of suitable variables allows simplification of the nonlinear system into a system of coupled linear integrodifferential equations. Particular solutions relate the plasma current to the helicity of the Alfven wave. Two separate and distinct agents contribute to the current drive process: (1) wave dissipation, and (2) spatial inhomogeneity of the plasma medium. The plasma inhomogeneities cause a direct transfer of helicity from the applied Alfven wave to the equilibrium magnetic field and are connected to the damping of a single component of the wave fluctuation due to phase mixing.

This paper identifies three distinct types of losses associated with high dielectric materials in a rf electric field, specifically in a rectangular TE102 microwave cavity. Various orientations of high dielectric structures relative to the electric field polarization have been studied using ansoft high frequency structure simulator (HFSS) (version 9.0, Pittsburgh, PA) and Computer Simulation Technology (CST) Microwave Studio (version 5.0, Wellesley Hills, MA). From the behavior of the electric fields inside high dielectrics in a rf field, the three forms of losses are quantified and their sum minimized by breaking up the sample into planar layers orientated perpendicular to the electric field and optimizing size. This work is important for electron paramagnetic resonance spectroscopy where the high dielectric material is frequently a spin-labeled protein sample in aqueous solution. Extension to Magnetic Resonance and other microwave applications are possible.

This article is concerned with cylindrical transverse electric TE011 and rectangular TE102 microwave cavity resonators commonly used in electron paramagnetic resonance (EPR) spectroscopy. In the cylindrical mode geometry considered here, the sample is along the z axis of the cylinder, dielectric disks of 1/4 wavelength thickness are placed at each end wall, and the diameter of the cylinder is set at the cutoff condition for propagation of microwave energy in a cylindrical waveguide at the desired microwave frequency. The microwave magnetic field is exactly uniform along the sample in the region between the dielectric disks and the resonant frequency is independent of the length of the cylinder without limit. The rectangular TE102 geometry is analogous, but here the microwave magnetic field is exactly uniform in a plane. A uniform microwave field along a line sample is highly advantageous in EPR spectroscopy compared with the usual sinusoidal variation, and these geometries are called “uniform field” modes...

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.

Magnetic field modulation is often introduced into a cylindrical TE011 electron paramagnetic resonance (EPR) cavity through silver plating over a nonconductive substrate. The plating thickness must be many times the skin depth of the rf and smaller than the skin depth of the modulation. We derive a parameter that quantifies the modulation field penetration and find that it also depends on resonator dimensions. Design criteria based on this parameter are presented graphically. This parameter is then used to predict the behavior of eddy currents in substrates of moderate conductivity, such as graphite. The conductivity of the graphite permits improved plating uniformity and permits use of electric discharge machining (EDM) techniques to make the resonator. EDM offers precision tolerances of 0.005 mm and is suitable for small, complicated shapes that are difficult to machine by other methods. Analytic predictions of the modulation penetration are compared with the results of finite-element simulations. Simul...

This article considers a Q-band cylindrical TE011 electron paramagnetic resonance cavity with slots cut parallel to wall currents to allow penetration of magnetic field modulation and with mode suppression gaps in the end regions of zero wall currents to reduce interference from nearby modes. Origins of the small amount of rf leakage generally observed from modulation slots have been studied using a finite element computer program and ways to eliminate this leakage have been found. The leakage is caused by field distortions from the waveguide coupling iris, which is centered on the cylindrical sidewall. The distortion is of two distinct types, which result in comparable leakage levels. One is from iris fields that have components perpendicular to the fields of the mode of interest. The iris near fields couple to a nonresonant circumferential radial mode in the modulation slots, like that of a sectorial waveguide horn. The other type of rf leakage is caused by coupling of the aperture to nearby cavity mode...

A spatially localized electron temperature elevation is observed near the electron-cyclotron resonance region. The properties of this phenomenon are examined in detail. The dependence of the temperature elevation upon launched wave amplitude and frequency relative to the local electron-cyclotron frequency, plasma density, neutral pressure, microwave cavity plasma source tuning, and probe type is discussed. These results are combined with detailed wave electric and magnetic field, emissive probe and spectral measurements and the use of different Langmuir probe types and orientations to characterize the temperature elevation, background plasma, and wave properties. It is found that the magnetic field and wave absorption near the electron-cyclotron resonance, probe type, and probe tip input impedance as seen from the plasma have important influences on the temperature elevation process. Two-probe correlation measurements are used to show that the elevation process exists in the radial neighborhood ( >

We explore fundamentals of low-frequency current drive produced by a packet of arbitrarily polarized nonlinear shear Alfven waves in an infinite, uniform magnetized plasma. Analysis of the magnetohydrodynamic equations with resistivity and viscosity yields coupled nonlinear equations for the Alfven wave amplitude and an induced magnetic field. Particular solutions relate the plasma current to the helicity of the Alfven wave and the difference between the viscosity and magnetic diffusivity.

Recent studies suggest that low frequency electromagnetic waves possessing helicity may drive currents in plasmas with greater efficiency than schemes based on linear momentum transfer to charged particles.1,2 A key issue is the transfer of wave helicity into the helicity of the equilibrium magnetic field. Previously we examined the conversion mechanism by following the dynamics of a packet of arbitrarily polarized Alfven waves propagating in an infinite uniformly magnetized plasma.3,4 Analysis of the equations of magnetohydrodynamics with resistivity and viscosity yielded a set of nonlinear equations governing the Alfven wave amplitude and an induced magnetic field. Solutions for the initial value problem4 related the induced plasma current to the helicity of the wave and the difference between the magnetic diffusivity and viscosity. In the present investigation we examine solutions for the boundary value problem.