Richard R. Mett

Kinetic theory of toroidicity-induced alfvén eigenmodes

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 ...

Arbitrary mode number boundary‐layer theory for nonideal toroidal Alfvén modes

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.

Axially uniform resonant cavity modes for potential use in electron paramagnetic resonance spectroscopy

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...

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

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.

Dielectric microwave resonators in TE011 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 Maxwells 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.

Cavities with axially uniform fields for use in electron paramagnetic resonance. II. Free space generalization

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.

Uniform radio frequency fields in loop-gap resonators for EPR spectroscopy

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.

Cavities with axially uniform fields for use in electron paramagnetic resonance. III. Re-entrant geometries

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.

Steady-state dynamo and current drive in a nonuniform bounded plasma

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...

Microwave leakage from field modulation slots in TE011 electron paramagnetic resonance cavities

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...