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NASA NTRS1993

Diffusion effects on the helium abundance of the solar transition region and corona

The diffusion of helium in the solar transition region is studied by solving the mass and momentum conservation equations for a hydrogen-helium plasma given a representative temperature profile. Steady state solutions show that two distinct atmospheres may result. In cases where the thermal force on alpha-particles is balanced by the partial pressure gradient force, helium is the dominant coronal species. On the other hand, if it is the frictional force between protons and alpha-particles which balances the thermal force on alpha-particles then hydrogen is the major coronal component. In order to explore which of these solutions are attainable within reasonable time scales, the time-dependent equations are solved, starting from an initial state with a uniform helium abundance of 10 percent. The atmosphere as a whole is close to hydrostatic equilibrium, but due the thermal forces the individual elements are not. This force inbalance leads to a differential flow between species. It is found that this differential flow leads to a significant enhancement of the coronal helium abundance. Even for the relatively shallow temperature gradient used the helium abundance in the lower corona increases to 30 percent over a 24 hr period.

Hansteen, Viggo H.↗
NASA NTRS1993

Fe/Mn in olivine of carbonaceous meteorites

Olivines in primitive meteorites show a range of Fe/Mn both within one grain and among grains suggesting that they have recorded changing conditions during or after growth. Because olivine should be an early forming phase, Fe/Mn is used here to infer these earliest conditions. Initial Fe/Mn in cores of isolated, euhedral forsterite in both C2 and C3 meteorites ranges from 25 to 35 but differs at grain edge. Murchison (C2) forsterites show Fe/Mn approaching 1.0 at the grain edge while Ornans Fe/Mn is near 60 at grain edge. These values are lower than the matrix Fe/Mn for both meteorites and the distinct difference in zoning profile indicates different processes operating during and after grain growth. The Fe/Mn of bulk samples from a particular source such as the Moon is nearly constant. Individual samples show variation suggesting that there is some fractionation of Mn from Fe. Minerals have their individual ranges of Fe/Mn which has been used to recognize different types of olivine within one meteorite. Extreme values of Fe/Mn below 1.0 occur in forsterite from some IDP's, UOC matrix, and C1 meteorites. There are apparently no detailed studies of Fe/Mn variation within single olivine grains. Forsterite grains in C2 and C3 carbonaceous chondrites show complex zoning, and the nearly pure forsterites (Fo greater than approximately 99.5) have high levels of some minor elements including Ti, Al, V, and Sc. There is disagreement on the original source of these grains and both chondrule and vapor growth have been proposed. In addition, there is clear evidence that diffusion has affected the outer margins but in some cases the whole grain. Within the cores, the FeO range is limited, and if growing under constant conditions, the Fe/Mn should be near constant as there is little fractionation of Mn from Fe by forsterite. Additionally, there are apparently no co-crystallizing phases as evidenced by a lack of common inclusions in the forsterites. These observations are now followed by analyses of isolated olivine grains in C2 and C3 meteorites.

Steele, Ian M.↗
NASA NTRS1983

Spectroscopy of V711 Tauri (= HR 1099) - Fundamental properties and evidence for starspots

New orbital elements have been determined for the bright RS CVn-type system V711 Tau. The spectroscopic period has been refined to 2.83774 d + or - 0.00001 d. The eccentricity is determined to be 0.014 + or - 0.009, and the inclination of the system is 33 deg + or - 2 deg. The masses, radii, and equatorial rotational velocities for each component are stated.Evolutionary models suggest that mass transfer may begin in 70 to 80 million years. High SNR Reticon observations at red wavelengths show substantial differences in rotational velocity and line strength between the two components, as well as asymmetries in all absorption lines of the more massive, active, cooler star. These asymmetries are correlated with photometric variations and move across the line profiles with time. They are the result of starspot regions rotating in and out of view.

Fekel, F. C., Jr.↗
NASA NTRS1994

A simulation of the intracluster medium with feedback from cluster galaxies

We detail method and report first results from a three-dimensional hydrodynamical and N-body simulation of the formation and evolution of a Coma-sized cluster of galaxies, with the intent of studying the history of the hot, X-ray emitting intracluster medium. Cluster gas, galaxies, and dark matter are included in the model. The galaxies and dark matter fell gravitational forces; the cluster gas also undergoes hydrodynamical effects such as shock heating and PdV work. For the first time in three dimensions, we include modeling of ejection of processed gas from the simulated galaxies by winds, including heating and heavy element enrichment. For comparison, we employ a `pure infall' simulation using the same initial conditions but with no galaxies or winds. We employ an extreme ejection history for galactic feedback in order to define the boundary of likely models. As expected, feedback raises the entropy of the intracluster gas, preventing it from collapsing to densities as high as those attained in the infall model. The effect is more pronounced in subclusters formed at high redshift. The cluster with feedback is always less X-ray luminous, but experiences more rapid luminosity evolution, than the pure infall cluster. Even employing an extreme ejection model, the final gas temperature is only approximately 15% larger than in the infall model. The radial temperature profile is very nearly isothermal within 1.5 Mpc. The cluster galaxies in the feedback model have a velocity dispersion approximately 15% lower than the dark matter. This results in the true ratio of specific energies in galaxies to gas being less than one, beta(sub spec) approximately 0.7. The infall model predicts beta(sub spec) approximately 1.2. Large excursions in these values occur over time, following the complex dynamical history of the cluster. The morphology of the X-ray emission is little affected by feedback. The emission profiles of both clusters are well described by the standard beta-model with beta(sub fit) approximately equal to 0.7 - 0.9. X-ray mass estimates based on the assumptions of hydrostatic equilibrium and the applicability of the beta-model are quite accurate in both cases. A strong, radial iron abundance gradient is present, which develops as a consequence of the steepening of the galaxy density profile over time. Spectroscopic observations using nonimaging detectors with wide (approximately 45 min) fields of view dramatically smear the gradient. Observations with arcminute resolution, made available with the ASCA satellite, would readily resolve the gradient.

Metzler, Christopher A.↗
NASA NTRS2000

Resin Film Infusion (RFI) Process Modeling for Large Transport Aircraft Wing Structures

This investigation completed the verification of a three-dimensional resin transfer molding/resin film infusion (RTM/RFI) process simulation model. The model incorporates resin flow through an anisotropic carbon fiber preform, cure kinetics of the resin, and heat transfer within the preform/tool assembly. The computer model can predict the flow front location, resin pressure distribution, and thermal profiles in the modeled part. The formulation for the flow model is given using the finite element/control volume (FE/CV) technique based on Darcy's Law of creeping flow through a porous media. The FE/CV technique is a numerically efficient method for finding the flow front location and the fluid pressure. The heat transfer model is based on the three-dimensional, transient heat conduction equation, including heat generation. Boundary conditions include specified temperature and convection. The code was designed with a modular approach so the flow and/or the thermal module may be turned on or off as desired. Both models are solved sequentially in a quasi-steady state fashion. A mesh refinement study was completed on a one-element thick model to determine the recommended size of elements that would result in a converged model for a typical RFI analysis. Guidelines are established for checking the convergence of a model, and the recommended element sizes are listed. Several experiments were conducted and computer simulations of the experiments were run to verify the simulation model. Isothermal, non-reacting flow in a T-stiffened section was simulated to verify the flow module. Predicted infiltration times were within 12-20% of measured times. The predicted pressures were approximately 50% of the measured pressures. A study was performed to attempt to explain the difference in pressures. Non-isothermal experiments with a reactive resin were modeled to verify the thermal module and the resin model. Two panels were manufactured using the RFI process. One was a stepped panel and the other was a panel with two 'T' stiffeners. The difference between the predicted infiltration times and the experimental times was 4% to 23%.

Loos, Alfred C.↗
NASA NTRS2005

Method for Estimating Thread Strength Reduction of Damaged Parent Holes with Inserts

During normal assembly and disassembly of bolted-joint components, thread damage and/or deformation may occur. If threads are overloaded, thread damage/deformation can also be anticipated. Typical inspection techniques (e.g. using GO-NO GO gages) may not provide adequate visibility of the extent of thread damage. More detailed inspection techniques have provided actual pitch-diameter profiles of damaged-hardware holes. A method to predict the reduction in thread shear-out capacity of damaged threaded holes has been developed. This method was based on testing and analytical modeling. Test samples were machined to simulate damaged holes in the hardware of interest. Test samples containing pristine parent-holes were also manufactured from the same bar-stock material to provide baseline results for comparison purposes. After the particular parent-hole thread profile was machined into each sample a helical insert was installed into the threaded hole. These samples were tested in a specially designed fixture to determine the maximum load required to shear out the parent threads. It was determined from the pristine-hole samples that, for the specific material tested, each individual thread could resist an average load of 3980 pounds. The shear-out loads of the holes having modified pitch diameters were compared to the ultimate loads of the specimens with pristine holes. An equivalent number of missing helical coil threads was then determined based on the ratio of shear-out loads for each thread configuration. These data were compared with the results from a finite element model (FEM). The model gave insights into the ability of the thread loads to redistribute for both pristine and simulated damage configurations. In this case, it was determined that the overall potential reduction in thread load-carrying capability in the hardware of interest was equal to having up to three fewer threads in the hole that bolt threads could engage. One- half of this potential reduction was due to local pitch-diameter variations and the other half was due to overall pitch-diameter enlargement beyond Class 2 fit. This result was important in that the thread shear capacity for this particular hardware design was the limiting structural capability. The details of the method development, including the supporting testing, data reduction and analytical model results comparison will be discussed hereafter.

Johnson, David L.↗
NASA NTRS2010

Evidence of Convective Redistribution of Carbon Monoxide in Aura Tropospheric Emission Sounder (TES) and Microwave Limb Sounder (MLS) Observations

Vertical convective transport is a key element of the tropospheric circulation. Convection lofts air from the boundary layer into the free troposphere, allowing surface emissions to travel much further, and altering the rate of chemical processes such as ozone production. This study uses satellite observations to focus on the convective transport of CO from the boundary layer to the mid and upper troposphere. Our hypothesis is that strong convection associated with high rain rate regions leads to a correlation between mid level and upper level CO amounts. We first test this hypothesis using the Global Modeling Initiative (GMI) chemistry and transport model. We find the correlation is robust and increases as the precipitation rate (the strength of convection) increases. We next examine three years of CO profiles from the Tropospheric Emission Sounder (TES) and Microwave Limb Sounder (MLS) instruments aboard EOS Aura. Rain rates are taken from the Tropical Rainfall Measuring Mission (TRMM) 3B-42 multi-satellite product. Again we find a correlation between mid-level and upper tropospheric CO, which increases with rain rate. Our result shows the critical importance of tropical convection in coupling vertical levels of the troposphere in the transport of trace gases. The effect is seen most clearly in strong convective regions such as the Inter-tropical Convergence Zone.

Manyin, Michael↗
NASA NTRS2023

Fitting Leak Test Report: Ground-Based Cryogenic Leak Test of Fittings for Cryogenic Fluid Management

EXECUTIVE SUMMARY Mechanically connected joints used in cryogenic fluid lines as part of space flight elements need to survive launch vibrations and remain leak-free to minimize the loss of on-board commodity and hazardous gas accumulation. In 2020, a cryogenic test apparatus was developed which can evaluate the leak performance of pressurized threaded fluid fittings. The fittings were mounted in the TVAC and cooled to cryogenic test temperature and pressurized with helium while the leak rate was measured using a calibrated GHe leak detector. The test articles for the initial proof of concept testing were ¼ and 1 inch Swagelok VCR fittings with three different types of seal rings copper, nickel, and Ni. Each fitting configuration (size/seal material) was subjected to two consecutive cryogenic thermal cycles, followed by exposure to a launch vibration profile at ambient temperature, after which two additional TVAC cycle tests were performed. The testing reported here is a continuation of the 2020 tests with a statistically significant large number of samples and test runs. Three Swagelok VCR fitting sizes were tested ¼, ½ and 1 inch, and five (5) samples of each fitting size, each sample was tested with SST and Ni seal rings (Total of 30 unique test articles). Each test article was subjected to four (4) thermal cycles. Half of these cycles were performed before vibration testing and half were performed after vibration testing. The vibration testing was performed to evaluate the ability of the fittings to survive launch-type vibration profiles and remain leak-free. Leak checking of each fitting was completed at temperatures between 20K – 30K. The test procedure in Section 8.0 was designed to facilitate a qualification test program by allowing a higher test throughput rate coupled with repeatable test profiles. Results were very positive and show that out of the 30 samples they all passed with leak rates a factor of 2-3 lower than the established 10-6sccs GHe leak threshold. The result showed the Ni seals had lower leak rate, but the SST was more rugged. There were two deviations where damage to the Ni seal ring during assembly resulted in a leaky fitting, this is discussed in Section 10.7 Test Deviations. These fittings show great promise for space flight use and further testing is recommended to fully qualify the fittings per the ASTM F1387-19 and/or other relevant NASA specifications. The test equipment hardware and software capability developed for this testing is generic and not restricted to VCR fittings. It can be employed to evaluate/qualify the leak performance of other types of fittings and a wide range of other cryogenic fluid components such as valves, gages, connectors, etc.

Cryogenic↗
NASA NTRS1989

Halogen Occultation Experiment (HALOE) optical filter characterization

The Halogen Occultation Experiment (HALOE) is a solar occultation experiment that will fly on the Upper Atmosphere Research Satellite to measure mixing ratio profiles of O3, H2O, NO2, NO, CH4, HCl, and HF. The inversion of the HALOE data will be critically dependent on a detailed knowledge of eight optical filters. A filter characterization program was undertaken to measure in-band transmissions, out-of-band transmissions, in-band transmission shifts with temperature, reflectivities, and age stability. Fourier Transform Infrared Spectrometers were used to perform measurements over the spectral interval 400/cm to 6300/cm (25 micrometers to 1.6 micrometers). Very high precision (0.1 percent T) in-band measurements and very high resolution (0.0001 percent T) out-of-band measurements have been made. The measurements revealed several conventional leaks at 0.01 percent transmission and greatly enhanced (1,000) leaks to the 2-element filters when placed in a Fabry-Perot cavity. Filter throughput changes by 5 percent for a 25 C change in filter temperature.

Harvey, Gale A.↗
NASA NTRS1988

Theoretical studies of mass loss and shock phenomena in cool star envelopes

To show the difficulty of producing the blue-shifted emission of (O I) and (S II) from T Tauri stars directly in the stellar wind, an element of gas in a radially expanding stellar wind was followed as it cooled and recombined. Results indicate that T Tauri winds must be heated at large distances from the star to produce the (S II) emission. A shock between the wind and the disk is an attractive mechanism to produce this heating. When the theory is applied to a simple disk model, a number of predictions and implications are evident, for example, that some T Tauri stars eject mass near the equatorial plane. In a second study, spectral energy distributions of T Tauri stars were analyzed to place limits on the amount of accretion which might occur during the early phase of stellar evolution. The best match to H-alpha line profiles is for models in which the turbulent velocity dominates close to the star, while expansion dominates farther out. Such a model predicts, for instance, that a mass loss rate of 1/10,000,000 solar masses per year is required to account for the blue-shifted Na I absorption of some objects.

Hartmann, Lee↗
NASA NTRSDate not supplied

Moss Tolerance of Deep Space-Like Ionizing Radiation, Singular or Combined With Spaceflight Microgravity-Preparation for the BRIC-27 Experiment to the ISS

Understanding how terrestrial life perceives and tolerates deep space environments is essential to advancing human space exploration missions and searching for life beyond our solar system. Throughout evolution moss adapted to living in extreme environments from the edge of habitability. Moss inhabits areas with high UVB/UVC photon levels such as polar regions subject to ozone holes, high elevation mountain environments, and sites with elevated ionizing particle levels such as those found at nuclear plant accident sites, atomic bomb test sites or radioactive element-rich regions. We investigate if moss tolerance of ionizing radiation encounter terrestrially extends to resistance to deep space ionizing radiation. We exposed moss to high energy ion beams simulating Galactic Cosmic Ray (GCRSim) and Solar Particle Event (SPESim) (NSRL, BNL) that permeate deep space, and moss was unharmed. We also exposed moss to high doses of gamma rays as released in astrophysical events, and moss survived absorption of extremely high doses. Next, we ask if moss tolerance of deep space-like ionizing radiation observed terrestrially differs from that in other deep space environments. In the upcoming BRIC-27 spaceflight experiment we will sequentially expose Antarctic moss C.purpureus to GCRSim and SPESim followed by exposure to spaceflight microgravity and compare gene expression profiles in deep space-like ionizing radiation, singular or combined with spaceflight microgravity. Additionally, we will compare gene expression profiles in spaceflight microgravity, singular or combined with deep space-like ionizing radiation. Hence, BRIC-27 will advance our understanding of the combined effects of both deep space ionizing radiation and microgravity, which may have different and more profound effects on plant physiology and performance than each condition separately.

Agata Klaudia Zupanska↗
NASA NTRS2003

Petrology and Physics of Magma Ocean Crystallization

Early Mars is thought to have been melted significantly by the conversion of kinetic energy to heat during accretion of planetesimals. The processes of solidification of a magma ocean determine initial planetary compositional differentiation and the stability of the resulting mantle density profile. The stability and compositional heterogeneity of the mantle have significance for magmatic source regions, convective instability, and magnetic field generation. Significant progress on the dynamical problem of magma ocean crystallization has been made by a number of workers. The work done under the 2003 MFRP grant further explored the implications of early physical processes on compositional heterogeneity in Mars. Our goals were to connect early physical processes in Mars evolution with the present planet's most ancient observable characteristics, including the early, strong magnetic field, the crustal dichotomy, and the compositional characteristics of the SNC meteorite's source regions as well as their formation as isotopically distinct compositions early in Mars's evolution. We had already established a possible relationship between the major element compositions of SNC meteorite sources and processes of Martian magma ocean crystallization and overturn, and under this grant extended the analysis to the crucial trace element and isotopic SNC signatures. This study then demonstrated the ability to create and end the magnetic field through magma ocean cumulate overturn and subsequent cooling, as well as the feasibility of creating a compositionally- and volumetrically-consistent crustal dichotomy through mode-1 overturn and simultaneous adiabatic melting.

Elkins-Tanton, Linda T.↗
NASA NTRS2005

Communications Blackout Predictions for Atmospheric Entry of Mars Science Laboratory

The Mars Science Laboratory (MSL) is expected to be a long-range, long-duration science laboratory rover on the Martian surface. MSL will provide a significant milestone that paves the way for future landed missions to Mars. NASA is studying options to launch MSL as early as 2009. There are three elements to the spacecraft; carrier (cruise stage), entry vehicle, and rover. The rover will have a UHF proximity link as the primary path for EDL communications and may have an X-band direct-to-Earth link as a back-up. Given the importance of collecting critical event telemetry data during atmospheric entry, it is important to understand the ability of a signal link to be maintained, especially during the period near peak convective heating. The received telemetry during entry (or played back later) will allow for the performance of the Entry-Descent-Landing technologies to be assessed. These technologies include guided entry for precision landing, a new sky-crane landing system and powered descent. MSL will undergo an entry profile that may result in a potential communications blackout caused by ionized particles for short periods near peak heating. The vehicle will use UHF and possibly X-band during the entry phase. The purpose of this rep0rt is to quantify or bound the likelihood of any such blackout at UHF frequencies (401 MHz) and X-band frequencies (8.4 GHz). Two entry trajectory scenarios were evaluated: a stressful entry trajectory to quantify an upper-bound for any possible blackout period, and a nominal trajectory to quantify likelihood of blackout for such cases.

communications↗
NASA NTRS2014

High-Fidelity Flash Lidar Model Development

NASA's Autonomous Landing and Hazard Avoidance Technologies (ALHAT) project is currently developing the critical technologies to safely and precisely navigate and land crew, cargo and robotic spacecraft vehicles on and around planetary bodies. One key element of this project is a high-fidelity Flash Lidar sensor that can generate three-dimensional (3-D) images of the planetary surface. These images are processed with hazard detection and avoidance and hazard relative navigation algorithms, and then are subsequently used by the Guidance, Navigation and Control subsystem to generate an optimal navigation solution. A complex, high-fidelity model of the Flash Lidar was developed in order to evaluate the performance of the sensor and its interaction with the interfacing ALHAT components on vehicles with different configurations and under different flight trajectories. The model contains a parameterized, general approach to Flash Lidar detection and reflects physical attributes such as range and electronic noise sources, and laser pulse temporal and spatial profiles. It also provides the realistic interaction of the laser pulse with terrain features that include varying albedo, boulders, craters slopes and shadows. This paper gives a description of the Flash Lidar model and presents results from the Lidar operating under different scenarios.

Hines, Glenn D.↗
NASA NTRS1975

Dynamical and photometric investigation of cometary type 2 tails

The absolute calibration of the photometric profile of the antitail of Comet Kohoutek 1973 XII on plates taken with the Curtis Schmidt telescope of the University of Michigan at the Cerro Tololo Inter-American Observatory is described in detail. The formula for the determination of the air mass, and the correction for atmospheric absorption and for the loss of light due to vignetting are included. The calibration stars were used to derive the coefficients converting the relative intensity scale to the absolute surface-brightness units. The extensive results of the study of the orbital evolution of vaporizing dust particles are listed in a tabular form. Gradual evaporation from the surface of a particle results typically in its expulsion from the solar system. The properties of the particle and the elements of its orbit at expulsion are given as functions of the particle's properties and orbit before appreciable evaporation commenced. Also given are circumstances at an encounter of an expelled particle with the earth as a function of the particle's properties. A few specific cases are represented graphically.

Sekanina, Z.↗
NASA NTRS2010

Meridional Flow Variations: Implications for Flux Transport Models

Observations of the transport of magnetic elements across the Sun's surface indicate that, in general, the meridional flow extends all the way to the poles. Furthermore, the speed of this flow varies systematically over each solar cycle faster at minimum and slower at maximum. The flow speed on the approach to this (Cycle 24) minimum was substantially faster than it was at the last minimum. This increased flow speed should have produced a short Cycle 23 with strong polar fields in the flux transport dynamos used to predict Cycle 24. This is contrary to what we have seen. The increased flow speed does produce weak polar fields in the surface flux transport models like those used to estimate past irradiance variations. However, these surface flux transport models use meridional flow profiles that do not agree with the observations. Both types of flux transport models are missing identifiable components. We note that the observed changes in the structure of the meridional flow profile are consistent with Spruit's model for the torsional oscillations - suggesting that there may be associated irradiance variations.

Hthaway, David H.↗
NASA NTRS1986

Gust response of hingeless rotors

The gust response of a coupled hingeless rotor-fuselage system is studied in both hover and forward flight. Each rotor blade undergoes flap bending, lag bending, and torsional deflections. The blades are discretized into beam elements, each with fifteen nodal degrees of freedom. The fuselage is permitted three translational (vertical, longitudinal, and lateral) and two rotational (pitch and roll) degrees of freedom. The formulation considers a three-dimensional gust field wherein each gust velocity component can have an arbitrary variation in space and time. Aerodynamic loads are obtained using quasisteady strip theory. Wake-induced effects are introduced through dynamic inflow modeling. Dynamic stall and reverse flow effects are also included. Equations governing the rotor-fuselage gust response are linearized about the vehicle propulsive trim state and the blade steady-state defected positions, and solved by time integration. The effects of several parameters on the helicopter gust response are illustrated, including dynamic inflow, lag stiffness, forward speed, gust profile, gust penetration rate, and gust velocity direction.

Bir, G. S.↗
NASA NTRS2008

Patterned Ferroelectric Films for Tunable Microwave Devices

Tunable microwave devices based on metal terminals connected by thin ferroelectric films can be made to perform better by patterning the films to include suitably dimensioned, positioned, and oriented constrictions. The patterns can be formed during fabrication by means of selective etching processes. If the width of the ferroelectric film in such a device is reduced at one or more locations, then both the microwave field and any applied DC bias (tuning) electric field become concentrated at those locations. The magnitudes of both the permittivity and the dielectric loss of a ferroelectric material are reduced by application of a DC field. Because the concentration of the DC field in the constriction(s) magnifies the permittivity- and loss-reducing effects of the applied DC voltage, the permittivity and dielectric loss in the constriction(s) are smaller in the constriction(s) than they are in the wider parts of the ferroelectric film. Furthermore, inasmuch as displacement current must flow through either the constriction(s) or the low-loss dielectric substrate, the net effect of the constriction(s) is equivalent to that of incorporating one or more low-loss, low-permittivity region(s) in series with the high-loss, high-permittivity regions. In a series circuit, the properties of the low-capacitance series element (in this case, the constriction) dominate the overall performance. Concomitantly, the capacitance between the metal terminals is reduced. By making the capacitance between the metal terminals small but tunable, a constriction increases the upper limit of the frequency range amenable to ferroelectric tuning. The present patterning concept is expected to be most advantageous for devices and circuits that must operate at frequencies from about 4 to about 60 GHz. A constriction can be designed such that the magnitude of the microwave electric field and the effective width of the region occupied by the microwave electric field become functions of the applied DC electric field, so that tunability is enhanced. It should even be possible to design the constriction to obtain a specific tuning-versus-voltage profile.

Miranda, Felix A.↗