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DOE OSTI2023

Hanford Waste Treatment Plant Effluent Management Facility Stack Effluent Monitoring: Sampling Probe Location Qualification Evaluation

The Hanford Tank Waste Treatment and Immobilization Plant Effluent Management Facility (EMF) stack monitor location was qualified using a combination of scale model stacks to mitigate the risk of identifying that the sampling location does not meet the qualification criteria on the full-scale stack. The LV-S1 scale model stack was used as a baseline, augmented by the LB-S1 and LV-S2 scale model stacks to address the Direct Feed Low Activity Waste Effluent Management Facility Vessel Vent Process (DVP) injection into the main Active Confinement Ventilation (ACV) system duct. As required by the American National Standards Institute/Health Physics Society (ANSI/HPS) N13.1-1999 standard, the scale model and its sampling locations were geometrically similar to the actual stack, and the Reynolds numbers for both the actual and model stacks were >10,000. An additional criterion is that the product of the hydraulic diameter and mean velocity (DV) of the full-scale stack must be between 1/6 DV and 6 DV of the scale model stack tests. The LV-S1, LB-S1, and LV-S2 scale model stack tests have met the criteria of the ANSI/HPS N13.1-1999 standard to demonstrate the stack sampling locations are well mixed. Verification tests of the EMF stack were performed at normal operating conditions. The minimum 1/6 DV value and the maximum 6 DV value from the scale model testing determine the range of stack flow rates for which the full-scale stack may be operated while remaining in compliance with the stack verification criterion. A practical range for the full-scale stack qualification uses the average DV through 6 DV from the scale model tests to compute the corresponding flow rates. Table S1 lists the operating flow rate along with the average and maximum qualified stack flow rate based on the LV-S1 scale model DV values. The operating flow is below the maximum qualified stack flow, which means that the scale model test results are acceptable for stack qualification. The remaining criteria for the stack verification to be considered valid involve the flow angle and velocity uniformity results. First, the flow angle at the full-scale stack must be ≤20°. Second, the velocity uniformity at the full-scale stack must be ≤20% coefficient of variance (COV). Finally, the velocity uniformity results for the actual and scale model stack tests must agree within 5% COV. These criteria were met through the full-scale stack test at the EMF. Flow angle results were <5°; all flow angle results were within the ≤20° criterion. The velocity uniformity results for each test condition ranged between 2.2% COV and 4.3% COV, all of which were within the range of the target % COV values from the scale model tests on the LV-S1, LB-S1, and LV S2 scale models. Based on these stack verification test results, the EMF filtered exhaust stack sampling location meets the qualification criteria provided in the ANSI/HPS N13.1-1999 standard for all planned fan operating configurations. This includes each combination of ACV fans with DVP exhausters. Further changes to the system configuration or operating conditions that are outside the qualified flow rates described in this report may require additional tests or analyses to determine compliance with the standard.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2023

TRISO fuel performance analysis: Uncertainty quantification toward optimization

Tri-structural isotropic (TRISO) fuel particles are a fuel form being considered for potential use in next-generation nuclear reactors (i.e., high-temperature gas-cooled reactors). Though the TRISO fuel manufacturing process has continually advanced in recent years, particle comparisons still reveal statistical variations and uncertainties in terms of geometric configurations and material properties. Given that the physical processes ongoing in TRISO fuel particles during reactor operation are highly correlated with each other, a small degree of uncertainty in one model may lead to significant uncertainty in another. This makes appropriate uncertainty quantification of TRISO fuel particles essential. However, one may wonder about the extent to which the current version of TRISO particles has been optimized, and whether any room remains for further improvements. This paper quantifies TRISO fuel performance model uncertainties that stem from geometric and material data. For this analysis, the BISON code was used, and the Advanced Gas Reactor (AGR)-2 experiment served as a reference case. A total of 10 5 calculations was performed for the uncertainty and optimization analysis, altering the geometric and material data within their uncertainty range. Lastly, the optimization potential of TRISO particles is evaluated from a fuel performance perspective.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS1983

A comprehensive method for preliminary design optimization of axial gas turbine stages. II - Code verification

The present effort represents an extension of previous work wherein a calculation model for performing rapid pitchline optimization of axial gas turbine geometry, including blade profiles, is developed. The model requires no specification of geometric constraints. Output includes aerodynamic performance (adiabatic efficiency), hub-tip flow-path geometry, blade chords, and estimates of blade shape. Presented herein is a verification of the aerodynamic performance portion of the model, whereby detailed turbine test-rig data, including rig geometry, is input to the model to determine whether tested performance can be predicted. An array of seven (7) NASA single-stage axial gas turbine configurations is investigated, ranging in size from 0.6 kg/s to 63.8 kg/s mass flow and in specific work output from 153 J/g to 558 J/g at design (hot) conditions; stage loading factor ranges from 1.15 to 4.66.

Jenkins, R. M.↗

DOE OSTI2022

Dark Energy Survey Year 3 results: Exploiting small-scale information with lensing shear ratios

Using the first three years of data from the Dark Energy Survey (DES), we use ratios of small-scale galaxy-galaxy lensing measurements around the same lens sample to constrain source redshift uncertainties, intrinsic alignments and other systematics or nuisance parameters of our model. Instead of using a simple geometric approach for the ratios as has been done in the past, we use the full modeling of the galaxy-galaxy lensing measurements, including the corresponding integration over the power spectrum and the contributions from intrinsic alignments and lens magnification. We perform extensive testing of the small-scale shear-ratio (SR) modeling by studying the impact of different effects such as the inclusion of baryonic physics, nonlinear biasing, halo occupation distribution descriptions and lens magnification, among others, and using realistic N -body simulations of the DES data. We validate the robustness of our constraints in the data by using two independent lens samples with different galaxy properties, and by deriving constraints using the corresponding large-scale ratios for which the modeling is simpler. The results applied to the DES Y3 data demonstrate how the ratios provide significant improvements in constraining power for several nuisance parameters in our model, especially on source redshift calibration and intrinsic alignments. For source redshifts, SR improves the constraints from the prior by up to 38% in some redshift bins. Such improvements, and especially the constraints it provides on intrinsic alignments, translate to tighter cosmological constraints when shear ratios are combined with cosmic shear and other 2pt functions. In particular, for the DES Y3 data, SR improves S 8 constraints from cosmic shear by up to 31%, and for the full combination of probes ( 3 × 2 pt ) by up to 10%. The shear ratios presented in this work are used as an additional likelihood for cosmic shear, 2 × 2 pt and the full 3 × 2 pt in the fiducial DES Y3 cosmological analysis.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1998

Boeing 18-Inch Fan Rig Broadband Noise Test

The purposes of the subject test were to identify and quantify the mechanisms by which fan broadband noise is produced, and to assess the validity of such theoretical models of those mechanisms as may be available. The test was conducted with the Boeing 18-inch fan rig in the Boeing Low-Speed Aeroacoustic Facility (LSAF). The rig was designed to be particularly clean and geometrically simple to facilitate theoretical modeling and to minimize sources of interfering noise. The inlet is cylindrical and is equipped with a boundary layer suction system. The fan is typical of modern high-by-pass ratio designs but is capable of operating with or without fan exit guide vanes (stators), and there is only a single flow stream. Fan loading and tip clearance are adjustable. Instrumentation included measurements of fan performance, the unsteady flow field incident on the fan and stators, and far-field and in-duct acoustic fields. The acoustic results were manipulated to estimate the noise generated by different sources. Significant fan broadband noise was found to come from the rotor self-noise as measured with clean inflow and no boundary layer. The rotor tip clearance affected rotor self-noise somewhat. The interaction of the rotor with inlet boundary layer turbulence is also a significant source, and is strongly affected by rotor tip clearance. High level noise can be generated by a high-order nonuniform rotating at a fraction of the fan speed, at least when tip clearance and loading are both large. Stator-generated noise is the loudest of the significant sources, by a small margin, at least on this rig. Stator noise is significantly affected by propagation through the fan.

Ganz, Ulrich W.↗

DOE OSTI2024

Stress intensity factor models using mechanics-guided decomposition and symbolic regression

The finite element method can be used to compute accurate stress intensity factors (SIFs) for cracks with complex geometries and boundary conditions. In contrast, handbook solutions act as surrogate SIF models that provide significantly faster evaluation times. However, the development of conventional surrogate SIF models relies on manual development based on low-order parameterizations. This limits surrogate model accuracy and generalizability. Here, in this paper, we develop a framework for the automated development of mechanics-guided handbook SIF solutions by using interpretable machine learning via genetic programming for symbolic regression (GPSR). Formalizing the mechanics-based approach of Raju and Newman, SIF training data is decomposed into multiple subsets. This decomposition enables parallel GPSR model development of subfunctions, each of which accounts for specific geometrical corrections with respect to a known analytical model. Using this mechanics-based approach with GPSR allows for equations to be learned with improved accuracy and reduced complexity relative to the Raju Newman equations while maintaining the inherent interpretability of mathematical expressions. In this paper, we present equations that match the complexity of the Raju Newman equations while having reduced error, as well as equations with similar errors and reduced complexity.

42 ENGINEERING↗

NASA NTRS1990

On the Response of the Special Sensor Microwave/Imager to the Marine Environment: Implications for Atmospheric Parameter Retrievals

A reasonably rigorous basis for understanding and extracting the physical information content of Special Sensor Microwave/Imager (SSM/I) satellite images of the marine environment is provided. To this end, a comprehensive algebraic parameterization is developed for the response of the SSM/I to a set of nine atmospheric and ocean surface parameters. The brightness temperature model includes a closed-form approximation to microwave radiative transfer in a non-scattering atmosphere and fitted models for surface emission and scattering based on geometric optics calculations for the roughened sea surface. The combined model is empirically tuned using suitable sets of SSM/I data and coincident surface observations. The brightness temperature model is then used to examine the sensitivity of the SSM/I to realistic variations in the scene being observed and to evaluate the theoretical maximum precision of global SSM/I retrievals of integrated water vapor, integrated cloud liquid water, and surface wind speed. A general minimum-variance method for optimally retrieving geophysical parameters from multichannel brightness temperature measurements is outlined, and several global statistical constraints of the type required by this method are computed. Finally, a unified set of efficient statistical and semi-physical algorithms is presented for obtaining fields of surface wind speed, integrated water vapor, cloud liquid water, and precipitation from SSM/I brightness temperature data. Features include: a semi-physical method for retrieving integrated cloud liquid water at 15 km resolution and with rms errors as small as approximately 0.02 kg/sq m; a 3-channel statistical algorithm for integrated water vapor which was constructed so as to have improved linear response to water vapor and reduced sensitivity to precipitation; and two complementary indices of precipitation activity (based on 37 GHz attenuation and 85 GHz scattering, respectively), each of which are relatively insensitive to variations in other environmental parameters.

Petty, Grant W.↗

NASA NTRS2001

Shock Formation of Slow Magnetosonic Waves in Coronal Plumes

We investigate the height of shock formation in coroner plumes for slow magnetosonic waves. The models take into account plume geometric spreading, heat conduction and radiative damping. The wave parameters as well as the spreading functions of the plumes and the base magnetic field strengths are given by empirical constraints mostly from Solar and Heliospheric Observatory/Ultraviolet Coronagraph Spectrometer (SOHO/UVCS). Our models show that shock formation occurs at low coronal heights, i.e., within 1.3 solar radius, depending on the model parameters. The shock formation is calculated using the well-established wave breaking condition given by the intersection of C+ characteristics in the space-time plane. Our models show that shock heating by slow magnetosonic waves is expected to be relevant at most heights in solar coronal plumes, although slow magnetosonic waves are most likely not a solely operating energy supply mechanism.

Cuntz, Manfred↗

NASA NTRS1993

Optimal design of composite hip implants using NASA technology

Using an adaptation of NASA software, we have investigated the use of numerical optimization techniques for the shape and material optimization of fiber composite hip implants. The original NASA inhouse codes, were originally developed for the optimization of aerospace structures. The adapted code, which was called OPORIM, couples numerical optimization algorithms with finite element analysis and composite laminate theory to perform design optimization using both shape and material design variables. The external and internal geometry of the implant and the surrounding bone is described with quintic spline curves. This geometric representation is then used to create an equivalent 2-D finite element model of the structure. Using laminate theory and the 3-D geometric information, equivalent stiffnesses are generated for each element of the 2-D finite element model, so that the 3-D stiffness of the structure can be approximated. The geometric information to construct the model of the femur was obtained from a CT scan. A variety of test cases were examined, incorporating several implant constructions and design variable sets. Typically the code was able to produce optimized shape and/or material parameters which substantially reduced stress concentrations in the bone adjacent of the implant. The results indicate that this technology can provide meaningful insight into the design of fiber composite hip implants.

Blake, T. A.↗

NASA NTRS1996

Structure and dynamics of the coronal magnetic field

The last few years have seen a marked increase in the sophistication of models of the solar corona. This has been brought about by a confluence of three key elements. First, the collection of high-resolution observations of the Sun, both in space and time, has grown tremendously. The SOHO (Solar Heliospheric Observatory) mission is providing additional correlated high-resolution magnetic, white-light and spectroscopic observations. Second, the power and availability of supercomputers has made two- and three-dimensional modeling routine. Third, the sophistication of the models themselves, both in their geometrical realism and in the detailed physics that has been included, has improved significantly. The support from our current Space Physics Theory grant has allowed us to exploit this confluence of capabilities. We have carried out direct comparisons between observations and models of the solar corona. The agreement between simulated coronal structure and observations has verified that the models are mature enough for detailed analysis, as we will describe. The development of this capability is especially timely, since observations obtained from three space missions that are underway (Ulysses, WIND and SOHO) offer an opportunity for significant advances in our understanding of the corona and heliosphere. Through this interplay of observations and theory we can improve our understanding of the Sun. Our achievements thus far include progress modeling the large-scale structure of the solar corona, three-dimensional models of active region fields, development of emerging flux and current, formation and evolution of coronal loops, and coronal heating by current filaments.

VanHoven, Gerard↗

NASA NTRS2011

Evidence for Dark Energy from the Cosmic Microwave Background Alone Using the Atacama Cosmology Telescope Lensing Measurements

For the first time, measurements of the cosmic microwave background radiation (CMB) alone favor cosmologies with w = -1 dark energy over models without dark energy at a 3.2-sigma level. We demonstrate this by combining the CMB lensing deflection power spectrum from the Atacama Cosmology Telescope with temperature and polarization power spectra from the "Wilkinson Microwave Anisotropy Probe. The lensing data break the geometric degeneracy of different cosmological models with similar CMB temperature power spectra. Our CMB-only measurement of the dark energy density Omega(delta) confirms other measurements from supernovae, galaxy clusters and baryon acoustic oscillations, and demonstrates the power of CMB lensing as a new cosmological tool.

Sherwin, Blake D.↗

DOE OSTI2024

Finite elements for Matérn-type random fields: Uncertainty in computational mechanics and design optimization

This work highlights an approach for incorporating realistic uncertainties into scientific computing workflows based on finite elements, focusing on prevalent applications in computational mechanics and design optimization. We leverage Matérn-type Gaussian random fields (GRFs) generated using the SPDE method to model aleatoric uncertainties, including environmental influences, variating material properties, and geometric ambiguities. Our focus lies on delivering practical GRF realizations that accurately capture imperfections and variations and understanding how they impact the predictions of computational models as well as the shape and topology of optimized designs. Here we describe a numerical algorithm based on solving a generalized SPDE to sample GRFs on arbitrary meshed domains. The algorithm leverages established techniques and integrates seamlessly with the open-source finite element library MFEM and associated scientific computing workflows, like those found in industrial and national laboratory settings. Our solver scales efficiently for large-scale problems and supports various domain types, including surfaces and embedded manifolds. We showcase its versatility through biomechanics and topology optimization applications, emphasizing the potential to influence these domains. The flexibility and efficiency of SPDE-based GRF generation empowers us to run large-scale optimization problems on 2D and 3D domains, including finding optimized designs on embedded surfaces, and to generate design features and topologies beyond the reach of conventional techniques. Moreover, these capabilities allow us to model and quantify geometric uncertainties on reconstructed submanifolds, such as the interpolated surfaces of cerebral aneurysms provided by postprocessing CT scans. In addition to offering benefits in these specific domains, the proposed techniques transcend specific applications and generalize to arbitrary forward and backward problems in uncertainty quantification involving finite elements.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Analysis of Postulated Accident Scenarios for the Transformational Challenge Reactor

The Transformational Challenge Reactor (TCR) is a helium-cooled, yttrium-hydride-moderated reactor that was designed for the U.S. Department of Energy Office of Nuclear Energy. A key objective of the TCR was to employ advanced manufacturing techniques in a nuclear system and demonstrate their potential for revolutionizing the nuclear reactor design process. One purpose of the present work is to demonstrate the safety of the TCR under postulated accidents. Based on RELAP5-3D and COMSOL analyses, the TCR remained below all current safety limits and far below the expected failure limits for the core materials. Another purpose of this work is to provide useful insights and recommendations regarding the application of RELAP5-3D to gas-cooled or other advanced reactors. A novel approach was implemented for simultaneously modeling conduction and radiation in RELAP5-3D, which was found to provide reasonable predictions of radial core, vessel, and ex-vessel heat transfer during postulated events. A multicode approach was also applied, in which high-fidelity COMSOL calculations were used to tune the radial heat transfer parameters in RELAP5-3D. The tuned RELAP5-3D model demonstrated comparable peak temperature predictions as COMSOL, despite a coarse treatment of the core in RELAP5-3D consisting of only two lumped heat structures. This high-fidelity tuning approach enabled enhanced accuracy as well as minimal complexity within the RELAP5-3D model, even for complex fuel geometric designs as in the TCR. Finally, investigations were made into the potential for flow reversal during a pressurized loss-of-forced-flow event in the TCR. The TCR is designed with downward helium flow through the core during normal operation. The RELAP5-3D model predicted that this downward flow would persist, without flow reversal, up to several days after the circulator trip. This was attributed to natural circulation hysteresis effects as have been noted in similar thermofluidic systems. Although flow stagnation and eventual reversal did not lead to unsafe TCR conditions, interesting spatial effects were observed which may have safety relevance for other reactor system designs and coolant types that are designed for downward core flow during normal operation, warranting closer investigation of the flow reversal phenomenon.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS1997

Micromechanical Modeling of Woven Metal Matrix Composites

This report presents the results of an extensive micromechanical modeling effort for woven metal matrix composites. The model is employed to predict the mechanical response of 8-harness (8H) satin weave carbon/copper (C/Cu) composites. Experimental mechanical results for this novel high thermal conductivity material were recently reported by Bednarcyk et al. along with preliminary model results. The micromechanics model developed herein is based on an embedded approach. A micromechanics model for the local (micro-scale) behavior of the woven composite, the original method of cells (Aboudi), is embedded in a global (macro-scale) micromechanics model (the three-dimensional generalized method of cells (GMC-3D) (Aboudi). This approach allows representation of true repeating unit cells for woven metal matrix composites via GMC-3D, and representation of local effects, such as matrix plasticity, yarn porosity, and imperfect fiber-matrix bonding. In addition, the equations of GMC-3D were reformulated to significantly reduce the number of unknown quantities that characterize the deformation fields at the microlevel in order to make possible the analysis of actual microstructures of woven composites. The resulting micromechanical model (WCGMC) provides an intermediate level of geometric representation, versatility, and computational efficiency with respect to previous analytical and numerical models for woven composites, but surpasses all previous modeling work by allowing the mechanical response of a woven metal matrix composite, with an elastoplastic matrix, to be examined for the first time. WCGMC is employed to examine the effects of composite microstructure, porosity, residual stresses, and imperfect fiber-matrix bonding on the predicted mechanical response of 8H satin C/Cu. The previously reported experimental results are summarized, and the model predictions are compared to monotonic and cyclic tensile and shear test data. By considering appropriate levels of porosity, residual stresses, and imperfect fiber-matrix debonding, reasonably good qualitative and quantitative correlation is achieved between model and experiment.

Bednarcyk, Brett A.↗

NASA NTRSDate not supplied

Application of Digital Image Correlation in Wind Tunnel

Digital image correlation (DIC) is a non-contact measurement technique that has been used in various applications in multiple industries, from microscopic specimens all the way to large scale structures. This project involved using DIC to capture wing deflection under simulated wind loading at various angles of attack (AoA). A subscale model of a fixed-wing aircraft, shown in Figure 1, was used in the 14-footby 22-footsubsonicwind tunnel at the NASA Langley Research Center. The setup used two pairs of cameras mounted on the ceiling of the tunnel to view the starboard and port side wings. Aluminum framing was used to rigidly mount the cameras to beams in the ceiling. Camera setup challenges due to the confined space included obtaining even lighting and working around infrared (IR) cameras that were used to capture the flow over the wing. Remote connection was used to access data acquisition computers from computers in the control room. Eight measurement locations on each wing were made of 1-inch-diametercircular silver dry transfer decals that did not alter the air flow across the wing. These circles were speckled with a black ink pen and were used for the IR camera as well as for DIC systems. A mock setup outside the wind tunnel was used to optimize the camera setup and verify that the speckled tape provided sufficient correlation. DIC was used to track the position of seven locations as the AoA of the subscale model changed from −10 degrees to +10 degrees in 1-degree increments. The model was rotated at a fixed height about the center of the fuselage from −7 degrees to +10 degrees. The height of the model had to be lowered to achieve AoA slower than −7degrees due to geometric constraints of the cart supporting the model and the wind tunnel. The source of light was stationary relative to the model, so the exposure time had to be adjusted for different wing regions and AoA values. The three-dimensional (3D) visualization of the markings and the two-dimensional (2D) projection of these points onto the port wing at 0-degree AoA is shown in Figure 2.

Matlock Mennu↗

NASA NTRS2013

Building a 2.5D Digital Elevation Model from 2D Imagery

When projecting imagery into a georeferenced coordinate frame, one needs to have some model of the geographical region that is being projected to. This model can sometimes be a simple geometrical curve, such as an ellipse or even a plane. However, to obtain accurate projections, one needs to have a more sophisticated model that encodes the undulations in the terrain including things like mountains, valleys, and even manmade structures. The product that is often used for this purpose is a Digital Elevation Model (DEM). The technology presented here generates a high-quality DEM from a collection of 2D images taken from multiple viewpoints, plus pose data for each of the images and a camera model for the sensor. The technology assumes that the images are all of the same region of the environment. The pose data for each image is used as an initial estimate of the geometric relationship between the images, but the pose data is often noisy and not of sufficient quality to build a high-quality DEM. Therefore, the source imagery is passed through a feature-tracking algorithm and multi-plane-homography algorithm, which refine the geometric transforms between images. The images and their refined poses are then passed to a stereo algorithm, which generates dense 3D data for each image in the sequence. The 3D data from each image is then placed into a consistent coordinate frame and passed to a routine that divides the coordinate frame into a number of cells. The 3D points that fall into each cell are collected, and basic statistics are applied to determine the elevation of that cell. The result of this step is a DEM that is in an arbitrary coordinate frame. This DEM is then filtered and smoothed in order to remove small artifacts. The final step in the algorithm is to take the initial DEM and rotate and translate it to be in the world coordinate frame [such as UTM (Universal Transverse Mercator), MGRS (Military Grid Reference System), or geodetic] such that it can be saved in a standard DEM format and used for projection.

Padgett, Curtis W.↗

NASA NTRS1980

Application of finite-element-techniques to the interaction of conduction and radiation in an absorbing, scattering and emitting medium

In this paper, the authors demonstrate that a Galerkin finite element method of analysis, utilizing isoparametric elements, offers a viable means of solving continuum thermal radiation problems with conduction in a participating medium. The participating medium was considered to be a gray radiation medium exhibiting isotropic absorption, emission, and scattering characteristics and optical properties that are independent of temperature. The medium was considered to be bounded by infinite parallel opaque, gray surfaces with diffuse emission and reflection characteristics. In solving this problem, a finite element formulation was developed to describe a system in radiative equilibrium. Then the results of this first analysis were linked with a second finite element model which incorporated conduction into the analysis. The results of this study were found to be in good agreement with existing published data. The model offers the following advantageous features: geometric generality, a computational algorithm which is 'convenient' and 'computable', and a functional basis for extension of the radiation model to higher order approximation.

Wu, S. T.↗

NASA NTRS1997

Validation of an Accurate Three-Dimensional Helical Slow-Wave Circuit Model

The helical slow-wave circuit embodies a helical coil of rectangular tape supported in a metal barrel by dielectric support rods. Although the helix slow-wave circuit remains the mainstay of the traveling-wave tube (TWT) industry because of its exceptionally wide bandwidth, a full helical circuit, without significant dimensional approximations, has not been successfully modeled until now. Numerous attempts have been made to analyze the helical slow-wave circuit so that the performance could be accurately predicted without actually building it, but because of its complex geometry, many geometrical approximations became necessary rendering the previous models inaccurate. In the course of this research it has been demonstrated that using the simulation code, MAFIA, the helical structure can be modeled with actual tape width and thickness, dielectric support rod geometry and materials. To demonstrate the accuracy of the MAFIA model, the cold-test parameters including dispersion, on-axis interaction impedance and attenuation have been calculated for several helical TWT slow-wave circuits with a variety of support rod geometries including rectangular and T-shaped rods, as well as various support rod materials including isotropic, anisotropic and partially metal coated dielectrics. Compared with experimentally measured results, the agreement is excellent. With the accuracy of the MAFIA helical model validated, the code was used to investigate several conventional geometric approximations in an attempt to obtain the most computationally efficient model. Several simplifications were made to a standard model including replacing the helical tape with filaments, and replacing rectangular support rods with shapes conforming to the cylindrical coordinate system with effective permittivity. The approximate models are compared with the standard model in terms of cold-test characteristics and computational time. The model was also used to determine the sensitivity of various circuit parameters including typical manufacturing dimensional tolerances and support rod permittivity. By varying the circuit parameters of an accurate model using MAFIA, these sensitivities can be computed for manufacturing concerns, and design optimization previous to fabrication, thus eliminating the need for costly experimental iterations. Several variations were made to a standard helical circuit using MAFIA to investigate the effect that variations on helical tape and support rod width, metallized loading height and support rod permittivity, have on TWT cold-test characteristics.

Kory, Carol L.↗