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At least 271 records · Page 15

Resonant and random excitations on the proton beam in the Large Hadron Collider for active halo control with pulsed hollow electron lenses

We present the results of numerical simulations and experimental studies about the effects of resonant and random excitations on proton losses, emittances, and beam distributions in the Large Hadron Collider (LHC). In addition to shedding light on complex nonlinear effects, these studies are applied to the design of hollow electron lenses (HEL) for active beam halo control. In the High-Luminosity Large Hadron Collider (HL-LHC), a considerable amount of energy will be stored in the beam tails. To control and clean the beam halo, the installation of two hollow electron lenses, one per beam, is being considered. In standard electron-lens operation, a proton bunch sees the same electron current at every revolution. Pulsed electron beam operation (i.e., different currents for different turns) is also considered, because it can widen the range of achievable halo removal rates. For an axially symmetric electron beam, only protons in the halo are excited. If a residual field is present at the location of the beam core, these particles are exposed to time-dependent transverse kicks and to noise. We discuss the numerical simulations and the experiments conducted in 2016 and 2017 at injection energy in the LHC. The excitation patterns were generated by the transverse feedback and damping system, which acted as a flexible source of dipole kicks. Proton beam losses, emittances, and transverse distributions were recorded as a function of excitation patterns and strengths. The resonant excitations induced rich dynamical effects and nontrivial changes of the beam distributions, which, to our knowledge, have not previously been observed and studied in this detail. We conclude with a discussion of the tolerable and achievable residual fields and proposals for further studies.

43 PARTICLE ACCELERATORS↗

Beam focusing and consequences for Doppler backscattering measurements

The phenomenon of focusing of microwave beams in a plasma near a turning-point caustic is discussed by exploiting the analytical solution to the Gaussian beam-tracing equations in the two-dimensional (2-D) linear-layer problem. The location of maximum beam focusing and the beam width at that location are studied in terms of the beam initial conditions. This focusing must be taken into account to interpret Doppler backscattering (DBS) measurements. We find that the filter function that characterises the scattering intensity contribution along the beam path through the plasma is inversely proportional to the beam width, predicting enhanced scattering from the beam focusing region. We show that the DBS signal enhancement for decreasing incident angles between the beam path and the density gradient is due to beam focusing and not due to forward scattering, as was originally proposed by (Gusakov et al., (Plasma Phys. Contr. Fusion, vol. 56, 2014, p. 0250092014, 2017); Plasma Phys. Rep. vol. 43(6), 2017, pp. 605–613). The analytic beam model is used to predict the measurement of the k y density-fluctuation wavenumber power spectrum via DBS, showing that, in an NSTX-inspired example, the spectral exponent of the turbulent, intermediate-to-high k y density-fluctuation spectrum might be quantitatively measurable via DBS, but not the spectral peak corresponding to the driving scale of the turbulent cascade.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

First-Principles Simulation of Beam-Induced Processes Underlying Atomic Manipulation in Electron Microscopes

The development of experimental methods and apparatuses capable of promoting atomically precise material manipulations holds great promise for realizing the ultimate limit of feature miniaturization in materials and devices. The ability to modify materials atom by atom is anticipated to usher in new technologies in areas as diverse as separation science, medicine, and quantum information science. Historically, scanning probe-based techniques have been the most prominent approaches in this space. However, these methods are best suited for the manipulation of surface-exposed regions of materials, as the strong perturbations required for bond scission are delivered most effectively to atoms in the near-proximity to the scanning probe. In contrast, convergent electron beams with energies tuned slightly below the threshold for inducing irreversible knock-on damage have recently been employed (within scanning transmission electron microscopy) to promote atomic-scale bond rearrangements in various beam-stable solids. Currently, however, the efficiency and selectivity of beam-induced atomic manipulation processes with focused electron beams are such that long irradiation times are required to induce a desired atomic rearrangement. With a better understanding of the underlying physics dictating the outcome of a given irradiation event, methods can be devised to improve the efficiency of these techniques so that their promise can be fully realized through widespread adoption.To this end, this Account details our recent efforts to develop and apply tractable first-principles simulation approaches for studying the response of materials to electric beam-like external electric potentials applied in real space. We briefly review the concepts and capabilities in the area of atomically precise materials manipulation and review the early demonstrations of accomplishments in this area, focusing on studies using scanned convergent electron beam probes in particular. We expound upon the depth of the challenge and identify critical shortcomings of theoretical methods that have previously been employed in the simulation of beam-induced processes. We then describe the computational methods that we have generalized from the concepts and tools most commonly applied to the study of molecular photochemistry and how our adaptations of these methods can be employed to capture the relevant dynamical phenomena for beam-induced processes ranging from the initial electron scattering to the ensuing multistate reactions. Here, we contextualize these methods within the current state of the art in this area, which has historically focused primarily on the simulation of inelastic image formation in the electron microscope for the purpose of interpreting the results of quantitative electron microscopy experiments. We demonstrate that the spatial distribution of state-specific excitation rates due to the presence of an external (probe) electric charge is inhomogeneous, such that irradiation at particular locations in materials can favor specific electronic transitions (and disallow others). In addition to the potential for excited-state reaction pathways to be accessed through the initial inelastic scattering of the tightly focused electron beam from the targeted atoms, we also identify favorable conditions for the electronically nonadiabatic evolution of the highly vibrationally excited system to open complex multistate reaction pathways. Implications of the early results for understanding the mechanisms and potential routes to improved efficiency and selectivity in beam-induced reactions are discussed. We conclude with a summary of the current state of theory and modeling capabilities in this area and provide our perspective on future directions for theoretical and experimental developments that we view as crucial to advancing the use of convergent electron beams in mode-specific, atomically precise platforms for direct-write materials modifications.

36 MATERIALS SCIENCE↗

Neutralization of ion beam by electron injection: Accumulation of cold electrons

Ion beam charge neutralization by electron injection is a complex kinetic process. Recent experiments show that the resulting self-potential of the ion beam after neutralization by plasma is much lower than the temperature of plasma electrons [Stepanov et al., Phys. Plasmas 23, 043113 (2016)], indicating that kinetic effects are important and may affect the neutralization of the ion beam. We performed a numerical study of the charge neutralization process of an ion beam making use of a two-dimensional electrostatic particle-in-cell code. The results show that the process of charge neutralization by electron injection is composed of two stages. During the first stage, the self-potential of the beam is higher than the temperature of injected electrons (T e /e) and all injected electrons are captured by the ion beam. During the second stage, hot electrons escape from the ion beam and the beam self-potential (φ) decreases because cold electrons slowly accumulate resulting in the beam self-potential φ to become much lower than Te/e in agreement with previous experimental observations at Princeton Advanced Teststand. We also determined that the resulting φ scales as φ~√T e , in agreement with previous experimental observations from Gabovich's group. In addition, the results show that the transverse position of the electron source has a great impact on ion beam neutralization. A slight shift of the electron source as relevant to the ion thrusters leads to a large increase in the beam self-potential because of an increase in potential energy of injected electrons.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Optimization of transformer ratio and beam loading in a plasma wakefield accelerator with a structure-exploiting algorithm

Plasma-based acceleration has emerged as a promising candidate as an accelerator technology for a future linear collider or a next-generation light source. We consider the plasma wakefield accelerator (PWFA) concept where a plasma wave wake is excited by a particle beam and a trailing beam surfs on the wake. For a linear collider, the energy transfer efficiency from the drive beam to the wake and from the wake to the trailing beam must be large, while the emittance and energy spread of the trailing bunch must be preserved. One way to simultaneously achieve this when accelerating electrons is to use longitudinally shaped bunches and nonlinear wakes. In the linear regime, there is an analytical formalism to obtain the optimal shapes. In the nonlinear regime, however, the optimal shape of the driver to maximize the energy transfer efficiency cannot be precisely obtained because currently no theory describes the wake structure and excitation process for all degrees of nonlinearity. In addition, the ion channel radius is not well defined at the front of the wake where the plasma electrons are not fully blown out by the drive beam. We present results using a novel optimization method to effectively determine a current profile for the drive and trailing beam in PWFA that provides low energy spread, low emittance, and high acceleration efficiency. We parameterize the longitudinal beam current profile as a piecewise-linear function and define optimization objectives. For the trailing beam, the algorithm converges quickly to a nearly inverse trapezoidal trailing beam current profile similar to that predicted by the ultrarelativistic limit of the nonlinear wakefield theory. For the drive beam, the beam profile found by the optimization in the nonlinear regime that maximizes the transformer ratio also resembles that predicted by linear theory. Furthermore, the current profiles found from the optimization method provide higher transformer ratios compared with the linear ramp predicted by the relativistic limit of the nonlinear theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Three-beam rotational coherent anti-Stokes Raman spectroscopy thermometry in scattering environments

Three-beam rotational coherent anti-Stokes Raman scattering (CARS) measurements performed in highly scattering environments are susceptible to contamination by two-beam CARS signals generated by the pump–probe and Stokes–probe interactions at the measurement volume. If this occurs, differences in the Raman excitation bandwidth between the two-beam and three-beam CARS signals can add significant errors to the spectral analysis. This interference to the best of our knowledge has not been acknowledged in previous three-beam rotational CARS experiments, but may introduce measurement errors up to 25% depending on the temperature, amount of scattering, and differences between the two-beam and three-beam Raman excitation bandwidths. Here, the presence of two-beam CARS signal contamination was experimentally verified using a femtosecond–picosecond rotational CARS instrument in two scattering environments: (1) a fireball generated by a laboratory-scale explosion that contained particulate matter, metal fragments, and soot, and (2) a flow of air and small liquid droplets. A polarization scheme is presented to overcome this interference. By rotating the pump and Stokes polarizations +55° and –55° from the probe, respectively, the two-beam and three-beam CARS signals are orthogonally polarized and can be separated using a polarization analyzer. Using this polarization arrangement, the Raman-resonant three-beam CARS signal amplitude is reduced by a factor of 2.3 compared to the case where all polarizations are parallel. This method is successfully demonstrated in both scattering environments. A theoretical model is presented, and the temperature measurement error is studied for different experimental conditions. The criteria for when this interference may be present are discussed.

42 ENGINEERING↗

Measurement techniques using the electron beam profile scanner at the Fermilab Main Injector

This work presents techniques for non-invasive transverse profile measurements of high-intensity proton beams using an Electron Beam Profile Scanner (EBPS). The EBPS utilizes low-energy electrons as a probe to analyze the transverse size of proton beams, allowing for potential analysis on a single-bunch basis. Recent upgrades to the Fermilab Main Injector have enhanced beam power on target to 1 MW, with future developments targeting 2 MW. The higher beam power has increased the demand for non-invasive diagnostics, as invasive methods can disrupt operations.The techniques presented include 1) the slow scan technique, which serves as a proof of concept for the probe beam, 2) the one-shot scan technique for measuring horizontal beam profiles, and 3) the raster scan technique for analyzing horizontal beam profiles as a function of the longitudinal distribution of the beam. The profiles obtained will be crucial for studying and understanding instabilities in high-power, high-intensity proton beams. This will contribute to optimizing the operation of high-power proton accelerators by minimizing beam loss, activation, and damage to both the diagnostics and the accelerator components.

Mwaniki, Matilda [IIT, Chicago]↗

Transport of 12 GeV positron beams at Ce+BAF

Jefferson Lab (JLab) is developing a concept to upgrade the Continuous Electron Beam Accelerator Facility (CEBAF) to additionally deliver spin-polarized continuous-wave positron beams for its nuclear physics program users (Ce+BAF 12 GeV). The concept involves repurposing the Low Energy Recirculator Facility (LERF) at JLab as a dual injector, first producing 100-300 MeV spin-polarized electron beams which are subsequently used for the generation and formation of 123 MeV continuous-wave positron beams. The positron beams are transported to CEBAF and injected for acceleration up to 12 GeV, tailored to the requirements of its four experimental halls. Given the higher emittance of the secondary positron beams, the CEBAF optics are optimized for low dispersion and low beta functions to enhance transmission within the Ce+BAF acceptance limits and with an R56 to manage the positron beams bunch length and energy spread. Potential bottlenecks are being investigated through both optical modeling and measurements using an electron beam, as well as degraded electron beams, to map the 6d acceptance of CEBAF as it is today. This presentation shares preliminary results from multi-particle tracking simulations of the positron beam up to 12 GeV, including spatial, momentum, and spin characteristics, and explores the feasibility of delivering beams simultaneously to multiple experimental halls via extraction optics.

Accelerator Physics↗

Northstar Mo100 Target Beam Spot Size Sensitivity Study

Northstar Mo100 target for production of the medical isotope Mo99 is particularly sensitive to beam over focusing because of the intended high power density. At 38 MeV and 6.32 mA (240 kW beam power, nominally 160 kW th in the target), small deviation from the nominal 12 mm FWHM beam can significantly increase the target disk temperatures and more importantly the load bearing target window temperature. A rhodotron will be the source of the electron beam to be used in the isotope production. This machine operates in a pulsed beam mode, currently expected to be at 50 Hz, which results in a 100 C temperature oscillation above and below the steady state temperature that is the focus of this study. This must be considered in the determination of minimum beam spot size that can be accepted by the target without risk of failure. In addition to the nominal beam spot size of 12 mm, the analysis of 10, 11 and 14.5 mm beam spot sizes are analyzed. The primary conclusion is that an over focused beam to just 11 mm FWHM is the minimum beam spot allowable, based on window temperature and the Ultimate Tensile Stress (UTS) of the window material Inconel 718 as a function of temperature. In contrast an under focused beam of 14.5 mm FWHM has much reduced target and window temperatures, but there is a resulting 6% drop in isotope production, all other factor staying the same. These results are presented herein.

07 ISOTOPE AND RADIATION SOURCES↗

Space Charge Simulations of High Intensity Proton Beams in the AGS Booster

Computer simulation studies have been performed to understand the beam behavior and to explore intensity limitations of proton beams in the AGS Booster at higher beam intensities. During the 100 GeV polarized proton operations of RHIC Run 2024, sPHENIX operated in modes with a crossing angle at collisions in order to mitigate beam-beam effects. Three different running modes were employed: (a) sPHENIX operated with a negative (-2 mrad) crossing angle, and STAR operated with 0 mrad. Both experiments were brought into collisions at the start of the store. (b) sPHENIX was brought into collisions with 0 mrad first. Then STAR was brought into collisions after the beam-beam parameter from sPHENIX reduced to below $10 \times 10^{-3}$. (c) sPHENIX operated with a positive (+1.5 mrad) crossing angle, and STAR operated with 0 mrad. Both experiments were brought into collisions at the start of the store. The collisions with a crossing angle of up to $\pm 2$ mrad, as in running modes (a) and (c), lead to large Piwinski angle in the new sPHENIX detector, which reduces luminosity if other parameters are unchanged. There are two ways to compensate the reduction in luminosity: squeeze $\beta^{*}$ if there is sufficient dynamic aperture, or increase the injected beam intensity. The first part of polarized proton operation during RHIC Run 2024 was dedicated to increasing the intensity. Different configurations were tested with crossing angle and lattice adjustments on RHIC. At the same time, new injector configurations were developed and tested in an effort to push for both higher intensity and better quality of the beam injected into RHIC. When the beam intensity is increased, space charge is a concern particularly in the lower energy stages of acceleration, such as during the injection and the early part of the Booster cycle, which could become a dominant effect in limiting the intensity of the beam that can be delivered to RHIC.

43 PARTICLE ACCELERATORS↗

Ku-band multiple beam antenna

The frequency reuse capability is demonstrated for a Ku-band multiple beam antenna which provides contiguous low sidelobe spot beams for point-to-point communications between any two points within the continental United States (CONUS), or regional coverage beams for direct broadcast systems. A spot beam antenna in the 14/21 GHz band which provides contiguous overlapping beams covering CONUS and two discrete beams covering Hawaii and Alaska were designed, developed, and tested. Two reflector antennas are required for providing contiguous coverage of CONUS. Each is comprised of one offset parabolic reflector, one flat polarization diplexer, and two separate planar array feeds. This antenna system provides contiguous spot beam coverage of CONUS, utilizing 15 beams. Also designed, developed and demonstrated was a shaped contoured beam antenna system which provides contiguous four time zone coverage of CONUS from a single offset parabolic reflector incorporating one flat polarization diplexer and two separate planar array feeds. The beams which illuminate the eastern time zone and the mountain time zone are horizontally polarized, while the beams which illuminate the central time zone and the pacific time zone are vertically polarized. Frequency reuse is achieved by amplitude and polarization isolation.

Chen, C. C.↗

Propagation of charge-neutral beams in space - Modifications when negative ions are present

Two-dimensional (three velocity component) electrostatic simulations are used to investigate the properties of a charge-neutral beam consisting of H(+), H(-), and electrons which will be used in the Beams on Rockets (BEAR) experiment to be launched in late 1987 or early 1988. For cross-field injection and beam densities much greater than the ambient plasma density, the beam splits into two approximately charge-neutral beams: a H(+)-e(-) beam that propagates down the field lines and a H(+)-H(-) beam that propagates at nearly the initial beam velocity on time scales less than the ion gyroperiod. Because of this splitting, space-charge oscillations are induced in the H(+)-H(-) component, which lead to its breakup. At lower beam densities, particularly when the beam electron density is less than about the density of the ambient plasma, the ambient plasma response reduces the space-charge fields as the beam splits and the space-charge oscillations are suppressed.

Winglee, R. M.↗

Scaling effects in the static and dynamic response of graphite-epoxy beam-columns

Scale model technology represents one method of investigating the behavior of advanced, weight-efficient composite structures under a variety of loading conditions. It is necessary, however, to understand the limitations involved in testing scale model structures before the technique can be fully utilized. These limitations, or scaling effects, are characterized. in the large deflection response and failure of composite beams. Scale model beams were loaded with an eccentric axial compressive load designed to produce large bending deflections and global failure. A dimensional analysis was performed on the composite beam-column loading configuration to determine a model law governing the system response. An experimental program was developed to validate the model law under both static and dynamic loading conditions. Laminate stacking sequences including unidirectional, angle ply, cross ply, and quasi-isotropic were tested to examine a diversity of composite response and failure modes. The model beams were loaded under scaled test conditions until catastrophic failure. A large deflection beam solution was developed to compare with the static experimental results and to analyze beam failure. Also, the finite element code DYCAST (DYnamic Crash Analysis of STructure) was used to model both the static and impulsive beam response. Static test results indicate that the unidirectional and cross ply beam responses scale as predicted by the model law, even under severe deformations. In general, failure modes were consistent between scale models within a laminate family; however, a significant scale effect was observed in strength. The scale effect in strength which was evident in the static tests was also observed in the dynamic tests. Scaling of load and strain time histories between the scale model beams and the prototypes was excellent for the unidirectional beams, but inconsistent results were obtained for the angle ply, cross ply, and quasi-isotropic beams. Results show that valuable information can be obtained from testing on scale model composite structures, especially in the linear elastic response region. However, due to scaling effects in the strength behavior of composite laminates, caution must be used in extrapolating data taken from a scale model test when that test involves failure of the structure.

Jackson, Karen E.↗

A simulation study of interactions of Space-Shuttle generated electron beams with ambient plasma and neutral gas

The object was to conduct large scale simulations of electron beams injected into space. The study of active injection of electron beams from spacecraft is important since it provides valuable insight into beam-plasma interactions and the development of current systems in the ionosphere. However, the beam injection itself is not simple, being constrained by the ability of the spacecraft to draw return current from the ambient plasma. The generation of these return currents is dependent on several factors, including the density of the ambient plasma relative to the beam density, the presence of neutrals around the spacecraft, the configuration of the spacecraft, and the motion of the spacecraft through the plasma. Two dimensional particle simulations with collisional processes included are used to show how these different and often coupled processes can be utilized to enhance beam propagation from the spacecraft. To understand the radical expansion of mechanism of an electron beam from a highly charged spacecraft, two dimensional particle in cell simulations were conducted for a high density electron beam injected parallel to magnetic fields from an isolated equipotential conductor into a cold background plasma. The simulations indicate that charge buildup at the beam stagnation point causes the beam to expand radially to the beam electron gyroradius.

Source record↗

A simulation study of interactions of space-shuttle generated electron beams with ambient plasma and neutral gas

The objective was to conduct large scale simulations of electron beams injected into space. The study of the active injection of electron beams from spacecraft is important, as it provides valuable insight into the plasma beam interactions and the development of current systems in the ionosphere. However, the beam injection itself is not simple, being constrained by the ability of the spacecraft to draw current from the ambient plasma. The generation of these return currents is dependent on several factors, including the density of the ambient plasma relative to the beam density, the presence of neutrals around the spacecraft, the configuration of the spacecraft, and the motion of the spacecraft through the plasma. Two dimensional (three velocity) particle simulations with collisional processes included are used to show how these different and often coupled processes can be used to enhance beam propagation from the spacecraft. To understand the radial expansion mechanism of an electron beam injected from a highly charged spacecraft, two dimensional particle-in-cell simulations were conducted for a high density electron beam injected parallel to magnetic fields from an isolated equipotential conductor into a cold background plasma. The simulations indicate that charge build-up at the beam stagnation point causes the beam to expand radially to the beam electron gyroradius.

Winglee, Robert M.↗

Use of particle beams for lunar prospecting

A key issue in choosing the appropriate site for a manned lunar base is the availability of resources, particularly oxygen and hydrogen for the production of water, and ores for the production of fuels and building materials. NASA has proposed two Lunar Scout missions that would orbit the Moon and use, among other instruments, a hard X-ray spectrometer, a neutron spectrometer, and a Ge gamma ray spectrometer to map the lunar surface. This passive instrumentation will have low resolution (tens of kilometers) due to the low signal levels produced by natural radioactivity and the interaction of cosmic rays and the solar wind with the lunar surface. This paper presents the results of a concept definition effort for a neutral particle beam lunar mapper probe. The idea of using particle beam probes to survey asteroids was first proposed by Sagdeev et al., and an ion beam device was fielded on the 1988 Soviet probe to the Mars moon Phobos. During the past five years, significant advances in the technology of neutral particle beams (NPB) have led to a suborbital flight of a neutral hydrogen beam device in the SDIO-sponsored BEAR experiment. An orbital experiment, the Neutral Particle Beam Far Field Optics Experiment (NPB-FOX) is presently in the preliminary design phase. The development of NPB accelerators that are space-operable leads one to consider the utility of these devices for probing the surface of the Moon using gamma ray, X-ray, and optical/UV spectroscopy to locate various elements and compounds. We consider the utility of the NPB-FOX satellite containing a 5-MeV particle beam accelerator as a probe in lunar orbit. Irradiation of the lunar surface by the particle beam will induce secondary and back scattered radiation from the lunar surface to be detected by a sensor that may be co-orbital with or on the particle beam satellite platform, or may be in a separate orbit. The secondary radiation is characteristic of the make-up of the lunar surface. The size of the spot irradiated by the beam is less than 1 km wide along the ground track of the satellite, resulting in the potential for high resolution. The fact that the probe could be placed in polar orbit would result in global coverage of the lunar surface. The orbital particle beam probe could provide the basis for selection of sites for more detailed prospecting by surface rovers.

Toepfer, A. J.↗

Optical beam forming techniques for phased array antennas

Conventional phased array antennas using waveguide or coax for signal distribution are impractical for large scale implementation on satellites or spacecraft because they exhibit prohibitively large system size, heavy weight, high attenuation loss, limited bandwidth, sensitivity to electromagnetic interference (EMI) temperature drifts and phase instability. However, optical beam forming systems are smaller, lighter, and more flexible. Three optical beam forming techniques are identified as applicable to large spaceborne phased array antennas. They are (1) the optical fiber replacement of conventional RF phased array distribution and control components, (2) spatial beam forming, and (3) optical beam splitting with integrated quasi-optical components. The optical fiber replacement and the spatial beam forming approaches were pursued by many organizations. Two new optical beam forming architectures are presented. Both architectures involve monolithic integration of the antenna radiating elements with quasi-optical grid detector arrays. The advantages of the grid detector array in the optical process are the higher power handling capability and the dynamic range. One architecture involves a modified version of the original spatial beam forming approach. The basic difference is the spatial light modulator (SLM) device for controlling the aperture field distribution. The original liquid crystal light valve SLM is replaced by an optical shuffling SLM, which was demonstrated for the 'smart pixel' technology. The advantages are the capability of generating the agile beams of a phased array antenna and to provide simultaneous transmit and receive functions. The second architecture considered is the optical beam splitting approach. This architecture involves an alternative amplitude control for each antenna element with an optical beam power divider comprised of mirrors and beam splitters. It also implements the quasi-optical grid phase shifter for phase control and grid amplifier for RF power. The advantages are no SLM is required for this approach, and the complete antenna system is capable of full monolithic integration.

Wu, Te-Kao↗

Extension of Ko Straight-Beam Displacement Theory to Deformed Shape Predictions of Slender Curved Structures

The Ko displacement theory originally developed for shape predictions of straight beams is extended to shape predictions of curved beams. The surface strains needed for shape predictions were analytically generated from finite-element nodal stress outputs. With the aid of finite-element displacement outputs, mathematical functional forms for curvature-effect correction terms are established and incorporated into straight-beam deflection equations for shape predictions of both cantilever and two-point supported curved beams. The newly established deflection equations for cantilever curved beams could provide quite accurate shape predictions for different cantilever curved beams, including the quarter-circle cantilever beam. Furthermore, the newly formulated deflection equations for two-point supported curved beams could provide accurate shape predictions for a range of two-point supported curved beams, including the full-circular ring. Accuracy of the newly developed curved-beam deflection equations is validated through shape prediction analysis of curved beams embedded in the windward shallow spherical shell of a generic crew exploration vehicle. A single-point collocation method for optimization of shape predictions is discussed in detail

Ko, William L.↗