Deflection Field Research Articles

Effect of non-Gaussian lensing deflections on CMB lensing measurements

We investigate the impact of non-Gaussian lensing deflections on measurements of the CMB lensing power spectrum. We find that the false assumption of their Gaussianity significantly biases these measurements in current and future experiments at the percent level. The bias is detected by comparing CMB lensing reconstructions from simulated CMB data lensed with Gaussian deflection fields to reconstructions from simulations lensed with fully non-Gaussian deflection fields. The non-Gaussian deflections are produced by ray-tracing through snapshots of an N-body simulation and capture both the non-Gaussianity induced by non-linear structure formation and by multiple correlated deflections. We find that the amplitude of the measured bias is in agreement with analytical predictions by B\"ohm et al. 2016. The bias is largest in temperature-based measurements and we do not find evidence for it in measurements from a combination of polarization fields ($EB,EB$). We argue that the non-Gaussian bias should be even more important for measurements of cross-correlations of CMB lensing with low-redshift tracers of large-scale structure.

Generation of THz Modulated Electron Bunches Using Transversally Polarized Waves to Drive a Dielectric Dual-Grating

We propose and design a dual dielectric grating structure for generating electron bunches with THz repetition frequency. Here we apply transversally polarized sub-terahertz waves to transversally illuminate a dielectric dual-grating, within which the sinusoidally varied deflection fields are induced and exerted on the electron bunches passing through the structure. The velocities of electrons within the bunches are modulated in the transversal direction, which then leads to the generation of a train of micro-bunches. The spectra of these micro-bunches have a series of profound high harmonics in the terahertz region. The simulation result of the electron beam’s bunching behavior is discussed in this paper.

Design for an aberration corrected scanning electron microscope using miniature electron mirrors

Resolution of scanning electron microscopes (SEMs) is determined by aberrations of the objective lens. It is well known that both spherical and chromatic aberrations can be compensated by placing a 90-degree bending magnet and an electron mirror in the beam path before the objective lens. Nevertheless, this approach has not led to wide use of these aberration correctors, partly because aberrations of the bending magnet can be a serious problem. A mirror corrector with two mirrors placed perpendicularly to the optic axis of an SEM and facing each other is proposed. As a result, only small-angle magnetic deflection is necessary to guide the electron beam around the top mirror to the bottom mirror and around the bottom mirror to the objective lens. The deflection angle, in the order of 50 mrad, is sufficiently small to avoid deflection aberrations. In addition, lateral dispersion at the sample plane can be avoided by making the deflection fields symmetric. Such a corrector system is only possible if the incoming beam can pass the top mirror at a distance in the order of millimeters, without being disturbed by the electric fields of electrodes of the mirror. It is proposed that condition can be satisfied with micro-scale electron optical elements fabricated by using MEMS technology. In the proposed corrector system, the micro-mirrors have to provide the exact negative spherical and chromatic aberrations for correcting the aberration of the objective lens. This exact tuning is accomplished by variable magnification between the micro-mirrors and the objective lens using an additional transfer lens.Extensive optical calculations are reported. Aberrations of the micro-mirrors were analyzed by numerical calculation. Dispersion and aberrations of the deflectors were calculated by using an analytical field model. Combination aberrations caused by the off-axis position of dispersive rays in the mirrors and objective lens were also analyzed. It is concluded that the proposed corrector system will be a promising candidate for simple and low-cost aberration correction in low-voltage SEMs.

Probabilistic buckling analysis of beam-column elements with geometric imperfections and various boundary conditions

Although the manufacturing process of structural members has been improved over the last decades, inherent geometric imperfections in slender beam-columns cannot be avoided altogether. Such imperfections largely affect the buckling behavior of the beam by modifying (reducing) the actual critical load in comparison with the theoretically perfect beam idealization. Whereas the deterministic characterization of such imperfections is a rather difficult task that should be performed from case to case, a more general approach would require dealing with imperfections within a probabilistic framework, i.e., treating them as random fields. The aim of this paper is to provide a simple but effective method to characterize probabilistically the response of imperfect beam-column elements based on the stochastic description of the imperfections. The proposed method assumes that the imperfections are expressed through series expansion wherein the critical shapes of the corresponding perfect beam represent the series polynomials. Once the continuum deflection field and the random imperfection field are discretized, some simple closed-form relationships between the imperfection parameters and the main response quantities (e.g. beam deflection and critical load) are established. In contrast to other methods, any type of boundary conditions can be incorporated without computational effort. A few boundary conditions are numerically investigated that clarify how the proposed method can be usefully employed to characterize the buckling response of imperfect beam-column elements probabilistically.

Analysis of size-dependent smart flexoelectric nanobeams

In this paper, the flexoelectric formulations of Timoshenko nanobeams are developed and the static deflection as well as the free vibration of nanobeams are extracted from the formulation under direct and inverse flexoelectric effects. Considering both the direct and the inverse flexoelectric effects, the governing equations and the associated boundary conditions of the nanobeams are developed. Afterwards, static and vibrational analyses are conducted on the Timoshenko and Euler-Bernoulli nanobeams subjected to cantilever and simply supported boundary conditions. Also, the exact solutions for the displacements and the electric potential are obtained in the static analysis. Finally, the effects of the flexoelectric coefficient and the size effect parameter on natural frequency, nanobeam deflection and electric field are investigated. The formulation developed in this study is validated by drawing a comparison between the present results and the results of previous studies. The results presented in this work might help to design advanced smart nanostructures in future studies.

Streak Camera for Strong-Field Ionization.

Ionization of an atom or molecule by a strong laser field produces suboptical cycle wave packets whose control has given rise to attosecond science. The final states of the wave packets depend on ionization and deflection by the laser field, which are convoluted in conventional experiments. Here, we demonstrate a technique enabling efficient electron deflection, separate from the field driving strong-field ionization. Using a midinfrared deflection field permits one to distinguish electron wave packets generated at different field maxima of an intense few-cycle visible laser pulse. We utilize this capability to trace the scattering of low-energy electrons driven by the midinfrared field. Our approach represents a general technique for studying and controlling strong-field ionization dynamics on the attosecond time scale.

An efficient multiple point selection study for mesh deformation using radial basis functions

The mesh deformation using radial basis functions (RBFs) is widely used in aerodynamic applications in the context of design & optimization and aeroelasticity. One reason is the good performance for test cases requiring only a few number of support points. But in test cases with complex deflection fields, requiring a large number of support points, the performance of the method degenerates. To improve an existing RBFs-based mesh-deformation method, an efficient multiple point selection method has been developed based on the conventional Greedy method. The interpolation error function of the RBFs-based model is analyzed, and multiple points with maximum local error are selected simultaneously into the support set, with which an interpolation model will be finally built to compute the displacements of the volume mesh nodes. To avoid too many redundant points for building the interpolation model, a threshold factor is conceived to limit the number of points selected. The computational cost by the Greedy method, the multi-level data reduction method and the developed method, are theoretically compared. Typical deformation problems are chosen as test cases for demonstrating current implementations, like a ninety-degree rotation of a NACA 0012 airfoil, the adjustment of the position of the slat and the flap of a high-lift airfoil, the bending of the DLR F6 configuration, and the shape modification of a hypersonic Rocket-Based Combined Cycle space vehicle. Further, the effect of the threshold factor is studied. The results show that the developed mesh-deformation method has a better efficiency than the Greedy method and the multi-level data reduction method, especially for test cases with complex deflection fields.

High intensity impact of granular matter with edge-clamped ductile plates

The deformation of ductile square stainless steel plates during central impact by high velocity, spherically symmetric granular particle shells has been investigated using an approach that combined large-scale experiments with numerical simulation. The study used suspended spherical explosive charges to accelerate 25–150 kg concentric shells of water saturated glass or higher density zirconia particles to velocities of 500–1200 m/s. The test charges were positioned above the center of 2.54 cm thick, 1.32 m × 1.32 m wide edge clamped panels made of 304 stainless steel, and their permanent deflection fields measured after testing. A novel edge restraint approach was utilized to avoid disruption of reflected particle flow over the impacted surface of the sample and so avoid plate failure near the gripped regions. The end of a Kolsky bar was positioned at a location symmetrically equivalent to the plate center, and was used to measure both the pressure and the specific impulse applied to the plate center. The evolution of the granular shell topology following charge detonation was characterized by analysis of high-speed video images. The radial expansion of the granular shells, the pressure and impulse that they transferred to the Kolsky bar, and the test plates out-of-plane displacement field were all well predicted by a discrete particle-based simulation approach. The study confirms earlier simplified model estimates of an approximately linear dependence of the plates out-of-plane displacement upon incident impulse, and validates the use of the edge restraint concept. It also experimentally identifies the existence of a granular shell velocity dependent instability at the leading edge of the fastest expanding granular shells.

Ambiguities in gravitational lens models: the density field from the source position transformation

Strong gravitational lensing is regarded as the most precise technique to measure the mass in the inner region of galaxies or galaxy clusters. In particular, the mass within one Einstein radius can be determined with an accuracy of order of a few percent or better, depending on the image configuration. For other radii, however, degeneracies exist between galaxy density profiles, precluding an accurate determination of the enclosed mass. The source position transformation (SPT), which includes the well-known mass-sheet transformation (MST) as a special case, describes this degeneracy of the lensing observables in a more general way. In this paper we explore properties of an SPT, removing the MST to leading order, i.e., we consider degeneracies which have not been described before. The deflection field $\boldsymbol{\hat{\alpha}}(\boldsymbol{\theta})$ resulting from an SPT is not curl-free in general, and thus not a deflection that can be obtained from a lensing mass distribution. Starting from a variational principle, we construct lensing potentials that give rise to a deflection field $\boldsymbol{\tilde{\alpha}}$, which differs from $\boldsymbol{\hat{\alpha}}$ by less than an observationally motivated upper limit. The corresponding mass distributions from these 'valid' SPTs are studied: their radial profiles are modified relative to the original mass distribution in a significant and non-trivial way, and originally axi-symmetric mass distributions can obtain a finite ellipticity. These results indicate a significant effect of the SPT on quantitative analyses of lens systems. We show that the mass inside the Einstein radius of the original mass distribution is conserved by the SPT; hence, as is the case for the MST, the SPT does not affect the mass determination at the Einstein radius. [...]

Leveraging Internal Viscous Flow to Extend the Capabilities of Beam-Shaped Soft Robotic Actuators.

Elastic deformation of beam-shaped structures due to embedded fluidic networks (EFNs) is mainly studied in the context of soft actuators and soft robotic applications. Currently, the effects of viscosity are not examined in such configurations. In this work, we introduce an internal viscous flow and present the extended range of actuation modes enabled by viscosity. We analyze the interaction between elastic deflection of a slender beam and viscous flow in a long serpentine channel embedded within the beam. The embedded network is positioned asymmetrically with regard to the neutral plane and thus pressure within the channel creates a local moment deforming the beam. Under assumptions of creeping flow and small deflections, we obtain a fourth-order integro-differential equation governing the time-dependent deflection field. This relation enables the design of complex time-varying deformation patterns of beams with EFNs. Leveraging viscosity allows to extend the capabilities of beam-shaped actuators such as creation of inertia-like standing and moving wave solutions in configurations with negligible inertia and limiting deformation to a small section of the actuator. The results are illustrated experimentally.

Experimental performance of an E×B chopper system

Beam operation of a novel $E\ifmmode\times\else\texttimes\fi{}B$ chopper system has started in the low-energy beam transport (LEBT) section of the accelerator-driven neutron source FRANZ. The chopper is designed for low-energy high-perveance beams and high repetition rates, and will finally operate with 120 keV protons. It combines a static magnetic deflection field with a pulsed electric compensation field in a Wien filter-type $E\ifmmode\times\else\texttimes\fi{}B$ configuration. The chopper was designed, manufactured and successfully commissioned at the required repetition rate of 257 kHz using a 14 keV helium beam with up to 3.5 mA of beam current. Beam pulses with rise times of $(120\ifmmode\pm\else\textpm\fi{}10)\text{ }\mathrm{ns}$, flat-top lengths of $(85\ifmmode\pm\else\textpm\fi{}10)\text{ }\mathrm{ns}$ to $(120\ifmmode\pm\else\textpm\fi{}10)\text{ }\mathrm{ns}$ and full width at half maximum (FWHM) between $(295\ifmmode\pm\else\textpm\fi{}10)\text{ }\mathrm{ns}$ and $(370\ifmmode\pm\else\textpm\fi{}10)\text{ }\mathrm{ns}$ were experimentally achieved.

PIC modeling of negative ion sources for fusion

This work represents the first attempt to model the full-size ITER negative ion source prototype including expansion, extraction and part of the acceleration regions keeping the resolution fine enough to resolve every single aperture of the extraction grid. The model consists of a 2.5-dimensional Particle-in-Cell/Monte Carlo Collision representation of the plane perpendicular to the filter field lines. Both the magnetic filter and electron deflection fields have been included. A negative ion current density of produced by neutral conversion from the plasma grid is used as fixed parameter, while negative ions produced by electron dissociative attachment of vibrationally excited molecules and by ionic conversion on plasma grid are self-consistently simulated. Results show the non-ambipolar character of the transport in the expansion region driven by electron magnetic drifts in the plane perpendicular to the filter field. It induces a top-bottom asymmetry detected up to the extraction grid which in turn leads to a tilted positive ion flow hitting the plasma grid and a tilted negative ion flow emitted from the plasma grid. As a consequence, the plasma structure is not uniform around the single aperture: the meniscus assumes a form of asymmetric lobe and a deeper potential well is detected from one side of the aperture relative to the other side. Therefore, the surface-produced contribution to the negative ion extraction is not equally distributed between both the sides around the aperture but it come mainly from the lower side of the grid giving an asymmetrical current distribution in the single beamlet.

Breaking through the false coincidence barrier in electron-ion coincidence experiments.

Photoelectron Photoion Coincidence (PEPICO) spectroscopy holds the promise of a universal, isomer-selective, and sensitive analytical technique for time-resolved quantitative analysis of bimolecular chemical reactions. Unfortunately, its low dynamic range of ∼103 has largely precluded its use for this purpose, where a dynamic range of at least 105 is generally required. This limitation is due to the false coincidence background common to all coincidence experiments, especially at high count rates. Electron/ion pairs emanating from separate ionization events but arriving within the ion time of flight (TOF) range of interest constitute the false coincidence background. Although this background has uniform intensity at every m/z value, the Poisson scatter in the false coincidence background obscures small signals. In this paper, temporal ion deflection coupled with a position-sensitive ion detector enables suppression of the false coincidence background, increasing the dynamic range in the PEPICO TOF mass spectrum by 2-3 orders of magnitude. The ions experience a time-dependent electric deflection field at a well-defined fraction of their time of flight. This deflection defines an m/z- and ionization-time dependent ion impact position for true coincidences, whereas false coincidences appear randomly outside this region and can be efficiently suppressed. When cold argon clusters are ionized, false coincidence suppression allows us to observe species up to Ar9+, whereas Ar4+ is the largest observable cluster under traditional operation. This advance provides mass-selected photoelectron spectra for fast, high sensitivity quantitative analysis of reacting systems.

A study on non-linear post-buckling behavior of tapered Timoshenko beam made of functionally graded material under in-plane thermal loadings

In the present work, the non-linear post-buckling load–deflection behavior of tapered functionally graded material beam is studied for different in-plane thermal loadings. Two different thermal loadings are considered. The first one is due to the uniform temperature rise and the second one is due to the steady-state heat conduction across the beam thickness leading to non-uniform temperature rise. The governing equations are derived using the principle of minimum total potential energy employing Timoshenko beam theory. The solution is obtained by approximating the displacement fields following Ritz method. Geometric non-linearity for large post-buckling behavior is considered using von Kármán type non-linear strain-displacement relationship. Stainless steel/silicon nitride functionally graded material beam is considered with temperature-dependent material properties. The validation of the present work is successfully performed using finite element software ANSYS and using the available result in the literature. The post-buckling load–deflection behavior in non-dimensional plane is presented for different taperness parameters and also for different volume fraction indices. Normalized transverse deflection fields are presented showing the shift of the point of maximum deflection for various deflection levels. The results are new of its kind and establish benchmark for studying non-linear thermo-mechanical behavior of tapered functionally graded material beam.

Experimental assessment of rectification algorithm in vision-based deflection measurement system

An uncertainty assessment of a vision-based method for the measurement of a structure’s in-plane deflection is presented. In the investigated approach, the displacements of measurement points in the structure under load are computed by means of digital image correlation. The application of homography mapping enables the deflection field to be computed from two images of the structure acquired from distinct points in space. The impact of the camera’s pose and changes in focal length on the performance of the developed vision algorithm is investigated. The paper presents and discusses the influence of rectification algorithm on the quality of the vision-based measurement system as well.

Study on crack-inclusion interaction using digital gradient sensing method

ABSTRACTThe interaction between matrix crack and a round inclusion was studied by the method of digital gradient sensing. First, the stress fields at the matrix crack tip in the neighbor of a round inclusion were derived based on transformation toughening theory and Eshelby inclusion method, and the effect of the inclusion on the stress intensity factor of the matrix crack was analyzed. Then, the non-contact optical measurement system of digital gradient sensing was built up, and a three-point bending test was carried out using a single-edge cracked specimen. The mode I stress intensity factor was extracted from the angular deflection of the light rays. Finally, the effect of the inclusion on the angular deflection fields and the stress intensity factor at the crack tip was analyzed experimentally. These results will play an important role for evaluating the fracture mechanism of crack-inclusion interaction in composites.

Assessment of a structural health monitoring technique through synthetic data generation

This work assesses the accuracy of a structural health monitoring (SHM) technique previously presented in the literature. The SHM technique under exam relies on a modal decomposition method and is intended to reconstruct the distributed deflection and strain fields from point-wise strain measurements at known locations. The objective of this work is to assess the reliability of such algorithm to variations of sensors number and their location. To this aim, the problem of a simply supported beam subjected to an impulsive loading is solved analytically and the results are used as synthetic input data for the SHM algorithm. The robustness of the SHM methodology has been also evaluated against erroneous choices of modal basis. Results show that sensors number and location play a primary role in the accuracy of the reconstruction, whereby the choice of the modal basis has a negligible influence on the results.

Inverse identification of time-harmonic loads acting on thin plates using approximated Green’s functions

In this paper, a non-iterative technique is proposed for the transverse load identification on Kirchhoff plates using approximate Green’s functions (AGFs). In this way, we firstly employ the recently introduced meshless method to construct the AGFs, as the combination of a series of Trefftz basis, i.e. Exponential basis functions (EBFs), and the fundamental solutions of the governing equation. As will be explained, using a proper set of EBFs, as well as a collocation technique, enables us to construct the AGFs for different types of domain shape and boundary conditions. In the second step, a set of artificially generated results, in the absence of realistic experimental results, are used to express the plate’s response field, i.e. deflection or velocity fields, as a series of AGFs through a collocation technique. It will be shown how the constant coefficients of the response series are related to the intensity of the reconstructed force at a set of selected points. The proposed method is capable of constructing both distributed and concentrated loads with desirable accuracy. This ability is shown in the solution of three sample problems of the static and time-harmonic force recovery.

Particle model of full-size ITER-relevant negative ion source

This work represents the first attempt to model the full-size ITER-relevant negative ion source including the expansion, extraction, and part of the acceleration regions keeping the mesh size fine enough to resolve every single aperture. The model consists of a 2.5D particle-in-cell Monte Carlo collision representation of the plane perpendicular to the filter field lines. Magnetic filter and electron deflection field have been included and a negative ion current density of j(H(-)) = 660 A/m(2) from the plasma grid (PG) is used as parameter for the neutral conversion. The driver is not yet included and a fixed ambipolar flux is emitted from the driver exit plane. Results show the strong asymmetry along the PG driven by the electron Hall (E × B and diamagnetic) drift perpendicular to the filter field. Such asymmetry creates an important dis-homogeneity in the electron current extracted from the different apertures. A steady state is not yet reached after 15 μs.

Extreme value statistics of cosmic microwave background lensing deflection angles

The smaller the angular scales on which the anisotropies of the cosmic microwave background (CMB) are probed the more important their distortion due to gravitational lensing becomes. Here we investigate the maxima and minima of the CMB lensing deflection field using general extreme value statistics. Since general extreme value statistics applies to uncorrelated data in first place we consider appropriately low-pass filtered deflection maps. Besides the suppression of correlations filtering is required for another reason: The lensing field itself is not directly observable but needs to be (statistically) reconstructed from the lensed CMB by means of a quadratic estimator. This reconstruction, though, is noise dominated and therefore requires smoothing, too. In idealized Gaussian realizations as well as in realistically reconstructed data we find that both maxima and minima of the deflection angle components follow consistently a general extreme value distribution of Weibull-type. However, its shape, location and scale parameters vary significantly between different realizations. The statistics' potential power to constrain cosmological models appears therefore rather limited.