Beam Approximation Research Articles

Simulated TEM imaging of a heavily irradiated metal

We recast the Howie–Whelan equations for generating simulated transmission electron microscope (TEM) images, replacing the dependence on local atomic displacements with atomic positions only. This allows rapid computation of simulated TEM images for arbitrarily complex atomistic configurations of lattice defects and dislocations in the dynamical two beam approximation directly from standard atomistic simulation output files. Large-scale massively-overlapping cascade simulations, performed with molecular dynamics, are used to generate representative high-dose nanoscale defect and dislocation microstructures in tungsten at room temperature. We then compare the simulated TEM images to experimental TEM images with similar irradiation and imaging conditions. The simulated TEM shows ‘white-dot’ damage in weak-beam dark-field imaging conditions, in agreement with our experimental observations and as expected from previous studies, and in bright-field conditions a dislocation network is observed. In this work we also compare the simulated images to the nanoscale lattice defects in the original atomic structures, and find that at high dose the white spots are not only created by small dislocation loops, but rather arise from nanoscale fluctuations in strains around curved sections of dislocation lines.

Calculation of spontaneous radiation during channeling of relativistic positrons in non-chiral nanotubes using a quadratic approximation

The work investigates the conditions for the possibility of using the quadratic approximation U(ρ) = αρ2 for the interaction potentials of channeled positrons with the inner walls of non-chiral carbon nanotubes of types (n, 0) and (n, n). In particular, (8, 0), (10, 0), (12, 0) and (8, 8), (10, 10), (12, 12) nanotubes were selected. In this case, when calculating the single-particle potential of the carbon atom, only the contribution of valence electrons was taken into account. As a result of this approximation, the parameters α were determined for all the nanotubes studied. Using wave functions and the corresponding quantum levels of transverse energy obtained by solving the Schrödinger equation, the probabilities of occupation of these levels were calculated for positron beams with zero angular dispersion moving along the axes of nanotubes. Based on this information, values of the longitudinal energy of positrons for which the quadratic approximation is applicable were determined for all the studied nanotubes. Spectral distributions of spontaneous radiation were calculated in the dipole approximation for non-dispersive relativistic positron beams, both within the framework of quantum-mechanical and classical approaches.

Strong diffraction of nonlinear surface acoustic waves in crystals

Nonlinear distortion and shock formation in planar surface acoustic waves in anisotropic crystals have been modeled without [Hamilton et al., JASA (1999)] and with [Cormack et al., JASA 2022] piezoelectricity. Weak diffraction has been included in the paraxial approximation for nonlinear surface wave beams in isotropic solids [Shull et al., JASA (1995)]. Here, a procedure for including strong diffraction, i.e., without the paraxial approximation, in the model for nonlinear surface waves in crystals is presented, which incorporates the angular spectrum approach described by Kharusi and Farnell (JASA 1970). Anisotropy is defined by expressing the phase speed of a plane wave, and therefore, the magnitude of the corresponding wavenumber, as a function of the direction of propagation. Next, an explicit expression relating the two wavenumber components in the planar surface along which the wave propagates must be obtained as a function of direction, requiring iterative solution of a transcendental relation. The beam is then propagated incrementally away from the source, advancing the angular spectrum in k-space and including nonlinear interactions in the spatial domain to characterize the combined effects of diffraction and nonlinearity. Preliminary results are presented for converging nonlinear surface waves in crystals. [Work supported by IR&D at ARL:UT.]

The Influence of PE Initial Field Construction Method on Radio Wave Propagation Loss and Tropospheric Duct Inversion

Parabolic equations (PE) are commonly employed for calculating the spatial propagation loss of wireless signals. The initial field is a crucial factor. To investigate the impact of construction accuracy on the calculation of radio wave propagation loss, we selected the half-wave dipole antenna and its Gaussian approximation to examine the influence of wide-angle PE modeling. We analyzed the disparities between the actual antenna pattern and the Gaussian beam approximation, as well as the discrepancies in the corresponding initial field and the calculation of radio wave propagation loss in PE modeling. The simulation results indicate that the error of the Gaussian approximation increases as the angle of departure from the antenna main beam increases, with a relative error of approximately 30% in the initial field. A comparison between the experimental test of the broadcast signal and the simulation calculation reveals that the model based on the actual antenna aligns more closely with the measured value on a flat underlying surface. However, in mountainous areas with significant fluctuations, the simulation results are consistent with each other and higher than the measured value. The inversion results obtained through the particle swarm optimization algorithm demonstrate that the model based on the actual antenna exhibits superior inversion accuracy for the tropospheric atmospheric duct structure.

Problem of Measuring Absorption Using Time-Resolved Photothermal Common-Path Interferometry under Conditions of Developed Heat Diffusion

We present a study of the problem of measuring ultra-low absorption in quartz materials using the time-resolved photothermal common-path interferometry (TPCI) method, which we proposed and elaborated, with allowance for developed heat diffusion in the samples. This task is related to the implementation of one of the ways of increasing the sensitivity of measurements, namely, increasing the energy of the heating pulse by increasing its duration. Analytical formulas for the time dependence of the power of the time-varying component of the probe radiation are obtained in the Gaussian approximation for the laser beams. A correction factor that takes into account the heat diffusion effect is calculated theoretically and used during calibration. The rate at which the power of the time-varying component decreases when the sample is cooled after the end of the heating pulse is calculated. When measuring in crystalline quartz, quartz glass, and also in air, the calculated rate coincided with the experimental one, which is additional evidence for the reliability of the calculations of the correction factor for calibrating the measurements. When the duration of the heating pulse is increased to 5 ms, the calculated sensitivity of the scheme for measuring absorption in quartz glasses is 2 × 10−9 cm−1.

Non-Hermitian Mode Cleaning in Periodically Modulated Multimode Fibers.

We show that the simultaneous modulation of the propagation constant and of the gain/loss coefficient along the graded index multimode fibers results in unidirectional coupling among the modes, which leads to either the enhancement or the reduction of the excitation of higher order transverse modes, depending on the modulation parameters. In the latter case, effective mode cleaning is predicted, ideally resulting in single-mode spatially coherent output. The effect is semi-analytically predicted on a simplified Gaussian beam approximation and numerically proven by solving the wave propagation equation introducing the non-Hermitian modulated potential.

ANALYSIS OF NONLINEAR RIGIDITY CHARACTERISTICS OF AIR BLOWER COMPRESSOR ELASTIC SUPPORTS

Vibrations of rotor systems are largely determined by elastic characteristics of supports. In the general case, the dependence of displacements on force for such supports is nonlinear. This applies to bearing supports of various types. In addition to bearings, elastic elements are also used in supports of rotor systems. They are designed to change the overall stiffness of the supports. The paper analyzes the radial stiffness of flexible ring dampers used in rotor supports. For this, two main approaches are proposed. The first is a conventional simulation of this problem of contact mechanics using the finite element method. The second is an analytical method that can be used as an alternative to expensive numerical calculations. This method is based on the principle of minimum additional energy. A special closed-form variational formulation is developed using the Euler-Bernoulli beam approximation for an elastic ring and a simplified model of normal contact on the ring flanges. It was shown that the surface tolerances of parts have a significant effect on the radial response of a flexible ring, which can become nonlinear. Tight fit of the ring on both sides makes it much stiffer, and non-tight fit leads to free movement of the rotor and much weaker damping of its movement. Both methods gave results that are consistent for the considered cases. By varying their design parameters, it is possible to adjust the rotor systems from critical modes of operation. Keywords: rotor system, elastic support, rigidity, finite element analysis, stress-strain state, contact interaction, principle of minimum additional energy

Numerical approximation of 3D particle beams by multi-scale paraxial Vlasov-Maxwell equations

Even now, solving numerically the 3D time-dependent Vlasov-Maxwell equations is a challenging problem. Hence, it is always interesting to develop simpler but accurate approximate models. By introducing a small parameter, we derived paraxial asymptotic models that approximate these equations, allowing us to treat relativistic cases, much slower beams or even non-relativistic cases. These models are static or quasi-static and with a nth order accuracy that may be chosen as required. Here, we propose a 3D numerical approximation of this multi-scale model. It is based, for the paraxial Maxwell model, on a finite element method coupled with a Particle-In-Cell approximation of the paraxial Vlasov model. Numerical results illustrated the efficiency of the method.

Relativistic space-charge field calculation by interpolation-based treecode

Space-charge effects are of great importance in particle accelerator physics. In the computational modeling, tree-based methods are increasingly used because of their effectiveness in handling non-uniform particle distributions and/or complex geometries. However, they are often formulated using an electrostatic force which is only a good approximation for low energy particle beams. For high energy, i.e., relativistic particle beams, the relativistic interaction kernel may need to be considered and the conventional treecode fails in this scenario. In this work, we formulate a treecode based on Lagrangian interpolation for computing the relativistic space-charge field. Two approaches are introduced to control the interpolation error. In the first approach, a modified admissibility condition is proposed for which the treecode can be used directly in the lab-frame. The second approach is based on the transformation of the particle beam to the rest-frame where the conventional admissibility condition can be used. Numerical simulation results using both methods will be compared and discussed.

Theoretical Analysis of Continuous-Wave Mid-Infrared Optical Vortex Source Generated by Singly Resonant Optical Parametric Oscillator

Due to the important application in the study of vibrational circular dichroism and helical dichroism of chiral molecules, the tunable vortex beam at mid-infrared region has attracted increasing attention. Based on orbital angular momentum (OAM) conservation in nonlinear interactions, the vortex pumped singly resonant optical parametric oscillator (SRO) is recognized as a versatile source of coherent vortex radiation providing high power and broad wavelength coverage from a single device. However, the low parametric gain and high oscillation threshold under continuous wave (cw) pumping has so far been the most challenging factor in generating cw tunable vortex beams. To predict the output characteristic of vortex pumped SRO, a theoretical model describing the vortex pumped SRO is needed. In this study, the theoretical model describing the vortex pumped SRO is set up under collimated Gaussian beam approximation. Output characteristics of different SROs are simulated numerically. By proper selection of pump scheme (such as double-pass pumping scheme), the vortex pumped mid-infrared SRO can oscillate at a relatively low pump power. By controlling the gain (mode overlap ratio between the pump and resonant wave in the nonlinear crystal) and loss (employing a spot-defect mirror with different defect size as the output coupler) of the resonant signal mode in the SRO, the OAM of the pump beam can be directionally transferred to a specific down converted beam. The transfer mechanism of the OAM among the pump light and the down-converted beams and factors affecting the transfer are studied. Our study provides the guidelines for the design and optimization of vortex pumped SRO under cw operation.

Analytical solution for a focused vortex beam radiated by a Gaussian source

Current interest in focused vortex beams is motivated by the ability to trap particles axially and laterally using the resulting radiation force. A simple closed-form solution is obtained in the Fresnel approximation for a sound beam radiated by a Gaussian source with time dependence e−iωt, focal length d, amplitude distribution exp(−r2/a2), and azimuthal phase dependence einθ, where θ is the angle in the plane perpendicular to the beam axis, and the integer n is the topological charge, referred to here as the vorticity. The solution is in good agreement with the pressure field predicted in the paraxial region by numerical evaluation of the Rayleigh integral. Of interest in optics as well as acoustics is the distance from the minimum along the beam axis to the first local maximum, referred to as the vortex ring. The present solution yields rn = ηnd/ka for the vortex ring radius in the focal plane, where k is the wavenumber, and ηn = 1.69 + 0.965(n−1) for vorticities in the range 1 ≤ n < O(20). Within this range the radius rn thus increases linearly with the vorticity. Results are also presented for dependence of the focusing gain on the vorticity. [CAG was supported by the ARL:UT Chester M. McKinney Graduate Fellowship in Acoustics.]

Wave focusing by submerged islands and gravitational analogues

We study water waves propagating over a smooth obstacle in a fluid of varying depth, motivated by the observation that submerged islands in the ocean act as effective lenses that increase the amplitude and destructive power of tsunami waves near focal points. We show that islands of substantial height (compared to the water depth) lead to strong focusing in their immediate vicinity, and generate caustics of either cusp or butterfly type. We highlight similarities and differences with focusing of (high-frequency) gravitational waves by a neutron star. In the linear regime, the comparison is made precise through an effective-spacetime description of the island-fluid system. This description is then put to practical use: We identify caustics by solving the Raychaudhuri equation (a transport equation) along rays of the effective metric. Next, the island-fluid scattering processes are examined in detail (i.e., deflection angle, phase shifts, scattering amplitudes) using numerical simulations and analytical techniques, including the eikonal approximation and its generalisation in the form of the Gaussian beam approximation. We show that the techniques capture the key features of the simulations. Finally, we extend the eikonal approximation to the dispersive regime, demonstrating that the essential features are robust in dispersive settings. This paves the way for future exploration in a controlled laboratory set-up.

Transfer matrix method for analysis of flow thermohydraulic characteristics with extremely nonlinear behavior of thermophysical properties using channel approach

The adaptation procedure of the transfer matrix method for the analysis of nonlinear thermohydraulic (TH) processes using the successful experience of the beam approximation approach is described. The basic principles of spatial and time discretization for the controlling equations system are formulated on the channel approach example. Introduced in the current study effective linearization concept based on “basic” and “corrective” values allowed to remove the restrictions on the medium state equations. The proposed efficient numerical algorithm considering the adaptation of the computational domain helps to solve one of the main problems – obtaining the convergent solution in the case of extremely nonlinear TH properties. Simple classic verification examples, for which theoretical solution exists, were used to test the correctness of applied method realization. The high stability of the suggested method is demonstrated when using implicit correlations for supercritical parameters. The proposed method for the elementary section does not impose restrictions on the type of boundary conditions, which is very important for the organization of branched pipeline systems calculation.

Numerical Approximation of 3d Particle Beams by Multi-Scale Paraxial Vlasov-Maxwell Equations

Numerical Approximation of 3d Particle Beams by Multi-Scale Paraxial Vlasov-Maxwell Equations

Neutrino beam driven instability of magnetosonic waves in the presence of oblique magnetic field and ion-neutral collisional effect in plasmas

The neutrino beam driven instability of fast and slow magnetosonic waves with oblique applied magnetic field in multi-component ion, electron and neutrino beam plasma is studied. The dissipation effects of ion-neutral collisions are also included in the model. The neutrino and electron interactions through electro-weak force are included. It is found that the dissipation of ion collisions has significant effect on the phase velocity of the wave propagation and growth rate of the neutrino beam driven instability. The analytical expression of the growth rate of the fast and slow magnetosonic waves instability is found under the weak neutrino beam approximation and in the absence of ions and neutrals (atoms) collision effect. The numerical illustration of growth rates of the fast and slow magnetosonic waves are also presented with variations of magnetic field angle, neutrino beam energy, neutrino beam density, magnetic field intensity. It is found that the growth rate of the fast magnetosonic wave is maximum in case of the perpendicular directed magnetic field to the direction of wave propagation, while growth rate of slow magnetosonic wave is minimum in that case. It is also noticed that growth rate of fast magnetosonic wave comes out to be larger (of the order tens) than the slow magnetosonic wave case, which is quite different from earlier published results of Type II core-collapse supernova.

Gravity Wave Focusing on the Antarctic Polar Vortex Using Gaussian Beam Approximation in Horizontally Nonuniform Flows

AbstractRay path theory is an asymptotic approximation to the wave equations. It represents efficiently gravity wave propagation in nonuniform background flows so that it is useful to develop schemes of gravity wave effects in general circulation models. One of the main limitations of ray path theory to be applied in realistic flows is in caustics where rays intersect and the ray solution has a singularity. Gaussian beam approximation is a higher-order asymptotic ray path approximation that considers neighboring rays to the central one, and thus, it is free of the singularities produced by caustics. A previous implementation of the Gaussian beam approximation assumes a horizontally uniform flow. In this work, we extend the Gaussian beam approximation to include horizontally nonuniform flows. Under these conditions, the wave packet can undergo horizontal wave refraction producing changes in the horizontal wavenumber, which affects the ray path as well as the ray tube cross-sectional area and so the wave amplitude via wave action conservation. As an evaluation of the Gaussian beam approximation in horizontally nonuniform flows, a series of proof-of-concept experiments is conducted comparing the approximation with the linear wave solution given by the WRF Model. A very good agreement in the wave field is found. An evaluation is conducted with conditions that mimic the Antarctic polar vortex and the orography of the southern flank of South America. The Gaussian beam approximation nicely reproduces the expected asymmetry of the wave field. A much stronger disturbance propagates toward higher latitudes (polar vortex) compared to lower latitudes.

The inverse strength problem for evaluation of bending stresses in pipelines during ground movements

Three variants of the engineering solution of inverse problems regarding the strength of pipeline sections bent as a result of ground movements or during an earthquake are proposed. The feature of this approach consists in calculation of stresses not by the forces acting on the pipe, but by the displacements or deflections. Therefore, full-scale measurements of the detected deviation of the pipe position from the planned pipeline route should be taken as initial data for estimating the values of additional bending stresses. The first problem considered is the assessment of the risk of pipeline malfunction upon sagging or bulging of the supports of aboveground pipelines. The problem is solved in the beam approximation. The pipeline is considered a statically indeterminate beam, one of the supports of which is forcibly moved to a given distance. For a once statically indeterminate beam, a system of four equations — two equilibrium equations and two integral equations for deflections — was solved numerically. The calculated values of three reactions of the supports and the angle of rotation of the pipe section on the first support are used to calculate bending moments, stresses and deflection lines. The problem for a thrice statically indeterminate beam under strain loading was also solved. The second goal is to model the stress-strain state of the pipeline proceeding from the tables of experimental data on the values of pipe deflections and their coordinates. The problem was also solved numerically, using the procedures of smoothing, linear interpolation and sequential differentiation. It is shown that taking into account the possible ambiguous solution of the inverse problem, we should not rely on the calculated values of transverse forces and distributed loads. It is enough to limit ourselves to the second coordinate derivative of the deflection. The third goal is to prevent accidents at the design stage. It is proposed to create a list of normalized deflection functions for modeling possible emergency situations for pipeline sections placed in difficult ground-geological conditions and seismically dangerous zones. The examples of such functions are given.

Stochastic analysis of lattice, nonlocal continuous beams in vibration

In this paper, we study the stochastic behavior of some lattice beams, called Hencky bar-chain model and their non-local continuous beam approximations. Hencky bar-chain model is a beam lattice composed of rigid segments, connected by some homogeneous rotational elastic links. In the present stochastic analysis, the stiffness of these elastic links is treated as a continuous random variable, with given probability density function. The fundamental eigenfrequency of the linear difference eigenvalue problem is also a random variable in this context. The reliability is defined as the probability that this fundamental frequency is less than an excitation frequency. This reliability function is exactly calculated for the lattice beam in conjunction with various boundary conditions. An exponential distribution is considered for the random stiffness of the elastic links. The stochastic lattice model is then compared to a stochastic nonlocal beam model, based on the continualization of the difference equation of the lattice model. The efficiency of the nonlocal beam model to approximate the lattice beam model is shown in presence of rotational elastic link randomness. We also compare such stochastic function with the one of a continuous local Euler-Bernoulli beam, with a special emphasis on scale effect in presence of randomness. Scale effect is captured both in deterministic and non-deterministic frameworks.

Analog time machine in a photonic system

Analogue physics has successfully tackled the problems of chromodynamics, event horizons, Big Bang and Universe expansion, and many others. Here, we suggest a photonic model system for a "time machine" based on the paraxial beam approximation. We demonstrate how the closed time-like curves and the well-known grandfather paradox can be studied experimentally in this system. We show how the Novikov's self-consistency principle is realized in quantum mechanics thanks to the Heisenberg's uncertainty principle.

Model of the Ultimate Stress State of the Coated Tool Cutter Material

The article proposes a model of the ultimate stress state of the material of the coated tool cutter. It is found that with an increase in the fracture toughness of a tool in connection with the material ductility the machining accuracy deteriorates due to arising elastic-plastic vibrations of the tool cutter. In case when no ultimate stress state is reached, that is, a tool operates in the elastic region, then an alternating stress distribution diagram is realized for the tool cutter at the beam approximation. Therefore, in addition to the frictional vibrations, arising from the interaction between the tool cutter and a workpiece, the elastic vibrations can arise, which affects the machining accuracy and the service life of the coated tool cutter. The use of coatings makes it possible not only to increase the wear resistance of cutting tools, but also to transform the stress distribution diagrams of the normal σN and tangential τγ contact stresses acting on the rake face of the cutting tool. In particular, it is possible to control the length of the total contact area between the chips and the tool rake face.