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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Metaplectic geometrical optics for modeling caustics in uniform and non-uniform media

As an approximate theory that is highly regarded for its computational efficiency, geometrical optics (GO) is widely used for modeling waves in various areas of physics. However, GO fails at caustics, which significantly limits its applicability. A new framework, called metaplectic geometrical optics (MGO), has recently been developed that allows caustics of certain types to be modeled accurately within the GO framework. Here, we extend MGO to the most general case. Further, to illustrate our new theory, we also apply it to several sample problems, including calculations of two-dimensional wavefields near fold and cusp caustics. In contrast with traditional GO solutions, the corresponding MGO solutions are finite everywhere and approximate the true wavefield well near these caustics.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Steepest-descent algorithm for simulating plasma-wave caustics via metaplectic geometrical optics

The design and optimization of radiofrequency-wave systems for fusion applications is often performed using ray-tracing codes, which rely on the geometrical-optics (GO) approximation. However, GO fails at wave cutoffs and caustics. To accurately model the wave behavior in these regions, more advanced and computationally expensive “full-wave” simulations are typically used, but this is not strictly necessary. A new generalized formulation called metaplectic geometrical optics (MGO) has been proposed that reinstates GO near caustics. The MGO framework yields an integral representation of the wavefield that must be evaluated numerically in general. We present an algorithm for computing these integrals using Gauss-Freud quadrature along the steepest-descent contours. Benchmarking is performed on the standard Airy problem, for which the exact solution is known analytically. Furthermore, the numerical MGO solution provided by the new algorithm agrees remarkably well with the exact solution and significantly improves on previously derived analytical approximations of the MGO integral.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Metaplectic geometrical optics for ray-based modeling of caustics: Theory and algorithms

The optimization of radio frequency-wave (RF) systems for fusion experiments is often performed using ray-tracing codes, which rely on the geometrical-optics (GO) approximation. However, GO fails at caustics such as cutoffs and focal points, erroneously predicting the wave intensity to be infinite. This is a critical shortcoming of GO, since the caustic wave intensity is often the quantity of interest, e.g., RF heating. Full-wave modeling can be used instead, but the computational cost limits the speed at which such optimizations can be performed. Here, we have developed a less expensive alternative called metaplectic geometrical optics (MGO). Instead of evolving waves in the usual x (coordinate) or k (spectral) representation, MGO uses a mixed X$\equiv$Ax+Bk representation. By continuously adjusting the matrix coefficients A and B along the rays, one can ensure that GO remains valid in the X coordinates without caustic singularities. The caustic-free result is then mapped back onto the original x space using metaplectic transforms. Here, we overview the MGO theory and review algorithms that will aid the development of an MGO-based ray-tracing code. We show how using orthosymplectic transformations leads to considerable simplifications compared to previously published MGO formulas. We also prove explicitly that MGO exactly reproduces standard GO when evaluated far from caustics (an important property that until now has only been inferred from numerical simulations), and we relate MGO to other semiclassical caustic-removal schemes published in the literature. Finally this discussion is then augmented by an explicit comparison of the computed spectrum for a wave bounded between two cutoffs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Geometrical optics without singularities: using the ray time as the coordinate space

Geometrical optics (GO) is widely used for reduced modelling of waves in plasmas, but it fails near reflection points, where it predicts a spurious singularity of the wave amplitude. We show how to avoid this singularity by adopting a different representation of the wave equation. Instead of the physical coordinate 𝑥 and the wavevector 𝑘, we use the ray time 𝜏 as the new canonical coordinate and the ray energy ℎ as the associated canonical momentum. To derive the envelope equation in the 𝜏-representation, we construct the Weyl symbol calculus on the (𝜏,ℎ) space and show that the corresponding Weyl symbols are related to their (𝑥,𝑘) counterparts by the Airy transform. This allows us to express the coefficients in the envelope equation through the known properties of the original dispersion operator. When necessary, solutions of this equation can be mapped to the 𝑥-space using a generalised metaplectic transform. However, the field per se might not even be needed in practice. Instead, knowing the corresponding Wigner function usually suffices for linear and quasilinear calculations. As a Weyl symbol itself, the Wigner function can be mapped analytically, using the aforementioned Airy transform. We show that the standard Airy patterns that form in regions where conventional GO fails are successfully reproduced within metaplectic GO (MGO) simply by remapping the field from the 𝜏-space to the 𝑥-space. An extension to mode-converting waves is also presented. This formulation, which we call generalised MGO, can be particularly useful, for example, for reduced modelling of the O–X conversion in inhomogeneous plasma near the critical density, an effect that is important for fusion applications and also occurs in the ionosphere. Overall, MGO can replace GO for any practical purposes, because it better handles cutoffs and is similar otherwise.

plasma waves↗
DOE OSTI2025

Combining geometric-optical and spectral invariants theories for modeling canopy fluorescence anisotropy

The spectral invariants theory ( p -theory) has received much attention in the field of quantitative remote sensing over the past few decades and has been adopted for modeling of canopy solar-induced chlorophyll fluorescence (SIF). However, the spectral invariant properties (SIP) in simple analytical formulae have not been applied for modeling canopy fluorescence anisotropy primarily because they are parameterized in terms of leaf total scattering, which precludes the differentiation between forward and backward leaf SIF emissions. In this study, we have developed the canopy-SIP SIF model by combining geometric-optical (GO) theory to account for asymmetric leaf SIF forward and backward emissions at the first-order scattering and by modeling multiple scattering based on the p-theory, thus avoiding the dependence on radiative transfer models. The applicability of the model simulations especially over 3D heterogeneous canopies was improved by incorporating canopy structure through multi-angular clumping index, and by modeling single scattering from the four components of the scene in view according to the GO approach. The results show good consistency with both the state-of-the-art SIF models and multi-angular field SIF observations over grass and chickpea canopies. Further, the coefficient of determination (R²) between the simulated SIF and field measurements was 0.75 (red) and 0.74 (far-red) for chickpea, and 0.65 (both red and far-red) for grass. The average relative error was approximately 3% for 1D homogeneous scenes when comparing the canopy-SIP SIF model simulations to the SCOPE model simulations, and around 4% for the 3D heterogeneous scene when comparing to the LESS model simulations. The results indicate that the proposed approach for separating asymmetric leaf SIF emissions is a robust way to keep a balance between satisfactory simulation accuracy and efficiency. Model simulations suggest that neglecting the leaf SIF asymmetry can lead to an underestimation of canopy red SIF by 6.3% to 42.6% for various leaf biochemical and canopy structural parameters. This study presents a simple but efficient analytical approach for canopy fluorescence modeling, with potential for large-scale canopy fluorescence simulations.

3D heterogeneous structure↗
DOE OSTI2021

Particle dynamics and geometric optics in Chern–Simons black holes

Highlights: • Black holes in Chern–Simons modified gravity have been studied. • The effects of the coupling constant of the Chern–Simons gravity on some physical quantities have been investigated. • The dependence of Hawking mass and Penrose process on the coupling constant is studied. • Rotation of the polarization vector is also studied for dependence on the Chern–Simons coupling constant. In this paper we study the effects of the coupling constant of the Chern–Simons modified gravity on some physical properties of black holes. The Hawking mass is one of the proposed definitions of quasilocal mass. We find that, for slowly rotating Chern–Simons black holes, the Hawking mass is independent of the coupling constant. Next, we show the dependence on the centre of mass energy, for two neutral colliding particles, of coupling constant and the rotation parameter. We also investigate energy extraction through Penrose process and find that the energy gain and efficiency of the Penrose process are independent of this coupling constant. Rotation of the polarization vector is also studied for dependence on the Chern–Simons coupling constant.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Geometric optics model of Thomson scattering enhanced by parametric coupling

We formulate a theory of Thomson scattering (TS) from inhomogeneous plasmas using a ray-tracing approach. The scattered radiation is described within the eikonal approximation, including convective gain arising from scattering instabilities driven by the TS probe laser. In the limit of a weak probe and vanishing gain, the theory recovers the standard TS cross section and scattered power due to volumetric particle noise. The ray-tracing formalism is implemented in a TS fitting framework, enabling accurate analysis of inhomogeneous plasmas whose background profiles can be provided by large-scale hydrodynamic simulations or experimental diagnostics. Here, several examples of synthetic TS spectra are presented, and further extensions of the theory are discussed.

Carleton, D. E. [University of Alberta, Edmonton, ↗
DOE OSTI2022

Chapter 3: Solar Optics and Principles

Solar irradiation originating from a finite-sized sun disc, as well as its various interactions with the atmosphere and reflective elements, results in the distribution of concentrated light at the receiver. The study of these interactions and the computation of the resulting flux distribution constitute the field of CSP optics. CSP optics is subdivided into two categories, namely, path-independent optics and geometric optics. This chapter deals primarily with the technology agnostic path-independent optics and attempts to convey some fundamental principles and to guide researchers. The path-independent optics introduced here includes sun shapes, the impact of surface microscopic and macroscopic structure, and atmospheric attenuation.

concentrating solar power↗
DOE OSTI2019

Quasioptical modeling of wave beams with and without mode conversion. I. Basic theory

This work opens a series of papers where we develop a general quasi-optical theory for mode-converting electromagnetic beams in plasma and implement it in a numerical algorithm. Here, the basic theory is introduced. We consider a general quasimonochromatic multicomponent wave in a weakly inhomogeneous linear medium with no sources. For any given dispersion operator that governs the wave field, we explicitly calculate the approximate operator that governs the wave envelope ψ to the second order in the geometrical-optics parameter. Then, we further simplify this envelope operator by assuming that the gradient of ψ transverse to the local group velocity is much larger than the corresponding parallel gradient. This leads to a parabolic differential equation for ψ (“quasioptical equation”) on the basis of the geometrical-optics polarization vectors. Scalar and mode-converting vector beams are described on the same footing. Here, we also explain how to apply this model to electromagnetic waves in general. In the next papers of this series, we report successful quasioptical modeling of radio frequency wave beams in magnetized plasma based on this theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Measuring the Burgers vector of dislocations with dark-field X-ray microscopy

The subsurface dynamics of dislocations are essential to many properties of bulk crystalline materials. However, it is challenging to characterize a bulk crystal by conventional transmission electron microscopy (TEM) due to the limited penetration depth of electrons. A novel X-ray imaging technique – dark-field X-ray microscopy (DFXM) – was developed to image hierarchical dislocation structures in bulk crystals. While today's DFXM can effectively map the line structures of dislocations, it is still challenging to quantify the Burgers vectors, the key characterization governing the dislocation behaviors. Here, we extend the 'invisibility criterion' formalism from the TEM theory to the geometrical-optics model of DFXM and demonstrate the consistency between DFXM and dark-field TEM using multi-diffraction-peak imaging for a single edge dislocation. Due to the practical difficulty of multi-peak DFXM experiments, we further study how the Burgers vector effect is encoded for a single-peak DFXM experiment. Using the geometrical-optics DFXM simulation, we explore the asymmetry of rocking tilt scans at different rolling tilts and develop a new method to characterize the Burgers vector. The conclusions of this study advance our understanding of the use of DFXM in characterizing individual dislocations, enabling the connection from bulk DFXM imaging to dislocation mechanics.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Spin Hall effect of radiofrequency waves in magnetized plasmas

In inhomogeneous media, electromagnetic-wave rays deviate from the trajectories predicted by the leading-order geometrical optics. This effect, called the spin Hall effect of light, is typically neglected in ray-tracing codes used for modeling waves in plasmas. Here, we demonstrate that the spin Hall effect can be significant for radiofrequency waves in toroidal magnetized plasmas whose parameters are in the ballpark of those used in fusion experiments. For example, an electron-cyclotron wave beam can deviate by as large as 10 wavelengths (~ 0.1 m) relative to the lowest-order ray trajectory in the poloidal direction. Finally, we calculate this displacement using gauge-invariant ray equations of extended geometrical optics, and we also compare our theoretical predictions with full-wave simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

A Theoretical Benchmark of the Geometric and Optical Properties for 3d Transition Metal Nanoclusters via Density Functional Theory

Understanding structure–property relationships in atomically precise metal nanoclusters is vital in finding selective and tunable catalysts. Here, in this study, density functional theory (DFT) was used to benchmark seven exchange correlation functionals at different basis sets for 17 atomically precise nanoclusters against experimentally determined geometries, band gaps, and optical gaps. The set contains both monometallic and bimetallic clusters that possess at least two types of 3d transition metals (specifically, Cu, Ni, Fe, or Co). The benchmark highlights that PBE0 is a good functional to use regardless of the basis set, and Minnesota functionals do well with respect to specific metals. Further, while long-range corrected functionals overestimate band and optical gaps, they model absorption features better than the other considered functionals. The study additionally looks at the photoinduced hydrogen evolution reaction (HER) and the CO 2 reduction mechanism on nanoclusters reported from the literature.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

batoid

Batoid is a c++ backed python optical raytracer. It uses geometric optics to characterize the optical performance of survey telescopes such as LSST, Subaru-HSC, Blanco-DECam, or Mayall-DESI.

Meyers, JoshuaE↗
DOE OSTI2023

A confocal laser-induced fluorescence diagnostic with an annular laser beam

Here, in this work, we report an annular beam confocal laser-induced fluorescence (LIF) configuration, which allows for high spatial resolution measurements of plasma properties in plasma setups and sources with limited optical access. The proposed LIF configuration utilizes the annular laser beam generated by a pair of diffractive axicons. The LIF signal is collected along the main optical axis within the ring region. It is shown experimentally that at a focal distance of 300 mm, a spatial resolution of ~5.3 mm can be achieved. Using geometric optics estimations, we showed that ~1 mm resolution at the same focal distance could potentially be achieved by modifying laser beam parameters. This approaches the localization accuracy of conventional LIF collection methods (with crossing laser beam injection and fluorescence collection optical paths). Measurements of the ion velocity distribution function in an argon plasma using both the confocal LIF with an annular laser beam and conventional LIF demonstrate a satisfactory agreement. The proposed LIF setup has potential applications for diagnostics in various plasma processing equipment and plasma sources, such as hollow cathodes, microplasmas, electric propulsion, etc.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

Ponderomotive recoil for electromagnetic waves

When waves damp or amplify on resonant particles in a plasma, nonresonant particles experience a recoil force that conserves the total momentum between particles and electromagnetic fields. This force is important to understand, as it can completely negate current drive and rotation drive mechanisms that are predicted on the basis of only resonant particles. Here, the existing electrostatic theory of this recoil force is extended to electromagnetic waves. While the result bears close similarity to historical fluid theories of laser–plasma interactions, it now incorporates both resonant and nonresonant particles, allowing momentum conservation to be self-consistently proven. Furthermore, the result is shown to be generally valid for kinetic plasmas, which is verified through single-particle hot-plasma simulations. Here, the new form of the force provides physical insight into the nature of the generalized Minkowski (plasmon) momentum of geometrical optics, which is shown to correspond to the momentum gained by the field and nonresonant particles as the wave is self-consistently ramped up from vanishing amplitude.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Simulated effect of edge plasma density parameters on lower hybrid wave scattering in EAST

The incorporation of lower hybrid (LH) wave spectrum broadening in the poloidal wavenumber (⁠k θ ) space at the last close field surface (LCFS) is reported to lead to better agreement of the modeled LH wave current profile with the experimental results [Baek et al., Nucl. Fusion 61, 106034 (2021)]. To further understand its underlying mechanism and find the possible influence factors, effects of wave scattering caused by drift-wave type density fluctuation on the probability distribution of the LH wave polar refractive index (⁠N θ ) at the LCFS are studied under density parameters in the scrape-off-layer. According to a scattering model [P. T. Bonoli and E. Ott, Phys Fluids 25(2), 359–375 (1982)], scattering probability and scattering angle distribution are two main factors that determine the degree of spectral broadening. Studies presented here show that the total scattering probability increases first and then decreases as the wave propagates toward a smaller normalized radius of poloidal magnetic flux (⁠ρ⁠). The degree of spectral broadening is found to depend on the density and density fluctuation together by changing the intensity and a proportion of the geometrical optics approximation term and the E×B drift term in the scattering model. Additionally, the fluctuation correlation length can significantly modify the probability distribution of N θ at the LCFS, which is found to significantly change the LH wave current profile.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Apparent superluminality of lensed gravitational waves

We consider gravitational wave (GW) sources with an associated electromagnetic (EM) counterpart, and analyze the time delay between both signals in the presence of lensing. If GWs have wavelengths comparable to the Schwarzschild radius of astrophysical lenses, they must be treated with wave optics, whereas EM waves are typically well within the approximation of geometric optics. Here, with concrete examples, we confirm that the GW signal never arrives before its EM counterpart, if both are emitted at the same time. However, during the inspiral of a binary, peaks of the GW waveform can arrive before their EM counterpart. We stress this is only an apparent superluminality since the GW waveform is both distorted and further delayed with respect to light. In any case, measuring the multi-messenger time delay and correctly interpreting it has important implications for unveiling the distribution of lenses, testing the nature of gravity, and probing the cosmological expansion history.

79 ASTRONOMY AND ASTROPHYSICS↗