Search NASA⌕ Search

SEARCH · Search NASA

Results for “Harmonic numbers”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Generalized Mercier stability criterion for stellarators

The Mercier criterion is a well-known stability criterion for tokamaks. It is derived from a 2 × 2 matrix eigenvalue problem arising from the expansion of resonant solutions about a singular surface where m−nq=0, with m and n being the poloidal and toroidal mode numbers, respectively, and q being the safety factor. The stability criterion is that the eigenvalues must be real, otherwise, the solution oscillates, violating the Newcomb crossing criterion. Because of the non-axisymmetry of stellarators, different toroidal as well as poloidal harmonics couple to each other. It follows that each singular surface can have multiple resonant harmonics, with multiplicity M≥1. The corresponding matrix eigenvalue problem involves a 2M×2M matrix, resulting in M pairs of positive and negative eigenvalues. The generalized stability criterion is that all eigenvalues must be real. While the original Mercier criterion can be expressed in terms of quadratures of equilibrium quantities over the singular surface, which can be evaluated anywhere, the generalized Mercier criterion can only be evaluated on rational q surfaces with a given set of resonant harmonics.

Physics↗
DOE OSTI2022

Gravity of two photon decay and its quantum coherence

A linear analytical solution is derived for the gravitational shock wave produced by a particle of mass M that decays into a pair of null particles. The resulting space-time is shown to be unperturbed and isotropic, except for a discontinuous perturbation on a spherical null shell. Formulae are derived for the perturbation as a function of polar angle, as measured by an observer at the origin observing clocks on a sphere at distance R. The effect of the shock is interpreted physically as an instantaneous displacement in time and velocity when the shock passes the clocks. The time displacement is shown to be anisotropic, dominated by a quadrupole harmonic aligned with the particle-decay axis, with a magnitude δτ ~ GM/c 3 , independent of R. The velocity displacement is isotropic. The solution is used to derive the gravitational effect of a quantum state with a superposition of a large number of randomly oriented, statistically isotropic particle decays. This approach is shown to provide a well-controlled approximation to estimate the magnitude of gravitational fluctuations in systems composed of null point particles up to the Planck energy in a causal diamond of duration τ = 2R/c, as well as quantum-gravitational fluctuations of black holes and cosmological horizons. Coherent large-angle quantum distortions of macroscopic geometry from fluctuations up to the Planck scale are shown to grow linearly with the duration, with a variance $\langle$δτ 2 $\rangle$ ~ τtP much larger than that produced in models without causal quantum coherence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Ka-Band ARM Zenith Radar Corrections (KAZRCOR, KAZRCFRCOR) Value-Added Products

The Ka-Band Atmospheric Radiation Measurement (ARM) Zenith Radar Corrections (KAZRCOR) and KA-Band ARM Zenith Radar CF-Radial, Corrected (KAZRCFRCOR) value-added products (VAPs) perform several corrections to the ingested KAZR moments and also create a significant detection mask for each radar mode. The VAPs compute gaseous attenuation as a function of time and radial distance from the radar antenna, based on ambient meteorological observations, and correct observed reflectivities for that effect. Mean Doppler velocities are dealiased to correct velocities whose magnitudes exceed the radar’s Nyquist velocity. Input KAZR data fields are passed through to the KAZRCOR or KAZRCFRCOR output files, in their native time and range coordinates. Complementary corrected reflectivity and velocity fields are provided, along with a mask of significant detections and a number of data quality flags. This report covers the KAZRCOR VAP as applied to the original KAZR radars and the upgraded KAZR2 radars. Originally, prior to late 2019, there were two separate code bases for the different radar versions. Following the harmonization of KAZR and KAZR2 data formats in 2019, only a single code base is required. The new combined KAZR and KAZR2 code base is called the KAZRCFRCOR VAP. The ‘cfr portion of the VAP name refers to the Radial Climate and Forecasting data format standards that are used in these data sets. Throughout this report, references to ‘KAZRCOR’ should be taken to apply to the ‘KAZRCFRCOR’ VAP as well unless there is an explicit statement to the contrary.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

High harmonic generation in mixed XUV and NIR fields at a free-electron laser

Abstract We present the results of an experiment investigating the generation of high-order harmonics by a femtosecond near-infrared (NIR) laser pulse in the presence of an extreme ultraviolet (XUV) field provided by a free-electron laser (FEL), a process referred to as XUV-assisted high-order harmonic generation (HHG). Our experimental findings show that the XUV field can lead to a small enhancement in the harmonic yield when the XUV and NIR pulses overlap in time, while a strong decrease of the HHG yield and a red shift of the HHG spectrum is observed when the XUV precedes the NIR pulse. The latter observations are in qualitative agreement with model calculations that consider the effect of a decreased number of neutral emitters but are at odds with the predicted effect of the correspondingly increased ionization fraction on the phase matching. Our study demonstrates the technical feasibility of XUV-assisted HHG experiments at FELs, which may provide new avenues to investigate correlation-driven electron dynamics as well as novel ways to study and control propagation effects and phase matching in HHG.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

Degenerate parametric down-conversion facilitated by exciton-plasmon polariton states in a nonlinear plasmonic cavity

Abstract We study the effect of degenerate parametric down-conversion (DPDC) in an ensemble of two-level quantum emitters (QEs) coupled via near-field interactions to a single surface plasmon (SP) mode of a nonlinear plasmonic cavity. For this purpose, we develop a quantum driven-dissipative model capturing non-equilibrium dynamics of the system in which incoherently pumped QEs have transition frequency tuned near the second-harmonic response of the SPs. Considering the strong coupling regime, i.e. the SP-QE interaction rate exceeds system dissipation rates, we find a critical SP-QE coupling attributed to the phase transition between normal and lasing steady states. Examining fluctuations above the system’s steady states, we predict new elementary excitations, namely, the exciton-plasmon polaritons formed by the two-SP quanta and single-exciton states of QEs. The contribution of two-SP quanta results in the linear scaling of the SP-QE interaction rate with the number of QEs,  o , as opposed to the  o -scaling known for the Dicke and Tavis–Cummings models. We further examine how SP-QE interaction scaling affects the polariton dispersions and power spectra in the vicinity of the critical coupling. For this purpose, we compare the calculation results assuming a finite ensemble of QEs and the model thermodynamic limit. The calculated power spectra predict an interplay of coherent photon emission by QEs near the second-harmonic frequency and correlated photon-pair emission at the fundamental frequency by the SPs (i.e. the photonic DPDC effect).

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2020

Ka-Band ARM Zenith Radar Corrections (KAZRCOR, KAZRCFRCOR) Value-Added Products

The KAZRCOR Value -added Product (VAP) performs several corrections to the ingested KAZR moments and also creates a significant detection mask for each radar mode. The VAP computes gaseous attenuation as a function of time and radial distance from the radar antenna, based on ambient meteorological observations, and corrects observed reflectivities for that effect. KAZRCOR also dealiases mean Doppler velocities to correct velocities whose magnitudes exceed the radar’s Nyquist velocity. Input KAZR data fields are passed through into the KAZRCOR output files, in their native time and range coordinates. Complementary corrected reflectivity and velocity fields are provided, along with a mask of significant detections and a number of data quality flags. This report covers the KAZRCOR VAP as applied to the original KAZR radars and the upgraded KAZR2 radars. Currently there are two separate code bases for the different radar versions, but once KAZR and KAZR2 data formats are harmonized, only a single code base will be required.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Full-wave simulation of ion cyclotron range of frequency heating in a mirror device

We are adapting the all-orders spectral algorithm (AORSA) [Jaeger Phys. Plasmas 8 (2001)] from tokamak geometry to axisymmetric magnetic mirror geometry. We will use the modified AORSA to study ion cyclotron range of frequency (ICRF) heating in the Wisconsin HTS Axisymmetric Mirror (WHAM) magnetic mirror device [D. Endrizzi J. Plasma Phys. 5 (2023)]. ICRF power will be used in WHAM to accelerate high-energy neutral beam injected deuterium ions with ion cyclotron absorption at the second to fourth harmonics of deuterium. At these harmonics, for the spatial scales present in WHAM, full-wave simulations most accurately capture wave propagation, including transmission, reflection, and absorption at the cyclotron layer. The antenna is modeled as a single strap with m = 0 excitation, where m is the azimuthal mode number. We present some preliminary results for wave coupling and heating.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

RESONANT MATCHING SECTION FOR CEBAF ENERGY UPGRADE

Thomas Jefferson National Accelerator Facility (Jeffer- son Lab) currently studies the feasibility of upgrading its energy to 22 GeV. It considers addition of six more linac passes. The highest energy passes will share two new arcs designed using the Fixed-Field Alternating Gradient (FFA) technology. The FFA arcs are built using permanent combined-function magnets. They will be connected to the linacs through transition sections that will match the optics of all six passes to the linacs. With the high number of con- straints and the limited space available, we are investigating a parametric resonance technique to match the optics quasi- independently at each energy. A resonance is excited at each individual energy to selectively control its optics. The reso- nant dipole and quadrupole kick harmonics are imposed for all energies simultaneously using Panofsky corrector mag- nets placed throughout the FFA arcs. This paper presents the current progress on that transition section design

Deitrick, K.↗
DOE OSTI2025

Physics-Driven Construction of Compact Primitive Gaussian Density Fitting Basis Sets

We present a model-assisted density fitting (MADF) basis set generator, an algorithm for generating primitive atomic Gaussian density fitting (DF) basis sets (DFBSs) from a contracted Gaussian orbital basis set (OBS). The MADF algorithm produces DFBSs suitable for accurate robust DF approximation of 2-particle interactions in mean-field and correlated electronic structures. The algorithm is designed to (a) saturate the OBS product space by a large regularized set of primitive solid-harmonic Gaussian shells with nonuniform distribution of exponents, followed by (b) pruning of the shells according to their contributions to the 2- body energy of a correlated atomic ensemble. Building the DFBS generator model almost exclusively on mathematical and physical principles allows one to limit the number of parameters that control the density fitting error to three, with a single set of parameters sufficient for computations with all basis cardinal numbers, with and without correlation of core electrons, with and without scalar and spin-dependent relativistic effects, spanning almost all of the Periodic Table. Performance assessment included basis sets up to quadruple-ζ quality from several major basis set families, using molecules composed of main-group, d-block, and f-block elements. The resulting DF errors in Hartree−Fock and second-order MP2 energies (with relativistic all-electron treatments, when appropriate) were on the order of 20 and 10 μE h per electron, respectively.

Approximation↗
DOE OSTI2020

Mechanistic understanding of catalytic conversion of ethanol to 1-butene over 2D-pillared MFI zeolite

Ethanol is an important C2 platform molecule for producing value-added chemicals and distillate hydrocarbon fuels (e.g., jet and diesel). Among these, catalytic upgrading of ethanol to butenes can generate valuable commodity chemicals (e.g., 1-butene) and provide C4 olefin intermediates that can be further upgraded to jet/diesel fuels. 2D zeolites offer hierarchical mesoporous structures, leading to improved mass transport and reduced diffusion length, which can help to address the coking challenges faced by ethanol conversion to hydrocarbons over 3D zeolites. In this study, we investigate the acid-catalyzed conversion of ethanol to 1-butene over the Brønsted acid sites (BAS) in 2D-pillared MFI zeolite (2D-PMFI) using ab initio molecular dynamics (AIMD) simulations, in situ diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS), and calorimetric measurements. A detailed thermodynamic analysis, using quasi-harmonic approximation (QHA), on the Gibbs free energy pathway of ethanol conversion shows that the consideration of entropy is critical to accurately capture the detailed thermodynamic profiles. The formation of bulky ethoxy-ethene complex is found to be a potential rate-determining step (RDS), proceeding via stepwise mechanism. The reactivity of 2D-PMFI can be further tuned by manipulating RDS through a careful control of number of BAS and operating temperatures. The accuracy of computational model is confirmed through the comparison of calculated vibrational density of states (VDOS) against the experimental DRIFTS measurements. Overall, our study provides mechanistic insights into ethanol upgrading over the 2D-PMFI and shows the importance of evaluating entropic effects in such confined system.

Ethanol conversion, 2D-pillared zeolite, MFI, Anha↗
DOE OSTI2021

SHarD: A beam dynamics simulation code for dielectric laser accelerators based on spatial harmonic field expansion

In order to demonstrate acceleration of electrons to relativistic scales by an on chip dielectric laser accelerator (DLA), a ponderomotive focusing scheme capable of capturing and transporting electrons through nanometer-scale apertures over extended interaction lengths has been proposed. Here we present a Matlab-based numerical code (SHarD) utilizing a spatial harmonic expansion of the fields within the dielectric structure to simulate the evolution of the beam phase space distribution in this scheme. The code can be used to optimize key-parameters for the accelerator performance such as the final energy, transverse spot size evolution and total number of electrons accelerated through currently fabricated structures. Eventually, the simulation model will be applied to inform the phase mask profile to be added to a pulse front tilt drive laser pulse using a liquid crystal mask in the experimental setup being assembled at UCLA Pegasus Laboratory.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2026

Enabling probabilistic learning on manifolds through double diffusion maps

Here, we present a generative learning framework for probabilistic sampling that extends Probabilistic Learning on Manifolds (PLoM), which is designed to generate statistically consistent realizations of a random vector in a finite-dimensional Euclidean space, informed by a (representative) set of observations. In its original form, PLoM constructs a reduced-order probabilistic model by combining three main components: (a) kernel density estimation to approximate the underlying probability measure, (b) Diffusion Maps to characterize the manifold of the data, and (c) a reduced-order Itô Stochastic Differential Equation (ISDE) to sample from the learned distribution. However, its sampling dynamics are posed in the ambient space and the retained number of reduced coordinates is chosen by projection-reconstruction error. In practice, this often (i) requires more coordinates than the data’s intrinsic dimension to achieve stable sampling and (ii) lacks a smooth, basis-independent lifting back to the data domain; moreover, standard Diffusion Maps emphasize harmonic eigenfunctions and can miss non-harmonic latent structure. We address these limitations by decoupling geometry learning from sampling: a first Diffusion Maps pass identifies non-harmonic coordinates on which we formulate a full-order ISDE directly in the latent space, while Double Diffusion Maps captures multiscale geometric features and Geometric Harmonics (GH) learns a smooth lifting map to the ambient variables that is independent of the particular diffusion basis. This hybrid design preserves the system’s dynamical richness with a compact geometric representation and enables principled out-of-sample inference. The effectiveness and robustness of the proposed method are illustrated through two numerical studies: one based on data generated from two-dimensional Hermite polynomial functions and another based on high-fidelity simulations of a detonation wave in a reactive flow.

Double diffusion maps↗
DOE OSTI2024

Wavelength modulation laser-induced fluorescence for plasma characterization

Laser-Induced Fluorescence (LIF) spectroscopy is an essential tool for probing ion and atom velocity distribution functions (VDFs) in complex plasmas. VDFs carry information about the kinetic properties of species that is critical for plasma characterization. Accurate interpretation of these functions is challenging due to factors such as multicomponent distributions, broadening effects, and background emissions. Our research investigates the use of Wavelength Modulation (WM) LIF to enhance the sensitivity of VDF measurements. Unlike standard Amplitude Modulation (AM) methods, WM–LIF measures the derivative of the LIF signal. This approach makes variations in VDF shape more pronounced. VDF measurements with WM–LIF were investigated with both numerical modeling and experimental measurements. The developed model enables the generation of both WM and AM signals, facilitating comparative analysis of fitting outcomes. Experiments were conducted in a weakly collisional argon plasma with magnetized electrons and non-magnetized ions. Measurements of the argon ion VDFs employed a narrow-band tunable diode laser, which scanned the 4p 4 D 7/2 –3d 4 F 9/2 transition centered at 664.553 nm in vacuum. A lock-in amplifier detected the second harmonic WM signal, which was generated by modulating the laser wavelength with an externally controlled piezo-driven mirror of the diode laser. Finally, our findings indicate that the WM–LIF signal is more sensitive to fitting parameters, allowing for better identification of VDF parameters such as the number of distribution components, their temperatures, and velocities. In addition, WM–LIF can serve as an independent method to verify AM measurements and is particularly beneficial in environments with substantial light noise or background emissions, such as those involving thermionic cathodes and reflective surfaces.

47 OTHER INSTRUMENTATION↗
DOE OSTI2026

Comparison between explicit and implicit discretization strategies for a dissipative thermal environment

We investigate strategies for simulating open quantum systems coupled to dissipative baths by comparing explicit wave function-based discretization [via multi-layer multi-configuration time-dependent Hartree (ML-MCTDH)] and the implicit density matrix-based master equation method [via tree tensor network hierarchical equations of motion (TTN-HEOM)]. For dissipative baths characterized by exponentially decaying bath correlation functions, the implicit discretization approach of HEOM—rooted in bath correlation function decompositions—proves significantly more efficient than explicit discretization of the bath into discrete harmonic modes. Explicit methods, like ML-MCTDH, require extensive mode discretization to approximate continuum baths, leading to computational bottlenecks. Case studies for two-level systems and a Fenna–Matthews–Olson complex model highlight TTN-HEOM’s superiority in capturing dissipative dynamics with relaxations with a minimal number of auxiliary modes, while the explicit methods are as exact as the HEOM in pure dephasing regimes. This comparison is enabled by the TENSO package, which has both ML-MCTDH and TTN-HEOM implemented using the same computational structure and propagation strategy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Incident excitation effects on ZnO-based photoluminescence

Zinc oxide (ZnO) is an attractive semiconductor material owing to a wide band gap, large exciton binding energy, and strong luminescent properties. Two distinct spectral regions are present in the room temperature emission of this material: a narrow line in the UV/near-UV region that is excitonic in nature and a lower energy broad emission band centered in the green/yellow region. Commercially available ZnO particles containing excess Zn and oxygen vacancy defect sites (referred to as ZnO:Zn) were excited using three light sources to study different radiative recombination regimes of the as-received powders. First, a UV LED at a center wavelength of 365 nm provided low irradiance (0.02–0.08 W/cm 2 ) with varying pulse widths (continuous operation to 16 ns). Second, the third harmonic of a pulsed Nd:YAG laser provided high irradiances (∼10 4 –10 6 W/cm 2 ) at a fixed nominal pulse width of 5 ns. Finally, a continuous polychromatic synchrotron X-ray source was also used to excite the ZnO:Zn powders. During UV LED excitation, a low number of carriers are created in the material, leading to an anticipated linear relationship between luminescence and irradiance. This held true for defect luminescence; however, there was an observed enhancement of exciton emission relative to the UV LED intensity as the pulse width was decreased, independent of irradiance. During UV laser excitation, the number of carriers was significantly increased, raising the material into a bimolecular recombination regime, which produced exciton emission much stronger than visible band emission. Finally, spectra obtained during synchrotron X-ray excitation, whose continuous illumination and higher penetration depth yielded higher emission from defect sites relative to exciton emission. A redshift in the exciton emission was also observed as excitation pulse width and sample temperature were varied, and is discussed.

Westphal, Eric Robert [Sandia National Lab. (SNL-N↗
DOE OSTI2022

Analysis of the classical trajectory treatment of photon dynamics for polaritonic phenomena

Simulating photon dynamics in strong light–matter coupling situations via classical trajectories is proving to be powerful and practical. Here, in this work, we analyze the performance of the approach through the lens of the exact factorization approach. Since the exact factorization enables a rigorous definition of the potentials driving the photonic motion, it allows us to identify that the underestimation of photon number and intensities observed in earlier work is primarily due to an inadequate accounting of light–matter correlation in the classical Ehrenfest force rather than errors from treating the photons quasiclassically per se. The latter becomes problematic when the number of photons per mode begins to exceed a half.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Particle Creation from Entanglement Entropy

We investigate how entanglement entropy can drive particle creation, deriving explicit relations between entropy and the radiated particle spectrum, the total number of particles, and the total energy. Particle production is computed for scenarios that include accelerated motion, black hole evaporation, and beta decay, validating against known results while also extending them. We focus primarily on the low-entropy limit (analogous to nonrelativistic motion), but also examine cases of significant particle production arising from harmonic cycles. The results establish an explicit operational link between information flow and matter creation, providing a concrete demonstration of “it from bit”.

Good, Michael R. R. [Nazarbayev University, Astana↗
DOE OSTI2024

Full wave modeling of radio-frequency beams in tokamaks in the electron cyclotron frequency range

Simulation of full wave, without paraxial approximation, high-resolution solution of wave equations in frequency domain in the electron cyclotron resonance (ECR) frequency range for realistic Tokamak plasma parameters became possible by using recently formulated hybrid iterative algorithm [Svidzinski et al., Phys. Plasmas 25, 082509 (2018)] for numerically solving discretized wave equations. This approach combines time evolution and iterative relaxation techniques into iteration cycles. This algorithm is implemented in 2D code FullWave, solving wave equations in Tokamaks in cold and hot plasma models, and it has been tested in 3D full wave iterative RF beams simulation tool, which is presently being developed to model 3D ECRH RF beams in fusion devices using dynamic grid adaptation. The results of 2D full wave modeling, assuming specified toroidal mode number, of ECRH RF beams in DIII-D plasma, performed in the cold and hot plasma models for outboard and top launch scenarios using FullWave are presented. Nonlocal hot plasma response model, based on accurate numerical solution of linearized Vlasov equation, is used to model beam propagation and absorption in the 2nd electron cyclotron harmonic region. Demonstration of capability of the hybrid iterative algorithm to model ECRH RF beams in 3D is made by simulating a substantial part of realistic beam in DIII-D, launched from outboard side of the machine. All relevant physics of RF beam propagation, most of which is not captured in paraxial approximation, such as beam's divergence, interference between the X and O modes in the beam, X-O mode conversion, beam splitting into the X and O mode beams, transformation of beam's cross section, and absorption at the 2nd electron cyclotron harmonic, is captured in the simulations. A numerical technique to find an optimal beam polarization at the launcher to launch a nearly pure X or O mode beam in plasma is developed and tested.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗