Search NASA⌕ Search

SEARCH · Search NASA

Results for “Analytic linearization”

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 631 records · Page 35
All sourcesNASA NTRSDOE OSTI
DOE OSTI2011

A resistive instability of lower hybrid-like waves in regions with parallel currents

The resistive instabilities and dispersion of obliquely propagating waves near the lower hybrid (LH) frequency are studied in plasma carrying a current parallel to the magnetic field. Possible applications of these instabilities include magnetic reconnection regions where LH-like waves may accelerate and heat both ions and electrons. A resistive instability is found in one of the four LH-like wave modes for electron drift speeds several times greater than the electron thermal speed for representative parameters. Numerical fully electromagnetic kinetic calculations of the solutions to the linear dispersion equation are compared with more approximate analytic calculations and show good agreement. The analytic results indicate that ion magnetization effects play a critical role in the resistive instability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2012

Quantum ring solitons and nonlocal effects in plasma wake field excitations

A theoretical investigation of the quantum transverse beam motion for a cold relativistic charged particle beam travelling in a cold, collisionless, strongly magnetized plasma is carried out. This is done by taking into account both the individual quantum nature of the beam particles (single-particle uncertainty relations and spin) and the self consistent interaction generated by the plasma wake field excitation. By adopting a fluid model of a strongly magnetized plasma, the analysis is carried out in the overdense regime (dilute beams) and in the long beam limit. It is shown that the quantum description of the collective transverse beam dynamics is provided by a pair of coupled nonlinear governing equations. It comprises a Poisson-like equation for the plasma wake potential (driven by the beam density) and a 2D spinorial Schroedinger equation for the wave function, whose squared modulus is proportional to the beam density, that is obtained in the Hartree's mean field approximation, after disregarding the exchange interactions. The analysis of this pair of equations, which in general exhibits a strong nonlocal character, is carried out analytically as well as numerically in both the linear and the nonlinear regimes, showing the existence of the quantum beam vortices in the form of Laguerre-Gauss modes and ring envelope solitons, respectively. In particular, when the relation between the plasma wake field response and the beam probability density is strictly local, the pair of the governing equations is reduced to the 2D Gross-Pitaevskii equation that allows one to establish the conditions for the self focusing and collapse. These conditions include the quantum nature of the beam particles. Finally, when the relation between the plasma wake field response and the beam probability density is moderately nonlocal, the above pair of equations permits to follow the spatio-temporal evolution of a quantum ring envelope soliton. Such a structure exhibits small or violent breathing, but it remains very stable for long time.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Plasma turbulence in the scrape-off layer of tokamak devices

Plasma turbulence is explored in the scrape-off layer of tokamak devices using three-dimensional global two-fluid simulations. Two transport regimes are discussed: one in which the turbulent fluctuations saturate nonlinearly due to the Kelvin-Helmholtz instability, and another in which the fluctuations saturate due to a local flattening of the plasma gradients and associated removal of the linear instability drive. Focusing on the latter regime, analytical estimates of the cross-field transport and plasma profile gradients are obtained that display Bohm-scaling diffusion properties.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Solitons and shocks in dense astrophysical magnetoplasmas with relativistic degenerate electrons and positrons

The linear and nonlinear properties of the ion-acoustic (IA) waves are investigated in a relativistically degenerate magnetoplasma, whose constituents are the electrons, positrons, and ions. The electrons and positrons are assumed to obey the Fermi-Dirac statistics, whereas the cold ions are taken to be inertial and magnetized. In linear analysis, various limiting cases are discussed both analytically and numerically. However, for nonlinear studies, the well-known reductive perturbation technique is employed to derive the Zakharov-Kuznetsov and Zakharov-Kuznetsov Burgers equations in the presence of relativistically degenerate electrons and positrons. Furthermore, with the use of hyperbolic tangent method, the equations are simplified to admit the soliton and shock wave solutions. Numerically, it is shown that the amplitude, width, and phase speed associated with the localized IA solitons and shocks are significantly influenced by the various intrinsic plasma parameters relevant to our model. The present analysis can be useful for understanding the collective processes in dense astrophysical environments like neutron stars, where the electrons and positrons are expected to be relativistic and degenerate.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Structural transition of vortices to nonlinear regimes in a dusty plasma

The structural transition of a steady state dust flow from linear to nonlinear regimes is analyzed using a two-dimensional hydrodynamic model for the dust fluid confined in an axisymmetric toroidal system along with an unbounded streaming plasma. Numerical solutions of the employed hydrodynamical model not only confirms the analytical structure of the driven dust vortex flow in the linear limit as reported in the previous analysis but also shows how the dust vortices are strongly affected by the nonlinear convective transport of the flow at the higher Reynolds number (Re) regime. Effects of various system parameters including external driving field and the Reynolds number are investigated within the linear to nonlinear transition regime 0.001 ≤ Re < 50. In agreement with relevant experimental observations, the steady flow structure which is symmetric around the center in the linear regime begins to turn asymmetric in the nonlinear regime. The structure of the steady dust flow is found to be influenced mainly by the dissipation scales due to kinematic viscosity, ion drag, and neutral collision in the nonlinear regime, whereas, in the linear regime, it is mainly controlled by the external driving field and the confining boundaries.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Extensions of a classical mechanics “piston-model” for understanding the impact of asymmetry on ICF implosions: The cases of mode 2, mode 2/1 coupling, time-dependent asymmetry, and the relationship to coast-time

As long suspected, low mode asymmetry in inertially confined fusion (ICF) implosions has been implicated as a performance limiting factor [Casey et al., “Evidence of three-dimensional asymmetries seeded by high-density carbon-ablator nonuniformity in experiments at the national ignition facility,” Phys. Rev. Lett. 126, 025002 (2021)]. Recently a non-linear, but solvable, theory [Hurricane et al., “An analytic asymmetric-piston model for the impact of mode-1 shell asymmetry on ICF implosions,” Phys. Plasmas 27, 062704 (2020)] based upon the simple picture of a pair of asymmetric pistons has generated new insights and provided some practical formulas for estimating the degradation of an implosion due to mode-1 asymmetry and demonstrated a previously unrecognized connection between measured hot-spot drift velocity, nuclear down-scatter ratio asymmetry, and the concept of residual kinetic energy (RKE). Asymmetry of the implosion “shell,” as opposed to asymmetry of the hot-spot, was key to the classical mechanics model because the majority of the kinetic energy in an implosion is carried by the shell. Herein, the two-piston model is extended to a six-piston model in order to capture mode-2 asymmetry and coupling between mode-1 and mode-2. A key result of this new six-piston model is that the weighted harmonic mean of shell areal density is the fundamental quantity that determines the RKE and performance degradations for a three-dimensional implosion. Agreement is found between the scalings coming from the theory and ICF implosion data from the National Ignition Facility and to large ensembles of detailed simulations. The connection between the piston model's dependence upon the radius of peak velocity and coast-time is also highlighted in this paper. Finally, by extending the two-piston model to include time-dependent “swing,” it is shown in the Appendix that the shell asymmetry at the time of stagnation dominates the solution for RKE.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Laser polarization effects on crossed-beam energy transfer in inertial confinement fusion

Crossed-beam energy transfer (CBET) is a consequential process in inertial confinement fusion (ICF) experiments. CBET depends on the polarization state of the interacting lasers and can, in turn, alter their polarization. Here, we derive analytical expressions for two-beam CBET with linearly and circularly polarized light, and present simulations of CBET that include polarization effects for ICF conditions relevant to experiments on the National Ignition Facility. The results show that CBET mixes the polarization of the beams as they propagate through the target and leads to azimuthal power imbalances between beams within a given cone (i.e., at the same polar angle in the target chamber). These variations are shown to correlate with variations in measured backscatter between beams of a same quadruplet. Using circularly polarized, instead of linearly polarized, light produces similar overall levels of CBET within a cone of beams but tends to reduce the azimuthal variations. This is expected to slightly improve irradiation symmetry and reduce the risk of backscatter from stimulated Brillouin scattering. Circular polarization may therefore be beneficial for the next generation of laser fusion drivers.

Physics - Plasma physics↗
DOE OSTI2026

Machine Learning–Augmented Laser-Induced Breakdown Spectroscopy for Spectral Discrimination of Iron Oxalates

Enhanced characterization and phase identification of post-PUREX Pu Oxalates (PuOXA) are pivotal for nonproliferation and pre-detonation nuclear forensics. Despite significant advances in the characterization of PuO 2 samples, little is known about the impact of both the chemical structure and oxidation states of PuOXA (i.e., Pu(III) and Pu(IV)) have on optical emission signatures. Here, we demonstrate the analytical capabilities of laser-induced breakdown spectroscopy (LIBS) applied to Fe(II) and Fe(III) oxalate samples as surrogates for PuOXA, highlighting the discriminating features in the LIBS emission spectra arising from differences in the oxidation states within mixed FeOXA samples. We report the enhancement of spectral feature selection using Principal Component Analysis (PCA), which enables the analytical superiority of machine learning algorithms such as Linear Discriminant Analysis (LDA), Quadratic Discriminant Analysis (QDA), Partial Least Squares Regression (PLSR), Support Vector Regression (SVR), and Random Forest Regression (RFR) over conventional univariate techniques for phase discrimination and chemometric analysis. Cluster analysis revealed how both matrix effects and laser ablation influence cluster separability by introducing spectral artifacts that misdirect the maximization of variance. PCA-selected emission lines were used in the regression models, demonstrating that both univariate and multivariate linear regression models (i.e., PLSR and SVR) can achieve acceptable performance, with machine learning models outperforming conventional calibration regressions. Furthermore, the application of non-linearly activated PCA-selected emission lines illustrates how simplifying the data while retaining captured variance enables the use of less complex and more computationally efficient models. Furthermore, this is particularly evident in the underperformance of RFR, which suffers from increased computational costs and overfitting owing to its high complexity.

Oxalates↗
DOE OSTI2014

Perpendicular diffusion of energetic particles in noisy reduced magnetohydrodynamic turbulence

A model for noisy reduced magnetohydrodynamic turbulence was recently proposed. This model was already used to study the random walk of magnetic field lines. In the current article we use the same model to investigate the diffusion of energetic particles across the mean magnetic field. To compute the perpendicular diffusion coefficient, two analytical theories are used, namely, the Non-Linear Guiding Center theory and the Unified Non-Linear Transport (UNLT) theory. It is shown that the two theories provide different results for the perpendicular diffusion coefficient. We also perform test-particle simulations for the aforementioned turbulence model. We show that only the UNLT theory describes perpendicular transport accurately, confirming that this is a powerful tool in diffusion theory.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

SELF-GRAVITATIONAL FORCE CALCULATION OF SECOND-ORDER ACCURACY FOR INFINITESIMALLY THIN GASEOUS DISKS IN POLAR COORDINATES

Investigating the evolution of disk galaxies and the dynamics of proto-stellar disks can involve the use of both a hydrodynamical and a Poisson solver. These systems are usually approximated as infinitesimally thin disks using two-dimensional Cartesian or polar coordinates. In Cartesian coordinates, the calculations of the hydrodynamics and self-gravitational forces are relatively straightforward for attaining second-order accuracy. However, in polar coordinates, a second-order calculation of self-gravitational forces is required for matching the second-order accuracy of hydrodynamical schemes. We present a direct algorithm for calculating self-gravitational forces with second-order accuracy without artificial boundary conditions. The Poisson integral in polar coordinates is expressed in a convolution form and the corresponding numerical complexity is nearly linear using a fast Fourier transform. Examples with analytic solutions are used to verify that the truncated error of this algorithm is of second order. The kernel integral around the singularity is applied to modify the particle method. The use of a softening length is avoided and the accuracy of the particle method is significantly improved.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Alpha Air Sample Counting Efficiency Versus Dust Loading: Evaluation of a Large Data Set

Dust loading on air sample filters is known to cause a loss of efficiency for direct counting of alpha activity on the filters, but the amount of dust loading and the correction factor needed to account for attenuated alpha particles is difficult to assess. In this paper, correction factors are developed by statistical analysis of a large database of air sample results for a uranium and plutonium processing facility at the Savannah River Site. As is typically the case, dust-loading data is not directly available, but sample volume is found to be a reasonable proxy measure; the amount of dust loading is inferred by a combination of the derived correction factors and a Monte Carlo model. The technique compares the distribution of activity ratios [beta/(beta + alpha)] by volume and applies a range of correction factors on the raw alpha count rate. The best-fit results with this method are compared with MCNP modeling of activity uniformly deposited in the dust and analytical laboratory results of digested filters. Finally, a linear fit is proposed to evenly-deposited alpha activity collected on filters with dust loading over a range of about 2 mg cm -2 to 1,000 mg cm -2 .

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2011

Nonlinearly PT-symmetric systems: Spontaneous symmetry breaking and transmission resonances

We consider a class of PT-symmetric systems which include mutually matched nonlinear loss and gain (in other words, a class of PT-invariant Hamiltonians in which both the harmonic and anharmonic parts are non-Hermitian). For a basic system in the form of a dimer, symmetric and asymmetric eigenstates, including multistable ones, are found analytically. We demonstrate that, if coupled to a linear chain, such a nonlinear PT-symmetric dimer generates previously unexplored types of nonlinear Fano resonances, with completely suppressed or greatly amplified transmission, as well as a regime similar to the electromagnetically induced transparency. The implementation of the systems is possible in various media admitting controllable linear and nonlinear amplification of waves.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2010

w-cosmological singularities

In this paper we characterize barotropic index singularities of homogeneous isotropic cosmological models [M. P. Dabrowski and T. Denkiewicz, Phys. Rev. D 79, 063521 (2009).]. They are shown to appear in cosmologies for which the scale factor is analytical with a Taylor series in which the linear and quadratic terms are absent. Though the barotropic index of the perfect fluid is singular, the singularities are weak, as it happens for other models for which the density and the pressure are regular.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2010

Fluid modes of a spherically confined Yukawa plasma

The normal modes of a three-dimensional Yukawa plasma in an isotropic harmonic confinement are investigated by solving the linearized cold fluid equations. The eigenmodes are found analytically and expressed in terms of hypergeometric functions. It is found that the mode frequencies solely depend on the dimensionless plasma parameter {xi}={kappa}R, where R is the plasma radius and {kappa} is the inverse screening length. The eigenfrequencies increase monotonically with {xi} and saturate in the limit {xi}{yields}{infinity}. Compared with the results in the Coulomb limit [D. H. E. Dubin, Phys. Rev. Lett. 66, 2076 (1991)], we find an additional class of modes characterized by the number n which determines the number of radial nodes in the perturbed potential. These modes originate from the degenerate bulk modes of the Coulomb system. Analytical formulas for the eigenfrequencies are derived for limiting cases.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Taylor-Expansion-Based Robust Power Flow in Unbalanced Distribution Systems: A Hybrid Data-Aided Method

Traditional power flow methods often adopt certain assumptions designed for passive balanced distribution systems, thus lacking practicality for unbalanced operation. moreover, their computation accuracy and efficiency are heavily subject to unknown errors and bad data in measurements or prediction data of distributed energy resources (ders). to address these issues, this paper proposes a hybrid data-aided robust power flow algorithm in unbalanced distribution systems, which combines taylor series expansion knowledge with a data-driven regression technique. the proposed method initiates a linearization power flow model to derive an explicitly analytical solution by modified taylor expansion. to mitigate the approximation loss that surges due to the der integration and bad data, we further develop a data-aided robust support vector regression approach to estimate the errors efficiently. comparative analysis in the 13-bus and 123-bus ieee unbalanced feeders shows that the proposed hybrid algorithm achieves superior computational efficiency, with guaranteed accuracy and robustness against outliers.

data-driven↗
DOE OSTI2019

Investigation on lateral resolution of surface slope profilers

Here, we investigate and compare the spatial (lateral) resolution, or more generally, the optical/instrumental transfer function (OTF/ITF) of surface slope measuring profilometers of two different types that are commonly used for high accuracy characterization of x-ray optics at the long-spatial-wavelength range. These are an autocollimator based profiler, Optical Surface Measuring System (OSMS), and a long trace profiler, LTP-II, both available at the Advanced Light Source (ALS) X-Ray Optics Lab (XROL). In the OSMS, an ELCOMAT-3000 electronic auto-collimator, vertically mounted to the translation carriage and equipped with an aperture of 2.5 mm diameter, is scanned along the surface under test. The LTP-II OTF has been measured for two different configurations, a classical two-beam pencil-beam-interferometry and a single-Gaussian-beam deflectometry. For the ITF calibration, we apply a recently developed method based on test surfaces with one-dimensional (1D) linear chirped height profiles of constant slope amplitude. Analytical expressions for the OTFs, empirically deduced based on the experimental results, are presented. We also discuss the application of the results of the ITF measurements and modeling to improve the surface slope metrology with state-of-the-art x-ray mirrors.

42 ENGINEERING↗
DOE OSTI2016

Attenuation of Bragg backscattering of electromagnetic waves from density fluctuations near the region of polarization degeneracy in magnetoactive plasma

Specific features of Bragg backscattering under conditions of strong polarization degeneracy near the cutoff surface in an anisotropic medium are studied analytically and numerically. It is shown that the linear interaction of normal waves can substantially affect wave scattering by suppressing the amplification of Bragg backscattering near the cutoff region in the case of weak coupling between normal waves.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Reactive Flows in Porous Media: Challenges in Theoretical and Numerical Methods

We review theoretical and computational research, primarily from the past 10 years, addressing the flow of reactive fluids in porous media. The focus is on systems where chemical reactions at the solid–fluid interface cause dissolution of the surrounding porous matrix, creating nonlinear feedback mechanisms that can often lead to greatly enhanced permeability. Here, we discuss insights into the evolution of geological forms that can be inferred from these feedback mechanisms, as well as some geotechnical applications such as enhanced oil recovery, hydraulic fracturing, and carbon sequestration. Until recently, most practical applications of reactive transport have been based on Darcy-scale modeling, where averaged equations for the flow and reactant transport are solved. We summarize the successes and limitations of volume averaging, which leads to Darcy-scale equations, as an introduction to pore-scale modeling. Pore-scale modeling is computationally intensive but offers new insights as well as tests of averaging theories and pore-network models. We include recent research devoted to validation of pore-scale simulations, particularly the use of visual observations from microfluidic experiments.

wormhole formation↗