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At least 1,099 records · Page 61
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Study of plasma equilibrium in toroidal fusion devices using mesh-free numerical calculation method

Plasma confinement using external magnetic field is one of the successful ways leading to the controlled nuclear fusion. Development and validation of the solution process for plasma equilibrium in the experimental toroidal fusion devices is the main subject of this work. Solution of the nonlinear 2D stationary problem as posed by the Grad-Shafranov equation gives quantitative information about plasma equilibrium inside the vacuum chamber of hot fusion devices. This study suggests solving plasma equilibrium equation which is essential in toroidal nuclear fusion devices, using a mesh-free method in a condition that the plasma boundary is unknown. The Grad-Shafranov equation has been solved numerically by the point interpolation collocation mesh-free method. Important features of this approach include truly mesh free, simple mathematical relationships between points and acceptable precision in comparison with the parametric results. The calculation process has been done by using the regular and irregular nodal distribution and support domains with different points. The relative error between numerical and analytical solution is discussed for several test examples such as small size Damavand tokamak, ITER-like equilibrium, NSTX-like equilibrium, and typical Spheromak.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

A numerical study of shock waves generated through laser ablation of explosives

Shock waves resulting from irradiation of energetic materials with a pulsed ultraviolet laser source have been shown to be an effective indicator for explosives detection. In this study, the features of shock wave propagation are explored theoretically. The initial stage of the shock motion is simulated as a one-dimensional process. As the nonlinear wave expands to form a blast wave, a system of conservation equations, simplified to the Euler equations, is employed to model wave propagation. The Euler equations are solved numerically by the 5th order weighted essentially non-oscillatory finite difference scheme with the time integration carried out using the 3rd order total variation diminishing Runge Kutta method. The numerical results for the shock wave evolution are compared with those obtained from experiments with a meltcast 2,6-dinitrotoluene sample. The calculations lay a theoretical foundation for a recently investigated technique for photoacoustically sensing explosives using a vibrometer.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2016

Numerical simulations of the ablative Rayleigh-Taylor instability in planar inertial-confinement-fusion targets using the FastRad3D code

The ablative Rayleigh-Taylor (RT) instability is a central issue in the performance of laser-accelerated inertial-confinement-fusion targets. Historically, the accurate numerical simulation of this instability has been a challenging task for many radiation hydrodynamics codes, particularly when it comes to capturing the ablatively stabilized region of the linear dispersion spectrum and modeling ab initio perturbations. Here, we present recent results from two-dimensional numerical simulations of the ablative RT instability in planar laser-ablated foils that were performed using the Eulerian code FastRad3D. Our study considers polystyrene, (cryogenic) deuterium-tritium, and beryllium target materials, quarter- and third-micron laser light, and low and high laser intensities. An initial single-mode surface perturbation is modeled in our simulations as a small modulation to the target mass density and the ablative RT growth-rate is calculated from the time history of areal-mass variations once the target reaches a steady-state acceleration. By performing a sequence of such simulations with different perturbation wavelengths, we generate a discrete dispersion spectrum for each of our examples and find that in all cases the linear RT growth-rate γ is well described by an expression of the form γ=α [kg/(1+ϵ kLm)]1/2−βkVa, where k is the perturbation wavenumber, g is the acceleration of the target, Lm is the minimum density scale-length, Va is the ablation velocity, and ϵ is either one or zero. The dimensionless coefficients α and β in the above formula depend on the particular target and laser parameters and are determined from two-dimensional simulation results through the use of a nonlinear curve-fitting procedure. While our findings are generally consistent with those of Betti et al. (Phys. Plasmas 5, 1446 (1998)), the ablative RT growth-rates predicted in this investigation are somewhat smaller than the values previously reported for the same target and laser parameters. It is speculated that differences in the equation-of-state and opacity models are largely responsible for the discrepancy. Resolution of this issue awaits the development of better experimental diagnostics capable of measuring small-wavelength (5–20 μm) perturbation growth due to the ablative RT instability in the linear regime.

Bates, J. W. (ORCID:0000000188087240)↗
DOE OSTI2018

Numerical simulation of runaway electrons: 3-D effects on synchrotron radiation and impurity-based runaway current dissipation

Numerical simulations of runaway electrons (REs) with a particular emphasis on orbit dependent effects in 3-D magnetic fields are presented. The simulations were performed using the recently developed Kinetic Orbit Runaway electron Code (KORC) that computes the full-orbit relativistic dynamics in prescribed electric and magnetic fields including radiation damping and collisions. The two main problems of interest are synchrotron radiation and impurity-based RE dissipation. Synchrotron radiation is studied in axisymmetric fields and in 3-D magnetic configurations exhibiting magnetic islands and stochasticity. For passing particles in axisymmetric fields, neglecting orbit effects might underestimate or overestimate the total radiation power depending on the direction of the radial shift of the drift orbits. For trapped particles, the spatial distribution of synchrotron radiation exhibits localized “hot” spots at the tips of the banana orbits. In general, the radiation power per particle for trapped particles is higher than the power emitted by passing particles. The spatial distribution of synchrotron radiation in stochastic magnetic fields, obtained using the MHD code NIMROD, is strongly influenced by the presence of magnetic islands. 3-D magnetic fields also introduce a toroidal dependence on the synchrotron spectra, and neglecting orbit effects underestimates the total radiation power. In the presence of magnetic islands, the radiation damping of trapped particles is larger than the radiation damping of passing particles. Results modeling synchrotron emission by RE in DIII-D quiescent plasmas are also presented. The computation uses EFIT reconstructed magnetic fields and RE energy distributions fitted to the experimental measurements. Qualitative agreement is observed between the numerical simulations and the experiments for simplified RE pitch angle distributions. However, it is noted that to achieve quantitative agreement, it is necessary to use pitch angle distributions that depart from simplified 2-D Fokker-Planck equilibria. Finally, using the guiding center orbit model (KORC-GC), a preliminary study of pellet mitigated discharges in DIII-D is presented. The dependence of RE energy decay and current dissipation on initial energy and ionization levels of neon impurities is studied. Furthermore, the computed decay rates are within the range of experimental observations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

High-order two-fluid plasma solver for direct numerical simulations of plasma flows with full transport phenomena

The two-fluid plasma equations for a single ion species, with full transport terms, including temperature and magnetic field dependent ion and electron viscous stresses and heat fluxes, frictional drag force, and ohmic heating terms, have been implemented in the CFDNS code and solved by using sixth-order non-dissipative compact finite differences for plasma flows in several different regimes. In order to be able to fully resolve all the dynamically relevant time and length scales, while maintaining computational feasibility, the assumptions of infinite speed of light and negligible electron inertia have been made. Non-dimensional analysis of the two-fluid plasma equations shows that, by varying the characteristic/background number density, length scale, temperature, and magnetic strength, the corresponding Hall, resistive, and ideal magnetohydrodynamic equations can be recovered as limiting cases. The accuracy and robustness of this two-fluid plasma solver in handling plasma flows in different regimes have been validated against four canonical problems: Alfven and whistler dispersion relations, electromagnetic plasma shock, and magnetic reconnection. For all test cases, by using physical dissipation and diffusion, with negligible numerical dissipation/diffusion, fully converged Direct Numerical Simulation (DNS)-like solutions are obtained when the ion Reynolds number based on the grid size is smaller than a threshold value which is about 2.3. For the magnetic reconnection problem, the results show that the magnetic flux saturation time and value converge when the ion and magnetic Reynolds numbers are large enough. Thus, the DNS-like results become relevant to practical problems with much larger Reynolds numbers.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Numerical tests of coherence-corrected surface hopping methods using a donor-bridge-acceptor model system

Surface hopping (SH) is a popular mixed quantum-classical method for modeling nonadiabatic excited state processes in molecules and condensed phase materials. The method is simple, efficient, and easy to implement, but the use of classical and independent nuclear trajectories introduces an overcoherence in the electronic density matrix which, if ignored, often leads to spurious results, such as overestimated reaction rates. Several methods have been proposed to incorporate decoherence into SH simulations, but a lack of insightful benchmarks makes their relative accuracy unknown. Herein, we run numerical simulations of common coherence-corrected SH methods including Truhlar’s decay-of-mixing (DOM) and Subotnik’s augmented SH using a Donor-bridge-Acceptor (DbA) model system. Numerical simulations are carried out in the superexchange regime, where charge transfer proceeds from a donor to an acceptor as a result of donor-bridge and bridge-acceptor couplings. The computed donor-to-acceptor reaction rates are compared to the reference Marcus theory results. For the DbA model under consideration, augmented SH recovers Marcus theory with quantitative accuracy, whereas DOM is only qualitatively accurate depending on whether predefined parameters in the decoherence rate are chosen wisely. We propose a general method for parameterizing the decoherence rate in the DOM method, which improves the method’s reaction rates and presumably increases its transferability. Altogether, the decoherence method of choice must be chosen with great care and this work provides insight using an exactly solvable model.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Numerical characterization of quasi-steady thermal load for thin crystal at cryogenic temperature with nondiffusive heat transfer

With dramatically improved brightness and repetition rate, the thermal load for crystal optics in x-ray free-electron laser applications has also significantly increased. To mitigate the thermal load, one effective method is cryogenic cooling. However, the emerging nondiffusive heat transfer phenomenon at cryogenic temperature may cause design failure if overlooked. To evaluate the optical performance of thin crystal optics under thermal load at cryogenic temperature, an integrated numerical tool is presented and applied to characterize the thermal load on thin crystals with nondiffusive phenomena accounted. Significant thermally induced distortion of the rocking curve is observed from numerical simulation, leading to potential seed power reduction in hard x-ray self-seeding application. Cryogenic cooling is confirmed necessary by simulation to handle the thermal load at high repetition rate operation.

42 ENGINEERING↗
DOE OSTI2022

Numerical simulation of a relativistic magnetron using a fluid electron model

An approach to numerically modeling relativistic magnetrons, in which the electrons are represented with a relativistic fluid, is described. A principal effect in the operation of a magnetron is space-charge-limited (SCL) emission of electrons from the cathode. We have developed an approximate SCL emission boundary condition for the fluid electron model. This boundary condition prescribes the flux of electrons as a function of the normal component of the electric field on the boundary. Here we show the results of a benchmarking activity that applies the fluid SCL boundary condition to the one-dimensional Child–Langmuir diode problem and a canonical two-dimensional diode problem. Simulation results for a two-dimensional A6 magnetron are then presented. Computed bunching of the electron cloud occurs and coincides with significant microwave power generation. Numerical convergence of the solution is considered. Sharp gradients in the solution quantities at the diocotron resonance, spanning an interval of three to four grid cells in the most well-resolved case, are present and likely affect convergence.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

1D model of tokamak scrape-off layer and divertor plasmas: Dimensionless parameters and the results of numerical simulations

Solutions of a 1D model of the scrape-off layer and a divertor plasma in a tokamak are analyzed on the basis of dimensionless parameters governing the physics of both plasma and neutral transport and atomic physics processes. Numerical simulations based on fluid plasma and Monte Carlo neutral modeling confirm earlier results obtained with simplified analytic considerations and numerical simulations performed with fluid neutral description and demonstrate bifurcation of plasma parameters. Further, these simulations also confirm that the major physical reasons for the rollover of the plasma flux to the target, which is the key feature of the phenomenon of divertor plasma detachment, are the impurity radiation loss and plasma recombination. It is suggested that simulations of the edge plasma based on dimensionless parameters provide a powerful tool for checking the consistency of the physics incorporated in existing complex 2D codes used for edge plasma modeling.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Numerical minimization of neoclassical poloidal viscosity for supersonic equilibria in tokamak geometry

Extensive experimental evidence has shown that the presence of poloidal flow in tokamaks can dramatically improve transport properties. However, theory indicates that poloidal flows are damped by poloidal viscosity, thus necessitating external drivers, such as neutral beam injection or radio frequency heating. In this work, ideal magnetohydrodynamic equilibria are calculated via the FORTRAN code FLOW [Guazzotto et al., Phys. Plasmas 11, 604 (2004)] and a postprocessor is used to estimate the neoclassical poloidal viscosity. The equilibrium inputs, which correspond to intuitive physical quantities, are then numerically optimized to reduce a viscosity figure of merit. We present supersonic equilibria in tokamak geometry with minimized neoclassical poloidal viscosities for various velocity free function inputs, plasma aspect ratios, and collisionality regimes. Benchmarks are made against an analytic theory as well as a classical expression of poloidal viscosity. Numerical confirmation of the analytic theory is obtained in the high aspect ratio and high collisionality limit. Good agreement is also seen near the plasma core and edge, with discrepancies arising in the intermediate region. Outside of these limits, rotation input function profiles are found that provide ∼order of magnitude improvements over the analytic theory, with additional progress being made toward predictions for tokamak-relevant equilibria.

Physics↗
DOE OSTI2024

Classifying photonic topology using the spectral localizer and numerical K -theory

Recently, the spectral localizer framework has emerged as an efficient approach for classifying topology in photonic systems featuring local nonlinearities and radiative environments. In nonlinear systems, this framework provides rigorous definitions for concepts such as topological solitons and topological dynamics, where a system’s occupation induces a local change in its topology due to nonlinearity. For systems embedded in radiative environments that do not possess a shared bulk spectral gap, this framework enables the identification of local topology and shows that local topological protection is preserved despite the lack of a common gap. However, as the spectral localizer framework is rooted in the mathematics of C*-algebras, and not vector bundles, understanding and using this framework requires developing intuition for a somewhat different set of underlying concepts than those that appear in traditional approaches for classifying material topology. In this tutorial, we introduce the spectral localizer framework from a ground-up perspective and provide physically motivated arguments for understanding its local topological markers and associated local measure of topological protection. In doing so, we provide numerous examples of the framework’s application to a variety of topological classes, including crystalline and higher-order topology. We then show how Maxwell’s equations can be reformulated to be compatible with the spectral localizer framework, including the possibility of radiative boundary conditions. To aid in this introduction, we also provide a physics-oriented introduction to multi-operator pseudospectral methods and numerical K-theory, two mathematical concepts that form the foundation for the spectral localizer framework. Finally, we provide some mathematically oriented comments on the C*-algebraic origins of this framework, including a discussion of real C*-algebras and graded C*-algebras that are necessary for incorporating physical symmetries. Looking forward, we hope that this tutorial will serve as an approachable starting point for learning the foundations of the spectral localizer framework.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Numerical simulation of the main characteristics of a high-pressure DF – CO{sub 2} laser for amplification of picosecond laser pulses

The gain characteristics of the medium of a pulsed DF – CO{sub 2} laser in the ten-micron region at the working gas pressures from 1 to 2.5 atm, which were experimentally determined in [4], are numerically simulated using a scheme that includes the main chemical and relaxation processes. It is shown that the chosen scheme of processes makes it possible (i) to numerically describe the experimental data on the temporal behaviour of gains; (ii) to explain the reason for early degradation of gains (at the degree of D{sub 2} transformation of about 20%); (iii) from comparison of experimental and calculated temporal gain profiles, to determine the degree of photodissociation of F{sub 2} molecules, which is an important parameter determining the operation of pulsed chemical DF – CO{sub 2} lasers; and (iv) to predict the gain characteristics of working mixtures depending on their composition and pressure and on the initiation parameters. The predicted gains in the mixtures of the optimal composition at a pressure of 2.5 atm, a degree of dissociation of F{sub 2} molecules per flash ∼1%, and a flash duration at half-width of ∼3 μs are ∼7 m{sup -1}. (lasers)

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

Numerical modelling of multimode fibre-optic communication lines

The results of numerical modelling of nonlinear propagation of an optical signal in multimode fibres with a small differential group delay are presented. It is found that the dependence of the error vector magnitude (EVM) on the differential group delay can be reduced by increasing the number of ADC samples per symbol in the numerical implementation of the differential group delay compensation algorithm in the receiver. The possibility of using multimode fibres with a small differential group delay for data transmission in modern digital communication systems is demonstrated. It is shown that with increasing number of modes the strong coupling regime provides a lower EVM level than the weak coupling one. (fibre-optic communication lines)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

Numerical Simulations of Flow-Induced Deflections in MITR LEU Fuel Plate Due to Channel Size Disparity

The hydromechanical stability of the fuel plates in parallel coolant channels of a Materials Testing Reactor (MTR) fuel element design is of great importance to the safety of research and test reactors. Previous analytical, experimental, and numerical efforts focused on parallel channels with the same or similar size; also, in the prior numerical simulations, the fuel plate was often assumed to be perfectly flat. This work presents the results of a fluid-structure interaction simulation performed to evaluate the flow-induced deflections of the fuel plates in the low-enriched uranium (LEU, <20 wt% 235 U) fuel element design for the conversion (from highly enriched uranium) of the Massachusetts Institute of Technology Reactor (MITR-II, also referred to as MITR). Various manufacturing and assembly tolerances of the MITR LEU elements are considered in the analysis, and the effects of channel size disparity, nonideal plate shape, and flow rate uncertainty are investigated. Results show that, for all cases analyzed, the deflection occurs toward the larger channel, and the change in any channel stripe remains small (less than 0.021 mm) compared to fabrication tolerances. In addition to simulation work, a hydraulic performance test of the MITR LEU fuel element is currently planned to support conversion to the use of LEU fuel.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

Numerical characterization of support recovery in sparse regression with correlated design

Sparse regression is employed in diverse scientific settings as a feature selection method. A pervasive aspect of scientific data is the presence of correlations between predictive features. These correlations hamper both feature selection and estimation and jeopardize conclusions drawn from estimated models. On the other hand, theoretical results on sparsity-inducing regularized regression have largely addressed conditions for selection consistency via asymptotics, and disregard the problem of model selection, whereby regularization parameters are chosen. In this numerical study, we address these issues through exhaustive characterization of the performance of several regression estimators, coupled with a range of model selection strategies. These estimators and selection criteria were examined across correlated regression problems with varying degrees of signal to noise, distributions of non-zero model coefficients, and model sparsity. Our results reveal a fundamental tradeoff between false positive and false negative control in all regression estimators and model selection criteria examined. Additionally, we numerically explore a transition point modulated by the signal-to-noise ratio and spectral properties of the design covariance matrix at which the selection accuracy of all considered algorithms degrades. Overall, we find that SCAD coupled with BIC or empirical Bayes model selection performs the best feature selection across the regression problems considered.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

NUMERICAL SIMULATION OF HOT ACCRETION FLOWS. I. A LARGE RADIAL DYNAMICAL RANGE AND THE DENSITY PROFILE OF ACCRETION FLOW

Numerical simulations of hot accretion flow, both hydrodynamical and magnetohydrodynamical, have shown that the mass accretion rate decreases with decreasing radius; consequently, the density profile of accretion flow becomes flatter than in the case of a constant accretion rate. This result has important theoretical and observational implications. However, because of technical difficulties, the radial dynamic range in almost all previous simulations usually spans at most two orders of magnitude. This small dynamical range, combined with the effects of boundary conditions, makes the simulation results suspect. In particular, the radial profiles of density and inflow rate may not be precise enough to be used to compare with observations. In this paper, we present a ''two-zone'' approach to expand the radial dynamical range from two to four orders of magnitude. We confirm previous results and find that from r{sub s} to 10{sup 4} r{sub s} the radial profiles of accretion rate and density can be well described by M-dot (r){proportional_to}r{sup s} and {rho}{proportional_to}r {sup -p}. The values of (s, p) are (0.48, 0.65) and (0.4, 0.85) for the viscous parameters {alpha} = 0.001 and {alpha} = 0.01, respectively. More precisely, the accretion rate is constant (i.e., s = 0) within {approx}10r{sub s}, but beyond 10r{sub s} we have s = 0.65 and 0.54 for {alpha} = 0.001 and 0.01, respectively. We find that the values of both s and p are similar in all numerical simulation works irrespective of whether a magnetic field is included or not and what kind of initial conditions are adopted. Such an apparently surprising ''common'' result can be explained by the most recent version of the adiabatic inflow-outflow model. The density profile we obtain is in good quantitative agreement with that obtained from the detailed observations and modeling of Sgr A* and NGC 3115. The origin and implications of such a profile will be investigated in a subsequent paper.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

A THREE-DIMENSIONAL NUMERICAL SOLUTION FOR THE SHAPE OF A ROTATIONALLY DISTORTED POLYTROPE OF INDEX UNITY

We present a new three-dimensional numerical method for calculating the non-spherical shape and internal structure of a model of a rapidly rotating gaseous body with a polytropic index of unity. The calculation is based on a finite-element method and accounts for the full effects of rotation. After validating the numerical approach against the asymptotic solution of Chandrasekhar that is valid only for a slowly rotating gaseous body, we apply it to models of Jupiter and a rapidly rotating, highly flattened star ({alpha} Eridani). In the case of Jupiter, the two-dimensional distributions of density and pressure are determined via a hybrid inverse approach by adjusting an a priori unknown coefficient in the equation of state until the model shape matches the observed shape of Jupiter. After obtaining the two-dimensional distribution of density, we then compute the zonal gravity coefficients and the total mass from the non-spherical model that takes full account of rotation-induced shape change. Our non-spherical model with a polytropic index of unity is able to produce the known mass of Jupiter with about 4% accuracy and the zonal gravitational coefficient J {sub 2} of Jupiter with better than 2% accuracy, a reasonable result considering that there is only one parameter in the model. For {alpha} Eridani, we calculate its rotationally distorted shape and internal structure based on the observationally deduced rotation rate and size of the star by using a similar hybrid inverse approach. Our model of the star closely approximates the observed flattening.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

RESONANT ABSORPTION OF TRANSVERSE OSCILLATIONS AND ASSOCIATED HEATING IN A SOLAR PROMINENCE. II. NUMERICAL ASPECTS

Transverse magnetohydrodynamic (MHD) waves are ubiquitous in the solar atmosphere and may be responsible for generating the Sun’s million-degree outer atmosphere. However, direct evidence of the dissipation process and heating from these waves remains elusive. Through advanced numerical simulations combined with appropriate forward modeling of a prominence flux tube, we provide the observational signatures of transverse MHD waves in prominence plasmas. We show that these signatures are characterized by a thread-like substructure, strong transverse dynamical coherence, an out-of-phase difference between plane-of-the-sky motions and line-of-sight velocities, and enhanced line broadening and heating around most of the flux tube. A complex combination between resonant absorption and Kelvin–Helmholtz instabilities (KHIs) takes place in which the KHI extracts the energy from the resonant layer and dissipates it through vortices and current sheets, which rapidly degenerate into turbulence. An inward enlargement of the boundary is produced in which the turbulent flows conserve the characteristic dynamics from the resonance, therefore guaranteeing detectability of the resonance imprints. We show that the features described in the accompanying paper through coordinated Hinode and Interface Region Imaging Spectrograph observations match the numerical results well.

79 ASTRONOMY AND ASTROPHYSICS↗