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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.

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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

Image-based spectral distortion correction for photon-counting x-ray detectors

Purpose: To investigate the feasibility of using an image-based method to correct for distortions induced by various artifacts in the x-ray spectrum recorded with photon-counting detectors for their application in breast computed tomography (CT). Methods: The polyenergetic incident spectrum was simulated with the tungsten anode spectral model using the interpolating polynomials (TASMIP) code and carefully calibrated to match the x-ray tube in this study. Experiments were performed on a Cadmium-Zinc-Telluride (CZT) photon-counting detector with five energy thresholds. Energy bins were adjusted to evenly distribute the recorded counts above the noise floor. BR12 phantoms of various thicknesses were used for calibration. A nonlinear function was selected to fit the count correlation between the simulated and the measured spectra in the calibration process. To evaluate the proposed spectral distortion correction method, an empirical fitting derived from the calibration process was applied on the raw images recorded for polymethyl methacrylate (PMMA) phantoms of 8.7, 48.8, and 100.0 mm. Both the corrected counts and the effective attenuation coefficient were compared to the simulated values for each of the five energy bins. The feasibility of applying the proposed method to quantitative material decomposition was tested using a dual-energy imaging technique with a three-material phantom that consisted of water, lipid, and protein. The performance of the spectral distortion correction method was quantified using the relative root-mean-square (RMS) error with respect to the expected values from simulations or areal analysis of the decomposition phantom. Results: The implementation of the proposed method reduced the relative RMS error of the output counts in the five energy bins with respect to the simulated incident counts from 23.0%, 33.0%, and 54.0% to 1.2%, 1.8%, and 7.7% for 8.7, 48.8, and 100.0 mm PMMA phantoms, respectively. The accuracy of the effective attenuation coefficient of PMMA estimate was also improved with the proposed spectral distortion correction. Finally, the relative RMS error of water, lipid, and protein decompositions in dual-energy imaging was significantly reduced from 53.4% to 6.8% after correction was applied. Conclusions: The study demonstrated that dramatic distortions in the recorded raw image yielded from a photon-counting detector could be expected, which presents great challenges for applying the quantitative material decomposition method in spectral CT. The proposed semi-empirical correction method can effectively reduce these errors caused by various artifacts, including pulse pileup and charge sharing effects. Furthermore, rather than detector-specific simulation packages, the method requires a relatively simple calibration process and knowledge about the incident spectrum. Therefore, it may be used as a generalized procedure for the spectral distortion correction of different photon-counting detectors in clinical breast CT systems.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS1989

A hybrid perturbation-Galerkin method for differential equations containing a parameter

A two-step hybrid perturbation-Galerkin method to solve a variety of differential equations which involve a parameter is presented and discussed. The method consists of: (1) the use of a perturbation method to determine the asymptotic expansion of the solution about one or more values of the parameter; and (2) the use of some of the perturbation coefficient functions as trial functions in the classical Bubnov-Galerkin method. This hybrid method has the potential of overcoming some of the drawbacks of the perturbation method and the Bubnov-Galerkin method when they are applied by themselves, while combining some of the good features of both. The proposed method is illustrated first with a simple linear two-point boundary value problem and is then applied to a nonlinear two-point boundary value problem in lubrication theory. The results obtained from the hybrid method are compared with approximate solutions obtained by purely numerical methods. Some general features of the method, as well as some special tips for its implementation, are discussed. A survey of some current research application areas is presented and its degree of applicability to broader problem areas is discussed.

Geer, James F.↗
DOE OSTI2017

Numerical approximations for the molecular beam epitaxial growth model based on the invariant energy quadratization method

The Molecular Beam Epitaxial model is derived from the variation of a free energy, that consists of either a fourth order Ginzburg–Landau double well potential or a nonlinear logarithmic potential in terms of the gradient of a height function. One challenge in solving the MBE model numerically is how to develop proper temporal discretization for the nonlinear terms in order to preserve energy stability at the time-discrete level. In this paper, we resolve this issue by developing a first and second order time-stepping scheme based on the “Invariant Energy Quadratization” (IEQ) method. The novelty is that all nonlinear terms are treated semi-explicitly, and the resulted semi-discrete equations form a linear system at each time step. Moreover, the linear operator is symmetric positive definite and thus can be solved efficiently. We then prove that all proposed schemes are unconditionally energy stable. The semi-discrete schemes are further discretized in space using finite difference methods and implemented on GPUs for high-performance computing. Various 2D and 3D numerical examples are presented to demonstrate stability and accuracy of the proposed schemes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2013

Assessment and characterization of the total geometric uncertainty in Gamma Knife radiosurgery using polymer gels

Purpose: This work proposes and implements an experimental methodology, based on polymer gels, for assessing the total geometric uncertainty and characterizing its contributors in Gamma Knife (GK) radiosurgery. Methods: A treatment plan consisting of 26, 4-mm GK single shot dose distributions, covering an extended region of the Leksell stereotactic space, was prepared and delivered to a polymer gel filled polymethyl methacrylate (PMMA) head phantom (16 cm diameter) used to accurately reproduce every link in the GK treatment chain. The center of each shot served as a 'control point' in the assessment of the GK total geometric uncertainty, which depends on (a) the spatial dose delivery uncertainty of the PERFEXION GK unit used in this work, (b) the spatial distortions inherent in MR images commonly used for target delineation, and (c) the geometric uncertainty contributor associated with the image registration procedure performed by the Leksell GammaPlan (LGP) treatment planning system (TPS), in the case that registration is directly based on the apparent fiducial locations depicted in each MR image by the N-shaped rods on the Leksell localization box. The irradiated phantom was MR imaged at 1.5 T employing a T2-weighted pulse sequence. Four image series were acquired by alternating the frequency encoding axis and reversing the read gradient polarity, thus allowing the characterization of the MR-related spatial distortions. Results: MR spatial distortions stemming from main field (B{sub 0}) inhomogeneity as well as from susceptibility and chemical shift phenomena (also known as sequence dependent distortions) were found to be of the order of 0.5 mm, while those owing to gradient nonlinearities (also known as sequence independent distortions) were found to increase with distance from the MR scanner isocenter extending up to 0.47 mm at an Euclidean distance of 69.6 mm. Regarding the LGP image registration procedure, the corresponding average contribution to the total geometric uncertainty ranged from 0.34 to 0.80 mm. The average total geometric uncertainty, which also includes the GK spatial dose delivery uncertainty, was found equal to (0.88 {+-} 0.16), (0.88 {+-} 0.26), (1.02 {+-} 0.09), and (1.15 {+-} 0.24) mm for the MR image series acquired with the read gradient polarity (direction) set toward right, left, posterior, and anterior, respectively. Conclusions: The implemented methodology seems capable of assessing the total geometric uncertainty, as well as of characterizing its contributors, ascribed to the entire GK treatment delivery (i.e., from MR imaging to GK dose delivery) for an extended region of the Leksell stereotactic space. Results obtained indicate that the selection of both the frequency encoding axis and the read gradient polarity during MRI acquisition may affect the magnitude as well as the spatial components of the total geometric uncertainty.

60 APPLIED LIFE SCIENCES↗
NASA NTRS2012

Design of Low Complexity Model Reference Adaptive Controllers

Flight research experiments have demonstrated that adaptive flight controls can be an effective technology for improving aircraft safety in the event of failures or damage. However, the nonlinear, timevarying nature of adaptive algorithms continues to challenge traditional methods for the verification and validation testing of safety-critical flight control systems. Increasingly complex adaptive control theories and designs are emerging, but only make testing challenges more difficult. A potential first step toward the acceptance of adaptive flight controllers by aircraft manufacturers, operators, and certification authorities is a very simple design that operates as an augmentation to a non-adaptive baseline controller. Three such controllers were developed as part of a National Aeronautics and Space Administration flight research experiment to determine the appropriate level of complexity required to restore acceptable handling qualities to an aircraft that has suffered failures or damage. The controllers consist of the same basic design, but incorporate incrementally-increasing levels of complexity. Derivations of the controllers and their adaptive parameter update laws are presented along with details of the controllers implementations.

Hanson, Curt↗
DOE OSTI2025

Perturbative model for the saturation of energetic-particle-driven modes limited by self-generated zonal modes

We present a simplified energy-conserving approach to incorporate wave–wave nonlinear effects within the framework commonly used to describe wave–particle nonlinearities. In particular, the effects of zonal mode (ZM) generation on the determination of the saturation amplitude of energetic particle (EP)-driven Alfvénic instabilities is studied. The model assumes that the zonal perturbations grow at a rate twice that of the original (pump) wave, consistent with a beat-driven (or force-driven) generation mechanism. The evolution and saturation of the mode amplitude are investigated both analytically and numerically within our reduced model assumptions, in both the collisionless and scattering-dominated regimes. These studies underscore the crucial role of sources and sinks in capturing the impact and the role of beat-driven zonal perturbations on mode evolution. In the realistic case of saturation set by sources and sinks, we discuss the role of a finite amplitude ZM in reducing microturbulent particle scattering, thus limiting the energy source for the resonant mode. We then discuss comparisons between the model’s predictions and simulation results. The model reproduces key features observed in gyrokinetic simulations as the reduction in saturated mode amplitude and the onset of wave–wave nonlinear effects as functions of mode growth rate and amplitude. Thanks to its simplicity, it can be readily implemented into codes based on reduced models, thereby improving their predictive capability for strongly driven instabilities.

Alfvén eigenmodes↗
DOE OSTI2013

Investigation of Response Amplitude Operators for Floating Offshore Wind Turbines: Preprint

This paper examines the consistency between response amplitude operators (RAOs) computed from WAMIT, a linear frequency-domain tool, to RAOs derived from time-domain computations based on white-noise wave excitation using FAST, a nonlinear aero-hydro-servo-elastic tool. The RAO comparison is first made for a rigid floating wind turbine without wind excitation. The investigation is further extended to examine how these RAOs change for a flexible and operational wind turbine. The RAOs are computed for below-rated, rated, and above-rated wind conditions. The method is applied to a floating wind system composed of the OC3-Hywind spar buoy and NREL 5-MW wind turbine. The responses are compared between FAST and WAMIT to verify the FAST model and to understand the influence of structural flexibility, aerodynamic damping, control actions, and waves on the system responses. The results show that based on the RAO computation procedure implemented, the WAMIT- and FAST-computed RAOs are similar (as expected) for a rigid turbine subjected to waves only. However, WAMIT is unable to model the excitation from a flexible turbine. Further, the presence of aerodynamic damping decreased the platform surge and pitch responses, as computed by both WAMIT and FAST when wind was included. Additionally, the influence of gyroscopic excitation increased the yaw response, which was captured by both WAMIT and FAST.

17 WIND ENERGY↗
DOE OSTI2014

Nonlinear force-free extrapolation of the coronal magnetic field based on the magnetohydrodynamic relaxation method

We develop a nonlinear force-free field (NLFFF) extrapolation code based on the magnetohydrodynamic (MHD) relaxation method. We extend the classical MHD relaxation method in two important ways. First, we introduce an algorithm initially proposed by Dedner et al. to effectively clean the numerical errors associated with ∇ · B . Second, the multigrid type method is implemented in our NLFFF to perform direct analysis of the high-resolution magnetogram data. As a result of these two implementations, we successfully extrapolated the high resolution force-free field introduced by Low and Lou with better accuracy in a drastically shorter time. We also applied our extrapolation method to the MHD solution obtained from the flux-emergence simulation by Magara. We found that NLFFF extrapolation may be less effective for reproducing areas higher than a half-domain, where some magnetic loops are found in a state of continuous upward expansion. However, an inverse S-shaped structure consisting of the sheared and twisted loops formed in the lower region can be captured well through our NLFFF extrapolation method. We further discuss how well these sheared and twisted fields are reconstructed by estimating the magnetic topology and twist quantitatively.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

Implicit high-order method for calculating rarefied gas flow in a planar microchannel

An efficient numerical algorithm for calculating rarefied gas flows in planar microchannels on the basis of the Boltzmann kinetic equation with the linearized S-model collision integral is presented. The algorithm consists of a high-order spatial discretisation on unstructured meshes, conservative procedure to calculate macroscopic quantities and efficient one-step implicit time evolution method. It therefore works across all flow regimes from the free-molecular to nearly continuum ones and provides rapid convergence to steady state solutions. The parallel implementation is provided via MPI programming paradigm. The performance of the method is illustrated by computing the flow for length to the width ratios for up to 10{sup 3} in the wide range of Knudsen numbers. Numerical estimates of efficiency of implicit time marching and parallel performance as well as convergence studies in both physical and velocity spaces are provided. The end effects and other essentially two-dimensional features of the flow are analysed and a detailed comparison with the case of an infinitely long channel is carried out. The presented numerical data can be used as reference for future studies of nonlinear flows as well as for comparison with other numerical approaches and flow models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Fully coupled hydro-mechanical numerical manifold modeling of porous rock with dominant fractures

Coupled hydro-mechanical (HM) processes are significant in geological engineering such as oil and gas extraction, geothermal energy, nuclear waste disposal and for the safety assessment of dam foundations and rock slopes, where the geological media usually consist of fractured rock masses. We developed a model for the analysis of coupled hydro-mechanical processes in porous rock containing dominant fractures, by using the numerical manifold method (NMM). In the current model, the fractures are regarded as different material domains from surrounding rock, i.e., finite-thickness fracture zones as porous media. Compared with the rock matrix, these fractured porous media are characterized with nonlinear behavior of hydraulic and mechanical properties, involving not only direct (poroelastic) coupling but also indirect (property change) coupling. By combining the potential energy associated with mechanical responses, fluid flow and solid–fluid interactions, a new formulation for direct HM coupling in porous media is established. For indirect coupling associated with fracture opening/closure, we developed a new approach implicitly considering the nonlinear properties by directly assembling the corresponding strain energy. Compared with traditional methods with approximation of the nonlinear constitutive equations, this new formulation achieves a more accurate representation of the nonlinear behavior. We implemented the new model for coupled HM analysis in NMM, which has fixed mathematical grid and accurate integration, and developed a new computer code. We tested the code for direct coupling on two classical poroelastic problems with coarse mesh and compared the results with the analytical solutions, achieving excellent agreement, respectively. We tested for indirect coupling on models with a single dominant fracture and obtained reasonable results. The current poroelastic NNM model with a continuous finite-thickness fracture zone will be further developed considering thin fractures in a discontinuous approach for a comprehensive model for HM analysis in fractured porous rock masses.

58 GEOSCIENCES↗
DOE OSTI2014

WE-D-BRF-05: Quantitative Dual-Energy CT Imaging for Proton Stopping Power Computation

Purpose: To extend the two-parameter separable basis-vector model (BVM) to estimation of proton stopping power from dual-energy CT (DECT) imaging. Methods: BVM assumes that the photon cross sections of any unknown material can be represented as a linear combination of the corresponding quantities for two bracketing basis materials. We show that both the electron density (ρe) and mean excitation energy (Iex) can be modeled by BVM, enabling stopping power to be estimated from the Bethe-Bloch equation. We have implemented an idealized post-processing dual energy imaging (pDECT) simulation consisting of monogenetic 45 keV and 80 keV scanning beams with polystyrene-water and water-CaCl2 solution basis pairs for soft tissues and bony tissues, respectively. The coefficients of 24 standard ICRU tissue compositions were estimated by pDECT. The corresponding ρe, Iex, and stopping power tables were evaluated via BVM and compared to tabulated ICRU 44 reference values. Results: BVM-based pDECT was found to estimate ρe and Iex with average and maximum errors of 0.5% and 2%, respectively, for the 24 tissues. Proton stopping power values at 175 MeV, show average/maximum errors of 0.8%/1.4%. For adipose, muscle and bone, these errors result range prediction accuracies less than 1%. Conclusion: A new two-parameter separable DECT model (BVM) for estimating proton stopping power was developed. Compared to competing parametric fit DECT models, BVM has the comparable prediction accuracy without necessitating iterative solution of nonlinear equations or a sample-dependent empirical relationship between effective atomic number and Iex. Based on the proton BVM, an efficient iterative statistical DECT reconstruction model is under development.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1991

A study of the response of nonlinear springs

The various phases to developing a methodology for studying the response of a spring-reinforced arch subjected to a point load are discussed. The arch is simply supported at its ends with both the spring and the point load assumed to be at midspan. The spring is present to off-set the typical snap through behavior normally associated with arches, and to provide a structure that responds with constant resistance over a finite displacement. The various phases discussed consist of the following: (1) development of the closed-form solution for the shallow arch case; (2) development of a finite difference analysis to study (shallow) arches; and (3) development of a finite element analysis for studying more general shallow and nonshallow arches. The two numerical analyses rely on a continuation scheme to move the solution past limit points, and to move onto bifurcated paths, both characteristics being common to the arch problem. An eigenvalue method is used for a continuation scheme. The finite difference analysis is based on a mixed formulation (force and displacement variables) of the governing equations. The governing equations for the mixed formulation are in first order form, making the finite difference implementation convenient. However, the mixed formulation is not well-suited for the eigenvalue continuation scheme. This provided the motivation for the displacement based finite element analysis. Both the finite difference and the finite element analyses are compared with the closed form shallow arch solution. Agreement is excellent, except for the potential problems with the finite difference analysis and the continuation scheme. Agreement between the finite element analysis and another investigator's numerical analysis for deep arches is also good.

Hyer, M. W.↗
NASA NTRS1997

An Algorithm for Integrated Subsystem Embodiment and System Synthesis

Consider the statement,'A system has two coupled subsystems, one of which dominates the design process. Each subsystem consists of discrete and continuous variables, and is solved using sequential analysis and solution.' To address this type of statement in the design of complex systems, three steps are required, namely, the embodiment of the statement in terms of entities on a computer, the mathematical formulation of subsystem models, and the resulting solution and system synthesis. In complex system decomposition, the subsystems are not isolated, self-supporting entities. Information such as constraints, goals, and design variables may be shared between entities. But many times in engineering problems, full communication and cooperation does not exist, information is incomplete, or one subsystem may dominate the design. Additionally, these engineering problems give rise to mathematical models involving nonlinear functions of both discrete and continuous design variables. In this dissertation an algorithm is developed to handle these types of scenarios for the domain-independent integration of subsystem embodiment, coordination, and system synthesis using constructs from Decision-Based Design, Game Theory, and Multidisciplinary Design Optimization. Implementation of the concept in this dissertation involves testing of the hypotheses using example problems and a motivating case study involving the design of a subsonic passenger aircraft.

Lewis, Kemper↗
DOE OSTI2018

NIMROD calculations of energetic particle driven toroidal Alfvén eigenmodes

Toroidal Alfvén eigenmodes (TAEs) are gap modes induced by the toroidicity of tokamak plasmas in the absence of continuum damping. They can be excited by energetic particles (EPs) when the EP drive exceeds other dampings, such as electron and ion Landau damping, and collisional and radiative damping. A TAE benchmark case, which was proposed by the International Tokamak Physics Activity group, is studied in this work. The numerical calculations of linear growth of TAEs driven by EPs in a circular-shaped, large aspect ratio tokamak have been performed using the Hybrid Kinetic-MHD (HK-MHD) model implemented in the NIMROD code. This HK-MHD model couples a δf particle-in-cell representation of EPs with the 3D MHD representation of the bulk plasma through moment closure for the momentum conservation equation. Both the excitation of TAEs and their transition to energetic particle modes (EPMs) have been observed. The influence of EP density, temperature, density gradient, and position of the maximum relative density gradient, on the frequency and the growth rate of TAEs are obtained, which are consistent with those from the eigen-analysis calculations, kinetic-MHD, and gyrokinetic simulations for an initial Maxwellian distribution of EPs. The relative pressure gradient of EP at the radial location of the TAE gap, which represents the drive strength of EPs, can strongly affect the growth rate of TAEs. Here, it is demonstrated that the mode transition due to EP drive variation leads to not only the change of frequency but also the change of the mode structure. This mechanism can be helpful in understanding the nonlinear physics of TAE/EPM, such as frequency chirping.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

On Practical Aspects of Variational Consistency in Contact Dynamics

Usage of contact mechanics methodologies is a pervasive modeling requirement in dynamic simulations. While for some trivial problems, solutions taken from analytical geometry are available, use of a finite element framework is common to achieve formulation generality. This work explores two dynamic contact formulations: one based on the traditional node-to-segment (NTS) approach, and a variationally consistent segment-to-segment (STS) mortar formulation. The NTS formulation employed here enforces the constraints kinematically (i.e., the interpenetration is enforced to the solver tolerance), whereas the mortar approach uses Lagrange multipliers to enforce the contact constraints. Both approaches are implemented in the open-source finite element framework Multiphysics Object-Oriented Simulation Environment (MOOSE). The results highlight two relevant contact-interface-related dynamic phenomena in finite element simulations. First, stabilization of contact constraints is discussed, taking into account the evolution of the total energy in a benchmark problem. Second, the influence of finite element discretization on both of the aforementioned contact formulations is analyzed by exercising a large-deformation example with continuous relative sliding. Variationally consistent contact approaches such as the mortar formulation lead to improved energy preservation and avoid spurious excitation of the system's frequencies. This is especially relevant in settings where inertia and vibrations are of importance.

42 ENGINEERING↗
DOE OSTI2020

A Tchebycheff-based multi-objective combined with a PSO–SQP dynamic real-time optimization framework for cycling energy systems

The aim in this work is to develop an optimization framework to address cycling of baseload energy systems due to the penetration of renewables into the grid. The developed strategy corresponds to a multi-objective and dynamic real-time optimization (MOO-DRTO) framework applied to a postcombustion MEA-based CO 2 capture process from a baseload coal-fired power plant under cycling conditions. A Tchebycheff-based method is used for the multi-objective optimization (MOO) component. Also, a hybrid approach consisting of Particle Swarm Optimization (PSO) and Sequential Quadratic Programming (SQP) is implemented for the first time in process systems engineering to solve the dynamic real-time optimization (DRTO) component. The objectives considered in the MOO-DRTO framework are economic and environmental. The proposed MOO-DRTO strategy is successfully implemented and 24-h optimal output trajectories for the carbon capture system under cycling are generated. Also, the optimal compromise is chosen from the Pareto front according to a set of selected weights for the objectives with minimal interaction between the framework and decision maker. The results indicated that the developed framework has potential to be extended to plant-wide optimization applications under cycling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2013

Electron and ion kinetic effects on non-linearly driven electron plasma and ion acoustic waves

Fully non-linear kinetic simulations of electron plasma and ion acoustic waves (IAWs) have been carried out with a new multi-species, parallelized Vlasov code. The numerical implementation of the Vlasov model and the methods used to compute the wave frequency are described in detail. For the first time, the nonlinear frequency of IAWs, combining the contributions from electron and ion kinetic effects and from harmonic generation, has been calculated and compared to Vlasov results. Excellent agreement of theory with simulation results is shown at all amplitudes, harmonic generation being an essential component at large amplitudes. For IAWs, the positive frequency shift from trapped electrons is confirmed and is dominant for the effective electron-to-ion temperature ratio, Z T{sub e}/T{sub i} Greater-Than-Or-Equivalent-To 10 with Z as the charge state. Furthermore, numerical results demonstrate unambiguously the dependence [R. L. Dewar, Phys. Fluids 15, 712 (1972)] of the kinetic shifts on details of the distribution of the trapped particles, which depends in turn on the conditions under which the waves were generated. The trapped particle fractions and energy distributions are derived and, upon inclusion of harmonic effects, shown to agree with the simulation results, completing a consistent picture. Fluid models of the wave evolution are considered but prove unable to capture essential details of the kinetic simulations. Detrapping by collisions and sideloss is also discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Integrating a ponderomotive guiding center algorithm into a quasi-static particle-in-cell code based on azimuthal mode decomposition

High fidelity modeling of plasma based acceleration (PBA) requires the use of three dimensional, fully nonlinear, and kinetic descriptions based on the particle-in-cell (PIC) method. In PBA an intense particle beam or laser (driver) propagates through a tenuous plasma whereby it excites a plasma wave wake. Three-dimensional PIC algorithms based on the quasi-static approximation (QSA) have been successfully applied to efficiently model the interaction between relativistic charged particle beams and plasma. In a QSA PIC algorithm, the plasma response to a charged particle beam or laser driver is calculated based on forces from the driver and self-consistent forces from the QSA form of Maxwell's equations. These fields are then used to advance the charged particle beam or laser forward by a large time step. Since the time step is not limited by the regular Courant-Friedrichs-Lewy (CFL) condition that constrains a standard 3D fully electromagnetic PIC code, a 3D QSA PIC code can achieve orders of magnitude speedup in performance. Recently, a new hybrid QSA PIC algorithm that combines another speedup technique known as an azimuthal Fourier decomposition has been proposed and implemented. This hybrid algorithm decomposes the electromagnetic fields, charge and current density into azimuthal harmonics and only the Fourier coefficients need to be updated, which can reduce the algorithmic complexity of a 3D code to that of a 2D code. Modeling the laser-plasma interaction in a full 3D electromagnetic PIC algorithm is very computationally expensive due the enormous disparity of physical scales to be resolved. In the QSA the laser is modeled using the ponderomotive guiding center (PGC) approach. We describe how to implement a PGC algorithm compatible for the QSA PIC algorithms based on the azimuthal mode expansion. Here this algorithm permits time steps orders of magnitude larger than the cell size and it can be asynchronously parallelized. Details on how this is implemented into the QSA PIC code that utilizes an azimuthal mode expansion, QPAD, are also described. Benchmarks and comparisons between a fully 3D explicit PIC code (OSIRIS), as well as a few examples related to laser wakefield acceleration, are presented.

97 MATHEMATICS AND COMPUTING↗