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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Verification of the PERSENT Software

Ongoing commercial design activities require a thorough verification of the Argonne Reactor Computation codes be performed. DIF3D is central to this system and substantial work has been done to verify its accuracy on several identified commercial needs. This manuscript details the verification work done on PERSENT which relies upon the DIF3D code for its forward and adjoint flux solution. Previous work identified the PERSENT features required to be verified to support commercial design activities, features of which are generally applicable to hexagonal-Z fast reactor designs. The scope of this verification effort includes verifying PERSENT’s ability to correctly calculate four key quantities: perturbation worth distributions, kinetics parameters, sensitivity coefficients, and cross section uncertainty quantification. This manuscript provides the verification tasks and their results with respect to these quantities needed for commercial design activities. For the perturbation worth distributions, hand calculations are deployed to verify the PERSENT calculated results. Similarly, hand calculation of the PERSENT computed kinetics parameters is also used to verify the PERSENT results. In both of these, the input to PERSENT is manipulated to ensure the hand calculation exactly matches the equations PERSENT is calculating. The sensitivity coefficients involve calculating the derivatives of a parameter (such as reactivity worth), with respect to the cross section data. Direct finite difference calculations with DIF3D are used to verify the PERSENT calculated results. For the uncertainty quantification, manufactured input to PERSENT is used to allow an exact hand calculation to reproduce the PERSENT calculated results. The work detailed in this report verified that significant issues were identified for earlier versions of PERSENT for sensitivity coefficients which were corrected in this work and thus version 12.1.0 of PERSENT must be used to reproduce all of the verified work in this report.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

VARI3D & PERSENT: Perturbation and Sensitivity Analysis

The nodal diffusion method is one of the most widely used approaches in modern reactor analysis. In the nodal diffusion method, a coarse multi-group set of “homogenized” parameters is constructed such that the complex geometry of a reactor core along with the energy dependence of neutron and gamma ray cross sections in a nuclear reactor are conserved in the simpler geometry. The homogenization is typically done on a fuel assembly level as is the case in the DIF3D code developed at Argonne National Laboratory. The nodal methodology is used primarily to predict fuel cycle behavior of nuclear systems of which there is a substantial amount of validation in the literature. Another use of the nodal method is to obtain reactivity coefficients and kinetics parameters for use in a safety analysis of a given nuclear reactor. While there are many ways to obtain reactivity worth and kinetics parameters, the work presented in this manuscript is unique as it provides the user with the ability to compute reactivity worths, kinetics parameters, and cross section sensitivities with a Cartesian and hexagonal geometry based transport code. This manuscript serves as a single manual for two separate codes: VARI3D and PERSENT. The VARI3D code (VARIational 3D) is based upon the classic finite difference diffusion theory solver available in DIF3D. The PERSENT code (PERturbation and SENitivity for Transport) is based upon the variational nodal method employed in DIF3D termed VARIANT. The VARIANT solver was added to DIF3D in 1995 and has seen continued development and use for the last 18 years. Because VARI3D primarily uses deprecated coding practices, rather than incorporating the perturbation and sensitivity treatments for transport within VARI3D, a new coding development was built using modern Fortran coding. The primary purpose of this manual is to describe the theory behind PERSENT (and by convenience, that of VARI3D) and discuss the input and output of PERSENT along with giving potential users an idea of how to use it. While this manuscript does describe the input and output of VARI3D, the PERSENT code is intended to be the replacement capability of VARI3D as PERSENT can generate nearly identical (if not superior) diffusion theory results. In this manuscript, the relevant aspects of generalized perturbation theory and exact perturbation theory that apply to both VARI3D and PERSENT are covered. The input and output of VARI3D is displayed by excerpting several of the example problems. Similarly, the input and output of PERSENT is displayed along with tips on how best to use the code. Note that the input and output of the inhomogeneous solver wrapped around DIF3D (DIF3D_IFS) is also discussed as it is needed to carry out some of the sensitivities in PERSENT such as reaction rate ratios. This manuscript describes several perturbation and sensitivity problems, and the results computed using PERSENT. From these sections, potential users should find that PERSENT provides not only the typical tables of numbers desired in perturbation and sensitivity analysis work, but also can visually plot the result for a more thorough understanding of the space and energy distribution (Section 5). Overall, PERSENT is observed to produce accurate reactivity worths and sensitivities for the displayed set of test problems and clearly demonstrates the need to have a transport-based sensitivity capability as evident from the thousands of percent errors observed in the 21-group hexagonal fast reactor problem (covered in Section 7). The uncertainty calculation capability is described in Section 3 and demonstrated in Section 7.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Hypercomplex Automatic Differentiation in the Eulerian Hydrocode PAGOSA

Enabling the computation of partial derivatives or sensitivities in production hydrocodes is beneficial for design, optimization, sensitivity analysis, and uncertainty quantification. Traditional finite difference approximations of these sensitivities are inefficient since convergence studies of the step size is required for each parameter of interest. For these reasons, HYPercomplex Automatic Differentiation (HYPAD) was implemented in the Eulerian hydrocode PAGOSA. HYPAD is analogous to forward-mode automatic differentiation except hypercomplex numbers (numbers with multiple imaginary parts) are used instead of dual numbers. Accurate partial derivatives can be computed of all state variables with respect to multiple input variables in a single run. The method was implemented using operator overloading to handle hypercomplex algebra. HYPAD was demonstrated and verified on Sod’s shock tube problem to compute derivatives of the state variables with respect to a material parameter, initial conditions, and geometry.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

DIF3D-VARIANT 12.0: Updates and New Features

The DIF3D code has been a workhorse of fast reactor analysis work at Argonne National Laboratory for over 40 years. In 1995, a transport option called VARIANT was added to DIF3D to improve the flux solutions for fast reactor problems which we term DIF3D-VARIANT today. DIF3D-VARIANT performs nodal neutron transport calculations using P N or SP N theory in Cartesian and hexagonal two- and three-dimensional geometries. The limited computing capabilities of the time restricted DIF3D-VARIANT to use at most a 6 th order spatial approximation combined with a P3 flux approximation and P1 scattering kernel for a 33 group structure on most studied reactor problems. Computer capabilities have increased steadily since 1995 and today much larger space-angle-energy approximations are possible. This manuscript serves as an update to the theory section of the original DIF3D-VARIANT manual and details more than twenty years of changes made to DIF3D to make version 12 which was released on November 1 st , 2024. The primary focus of the initial work was to extend the space-angle approximations available in DIF3D-VARIANT such that the error due to transport approximations could be better understood. This work was started and completed in 2002 and marked the official version 10. Unfortunately, those higher order approximations could not be used at that time due to the memory constraints of the BPOINTER part of DIF3D (limited to 2 GB). In version 11, completed in 2012, BPOINTER was circumvented in DIF3D-VARIANT for the largest arrays by introducing a Fortran 90 module called LMA (Large Memory Array). This seamlessly replaces all of the functionality of the BPOINTER concept, but it allows 64 bit addressing for every array such that they can be larger than 2 GB. It is now common for DIF3D-VARIANT jobs to consume 50 GB of memory on modern workstations when using high order space-angle approximations and a large number of groups. Many improvements were made to version 11 from 2012 to 2022 when work to create version 12 started. For version 12, several parts of DIF3D were updated to improve performance and thread parallelism was introduced to further reduce the runtime. Numerous minor bugs were discovered in DIF3D-VARIANT as part of the process of creating the perturbation and sensitivity code PERSENT. All of these algorithmic problems were identified in the transition from version 10 to version 11 which prevented DIF3D-VARIANT from running efficiently and reliably. Firstly, the coarse mesh rebalance scheme would routinely diverge and a study detailed in this report demonstrates how it was also typically not effective. This is not a failure of the coarse mesh rebalance methodology, but a failure of its implementation in DIF3D-VARIANT for hexagonal geometries. The fission source extrapolation algorithm was also found to be unreliable on larger group structure problems, leading to divergence in some cases and a negligible improvement in performance overall. Finally, the “Omega” acceleration applied to the partial current solver routine of DIF3D-VARIANT was found to cause DIF3D-VARIANT to converge to the wrong answer. To resolve these issues, both the coarse mesh rebalance and fission source extrapolation were permanently disabled in version 11. The Tchebychev acceleration was put in as a temporary reliable alternative but it is generally inferior to coarse mesh rebalance or coarse mesh finite difference. For the Omega acceleration, the factor was restricted to guarantee that it would not cause follow-on errors in PERSENT. Due to limited funding to support maintenance and development of DIF3D in the last 10 years, no effort was spent since to resolve the outer iteration acceleration. Except for the threading work, all of the changes discussed in this manuscript refer to changes made between version 10 and version 11. Performance comparisons are done to demonstrate the improvements from version 9 to version 12. As will be demonstrated, the updated versi

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Implementation of Perturbation Theory and Sensitivity Capabilities in Griffin

Griffin is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor Multiphysics analysis application, jointly developed by Argonne and Idaho National Laboratories under the DOE-NE NEAMS program. This fiscal year, capabilities for reactivity and sensitivity evaluation using perturbation methods were implemented and verified. The First Order Perturbation Method (FOPT) was employed to compute reactivity worth resulting from small perturbations in input parameters, while the Generalized Perturbation Theory (GPT) was used to evaluate sensitivities of a range of response types, including reaction rate ratio, k-eigenvalue, neutron generation time, and effective delayed neutron fraction. These perturbation methods enable users to quantify how response quantities change due to a perturbation in a input parameter without explicitly performing an additional transport simulation for each perturbed state. In particular, the GPT formulation accounts for indirect effects arising from flux changes by solving generalized inhomogeneous equations, for which a Neumann series-based iterative solution method was developed and implemented in Griffin. The implemented reactivity and sensitivity evaluation capabilities were verified using two test problems: an infinite homogeneous system and a two-dimensional hexagonal core. The results showed excellent agreement with reference solutions obtained by a direct method based on finite difference approximation as well as GPT-based results from the PERSENT code, confirming the accuracy of both reactivity and sensitivity evaluations. Additionally, preliminary uncertainty quantification (UQ) results were obtained by combining the sensitivity values computed using GPT and external covariance data, demonstrating that the implemented sensitivity results can be reliably used for uncertainty calculations. To further demonstrate the generality and practical strength of the implementation, the sensitivity evaluation capability was successfully applied to the Empire microreactor with a geometrically complex design that poses significant modeling challenges. The results confirm that Griffin enables sensitivity evaluations even for irregular and highly heterogeneous reactor configurations, thereby establishing a foundation for UQ applications in advanced reactor designs and analyses.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

Subplane Decusping for BWRs in MPACT

Control blade cusping can introduce significant error in boiling water reactor (BWR) calculations with MPACT when blade tips fall partway within an axial method of characteristics (MOC) plane, requiring homogenization of controlled and uncontrolled regions. This work implements subplane decusping for BWRs in MPACT by enabling BWR-compatible subplane coarse mesh finite difference (CMFD) and extending the existing decusping framework to represent between-assembly control blades that insert from the bottom of the core. The method resolves axial heterogeneity on a refined subplane mesh in the low-order solve and uses the resulting subplane flux shape to form flux-volume homogenized transport cross sections for the partially rodded MOC plane. The capability is evaluated using a single physics General Electric (GE)-14 assembly and a multiphysics Peach Bottom Unit 2 Type 1 assembly (PB2T1A) with thermal hydraulic feedback. In both cases, coarse axial meshes with and without subplane decusping are compared against fine mesh reference solutions over the full range of blade withdrawal positions. Subplane decusping reduces maximum/average eigenvalue errors from 3,369/220 pcm to 303/36 pcm for GE-14 and from 6,689/585 pcm to 1,582/109 pcm for PB2T1A. Additionally, it reduces pin power root mean square errors from 5.2%/0.8% to 1.8%/0.2% for GE-14 and from 6.9%/0.6% to 2.3%/0.1% for PB2T1A. These results demonstrate an effective, practical correction for BWR blade cusping in VERA-MPACT.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

Determination of Oscillator Strength of CdSe Nanoplatelets from Strong Light-Matter Coupling

We report exciton-polaritons formed from core-only, core-crown, and core-shell NPLs, which, alongside finite-difference time-domain (FDTD) simulations of Fabry-Pérot cavity mode volume, allow for the verification of core-only and determination of core-crown and core-shell oscillator strengths. Additionally, we show that polaritons can be used not only as a means of altering the properties of coupled emitters, but as an analytical tool to better understand the properties of coupled emitters.

Hancock, Benjamin↗
DOE OSTI2020

Solving Coupled Cluster Equations by the Newton Krylov Method

We describe using the Newton Krylov method to solve the coupled cluster equation. The method uses a Krylov iterative method to compute the Newton correction to the approximate coupled cluster amplitude. The multiplication of the Jacobian with a vector, which is required in each step of a Krylov iterative method such as the Generalized Minimum Residual (GMRES) method, is carried out through a finite difference approximation, and requires an additional residual evaluation. The overall cost of the method is determined by the sum of the inner Krylov and outer Newton iterations. We discuss the termination criterion used for the inner iteration and show how to apply pre-conditioners to accelerate convergence. We will also examine the use of regularization technique to improve the stability of convergence and compare the method with the widely used direct inversion of iterative subspace (DIIS) methods through numerical examples.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Efficient Ensemble-Based Stochastic Gradient Methods for Optimization Under Geological Uncertainty

Ensemble-based stochastic gradient methods, such as the ensemble optimization (EnOpt) method, the simplex gradient (SG) method, and the stochastic simplex approximate gradient (StoSAG) method, approximate the gradient of an objective function using an ensemble of perturbed control vectors. These methods are increasingly used in solving reservoir optimization problems because they are not only easy to parallelize and couple with any simulator but also computationally more efficient than the conventional finite-difference method for gradient calculations. In this work, we show that EnOpt may fail to achieve sufficient improvement of the objective function when the differences between the objective function values of perturbed control variables and their ensemble mean are large. On the basis of the comparison of EnOpt and SG, we propose a hybrid gradient of EnOpt and SG to save on the computational cost of SG. We also suggest practical ways to reduce the computational cost of EnOpt and StoSAG by approximating the objective function values of unperturbed control variables using the values of perturbed ones. We first demonstrate the performance of our improved ensemble schemes using a benchmark problem. Results show that the proposed gradients saved about 30–50% of the computational cost of the same optimization by using EnOpt, SG, and StoSAG. As a real application, we consider pressure management in carbon storage reservoirs, for which brine extraction wells need to be optimally placed to reduce reservoir pressure buildup while maximizing the net present value. Results show that our improved schemes reduce the computational cost significantly.

58 GEOSCIENCES↗
DOE OSTI2024

Assessing the release, transport, and retention of radioactive aerosols from hypothetical breaches in spent fuel storage canisters

Interim dry storage of spent nuclear fuel involves storing the fuel in welded stainless-steel canisters. Under certain conditions, the canisters could be subjected to environments that may promote stress corrosion cracking leading to a risk of breach and release of aerosol-sized particulate from the interior of the canister to the external environment through the crack. Research is currently under way by several laboratories to better understand the formation and propagation of stress corrosion cracks, however little work has been done to quantitatively assess the potential aerosol release. The purpose of the present work is to introduce a reliable generic numerical model for prediction of aerosol transport, deposition, and plugging in leak paths similar to stress corrosion cracks, while accounting for potential plugging from particle deposition. The model is dynamic (changing leak path geometry due to plugging) and it relies on the numerical solution of the aerosol transport equation in one dimension using finite differences. The model’s capabilities were also incorporated into a Graphical User Interface (GUI) that was developed to enhance user accessibility. Model validation efforts presented in this paper compare the model’s predictions with recent experimental data from Sandia National Laboratories (SNL) and results available in literature. We expect this model to improve the accuracy of consequence assessments and reduce the uncertainty of radiological consequence estimations in the remote event of a through-wall breach in dry cask storage systems.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2022

Photonic Luminescent Solar Concentrator Design for High Efficiency, Low Cost Multijunction Photovoltaics

Despite the extraordinary advances in solar cell efficiency in laboratory settings, the deployment of solar cells continues to be limited to low efficiency (<25%) silicon cells because of cost. In this work, we take advantage of the extraordinary optical properties afforded by nanophotonic structures to create a photonic luminescent solar concentrator for an InGaP-Si multijunction concentrator cell. Finite difference time domain (FDTD) simulations demonstrated a concentrator that could effectively capture, downconvert, and guide concentrated light to an InGaP subcell while still transmitting longer wavelengths to a Si subcell. We fabricated the photonic luminescent solar concentrator, which was comprised of CdSe/CdS quantum dots embedded within alternating layers of Si 3 N 4 and SiO 2 , and experimentally verified the optical performance, showing a 40% increase in light guiding and a significant reduction in reabsorption losses in the plane of the luminescent concentrator as compared to traditional designs. Finally, we utilized modified detailed balance calculations that accounted for cell and optical losses and showed >30% efficiencies are possible with this design, demonstrating the potential to meet the demands for high efficiency, inexpensive solar modules.

Eisler, Carissa N.↗
DOE OSTI2025

An Early Investigation of the HHL Quantum Linear Solver for Scientific Applications

In this paper, we explore using the Harrow–Hassidim–Lloyd (HHL) algorithm to address scientific and engineering problems through quantum computing, utilizing the NWQSim simulation package on a high-performance computing platform. Focusing on domains such as power-grid management and climate projection, we demonstrate the correlations of the accuracy of quantum phase estimation, along with various properties of coefficient matrices, on the final solution and quantum resource cost in iterative and non-iterative numerical methods such as the Newton–Raphson method and finite difference method, as well as their impacts on quantum error correction costs using the Microsoft Azure Quantum resource estimator. We summarize the exponential resource cost from quantum phase estimation before and after quantum error correction and illustrate a potential way to reduce the demands on physical qubits. This work lays down a preliminary step for future investigations, urging a closer examination of quantum algorithms’ scalability and efficiency in domain applications.

hybrid software for QC-HPC↗
DOE OSTI2022

Physics-Informed Neural Network Solution of Point Kinetics Equations for a Nuclear Reactor Digital Twin

A digital twin (DT) for nuclear reactor monitoring can be implemented using either a differential equations-based physics model or a data-driven machine learning model. The challenge of a physics-model-based DT consists of achieving sufficient model fidelity to represent a complex experimental system, whereas the challenge of a data-driven DT consists of extensive training requirements and a potential lack of predictive ability. We investigate the performance of a hybrid approach, which is based on physics-informed neural networks (PINNs) that encode fundamental physical laws into the loss function of the neural network. We develop a PINN model to solve the point kinetic equations (PKEs), which are time-dependent, stiff, nonlinear, ordinary differential equations that constitute a nuclear reactor reduced-order model under the approximation of ignoring spatial dependence of the neutron flux. The PINN model solution of PKEs is developed to monitor the start-up transient of Purdue University Reactor Number One (PUR-1) using experimental parameters for the reactivity feedback schedule and the neutron source. The results demonstrate strong agreement between the PINN solution and finite difference numerical solution of PKEs. We investigate PINNs performance in both data interpolation and extrapolation. For the test cases considered, the extrapolation errors are comparable to those of interpolation predictions. Extrapolation accuracy decreases with increasing time interval.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Plasmonic Core–Shell–Satellites with Abundant Electromagnetic Hotspots for Highly Sensitive and Reproducible SERS Detection

In this work, we develop a Ag@Al2O3@Ag plasmonic core–shell–satellite (PCSS) to achieve highly sensitive and reproducible surface-enhanced Raman spectroscopy (SERS) detection of probe molecules. To fabricate PCSS nanostructures, we employ a simple hierarchical dewetting process of Ag films coupled with an atomic layer deposition (ALD) method for the Al2O3 shell. Compared to bare Ag nanoparticles, several advantages of fabricating PCSS nanostructures are discovered, including high surface roughness, high density of nanogaps between Ag core and Ag satellites, and nanogaps between adjacent Ag satellites. Finite-difference time-domain (FDTD) simulations of the PCSS nanostructure confirm an enhancement in the electromagnetic field intensity (hotspots) in the nanogap between the Ag core and the satellite generated by the Al2O3 shell, due to the strong core–satellite plasmonic coupling. The as-prepared PCSS-based SERS substrate demonstrates an enhancement factor (EF) of 1.7 × 107 and relative standard deviation (RSD) of ~7%, endowing our SERS platform with highly sensitive and reproducible detection of R6G molecules. We think that this method provides a simple approach for the fabrication of PCSS by a solid-state technique and a basis for developing a highly SERS-active substrate for practical applications.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

Asymmetric Dual-Grating Dielectric Laser Accelerator Optimization

Although hundreds of keV in energy gain have already been demonstrated in dielectric laser accelerators (DLAs), the challenge of creating structures that can confine electrons for multiple millimeters remains. We focus here on dual gratings with single-sided drive, which have experimentally demonstrated energy modulation numerous times. Using a Finite-Difference Time-Domain simulation to find the fields within various DLA structures and correlating these results with particle tracking simulation, we look at the impact of teeth height and width, as well as gap and offset, on the performance of these structures. We find a tradeoff between electron throughput and acceleration; however, we also find that for any given grating geometry, there is a gap and offset that will allow some charge acceleration. For our 780 nm laser wavelength, this results in a 1200 nm optimal gap size for most gratings.

Crisp, Sophie (ORCID:0000000327503727)↗
DOE OSTI2024

Tensor Network Space-Time Spectral Collocation Method for Time-Dependent Convection-Diffusion-Reaction Equations

Emerging tensor network techniques for solutions of partial differential equations (PDEs), known for their ability to break the curse of dimensionality, deliver new mathematical methods for ultra-fast numerical solutions of high-dimensional problems. Here, we introduce a Tensor Train (TT) Chebyshev spectral collocation method, in both space and time, for the solution of the time-dependent convection-diffusion-reaction (CDR) equation with inhomogeneous boundary conditions, in Cartesian geometry. Previous methods for numerical solution of time-dependent PDEs often used finite difference for time, and a spectral scheme for the spatial dimensions, which led to a slow linear convergence. Spectral collocation space-time methods show exponential convergence; however, for realistic problems they need to solve large four-dimensional systems. We overcome this difficulty by using a TT approach, as its complexity only grows linearly with the number of dimensions. We show that our TT space-time Chebyshev spectral collocation method converges exponentially, when the solution of the CDR is smooth, and demonstrate that it leads to a very high compression of linear operators from terabytes to kilobytes in TT-format, and a speedup of tens of thousands of times when compared to a full-grid space-time spectral method. These advantages allow us to obtain the solutions at much higher resolutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Ultrafast Laser Material Damage Simulation—A New Look at an Old Problem

The chirped pulse amplification technique has enabled the generation of pulses of a few femtosecond duration with peak powers multi-Tera and Peta–Watt in the near infrared. Its implementation to realize even shorter pulse duration, higher energy, and higher repetition rate laser systems relies on overcoming the limitations imposed by laser damage of critical components. In particular, the laser damage of coatings in the amplifiers and in post-compression optics have become a bottleneck. The robustness of optical coatings is typically evaluated numerically through steady-state simulations of electric field enhancement in multilayer stacks. However, this approach cannot capture crucial characteristics of femtosecond laser induced damage (LID), as it only considers the geometry of the multilayer stack and the optical properties of the materials composing the stack. This approach neglects that in the interaction of an ultrashort pulse and the materials there is plasma generation and associated material modifications. Here, we present a numerical approach to estimate the LID threshold of dielectric multilayer coatings based on strong field electronic dynamics. In this dynamic scheme, the electric field propagation, photoionization, impact ionization, and electron heating are incorporated through a finite-difference time-domain algorithm. We applied our method to simulate the LID threshold of bulk fused silica, and of multilayer dielectric mirrors and gratings. The results are then compared with experimental measurements. The salient aspects of our model, such as the implementation of the Keldysh photoionization model, the impact ionization model, the electron collision model for ‘low’-temperature, dense plasma, and the LID threshold criterion for few-cycle pulses are discussed.

36 MATERIALS SCIENCE↗