Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “operator theory”

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

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

At least 1,027 records · Page 57

High entropy alloys: A focused review of mechanical properties and deformation mechanisms

The high-entropy alloy (HEA) concept was based on the idea that high mixing entropy can promote formation of stable single-phase microstructures. During the past 15 years, various alloy systems have been explored to identify HEA systems with improved property combinations, leading to an extraordinary growth of this field. In the large pool of alloys with varying characteristics, the first single-phase HEA with good tensile properties, the equiatomic CrMnFeCoNi alloy has become the benchmark material, and it forms the basis of much of our current fundamental understanding of HEA mechanical behavior. As the field is evolving to the more broadly defined complex concentrated alloys (CCAs) and the available data in the literature increase exponentially, a fundamental question remains unchanged: how special are these new materials? In the first part of this review, select mechanical properties of HEAs and CCAs are compared with those of conventional engineering alloys. This task is difficult because of the limited tensile data available for HEAs and CCAs. Additionally, the wider suite of mechanical properties needed to assess structural materials is woefully lacking. Nonetheless, our evaluations have not revealed many HEAs or CCAs with properties far exceeding those of conventional engineering alloys, although specific alloys can show notable enhancements in specific properties. Consequently, it is reasonable to first approach the understanding of HEAs and CCAs through the assessment of how the well-established deformation mechanisms in conventional alloys operate or are modified in the presence of the high local complexity of the HEAs and CCAs. The second part of the paper provides a detailed review of the deformation mechanisms of HEAs with the FCC and BCC structures. For the former, we chose the CrMnFeCoNi (Cantor) alloy because it is the alloy on which the most rigorous and thorough investigations have been performed and, for the latter, we chose the TiZrHfNbTa (Senkov) alloy because this is one of the few refractory HEAs that exhibits any tensile ductility at room temperature. As expected, our review shows that the fundamental deformation mechanisms in these systems, and their dependence on basic physical properties, are broadly similar to those of conventional FCC and BCC metals. The third part of this review examines the theoretical and modeling efforts to date that seek to provide either qualitative or quantitative understanding of the mechanical performance of FCC and BCC HEAs. Since experiments reveal no fundamentally new mechanisms of deformation, this section starts with an overview of modeling perspectives and fundamental considerations. Next, the review turns to the evolution of modeling and predictions as compared to recent experiments, highlighting both successes and limitations. Finally, in spite of some significant successes, important directions for further theory development are discussed. Overall, while the individual deformation mechanisms or properties of the HEAs and CCAs are not, by and large, “special” relative to conventional alloys, the present HEA rush remains valuable because the compositional freedom that comes from the multi-element space will allow exploration of whether multiple mechanisms can operate sequentially or simultaneously, which may yet lead to the creation of new alloys with a spectrum of mechanical properties that are significantly superior to those of current engineering alloys.

36 MATERIALS SCIENCE↗

AEcroscopy: A Software–Hardware Framework Empowering Microscopy Toward Automated and Autonomous Experimentation

Microscopy has been pivotal in improving the understanding of structure-function relationships at the nanoscale and is by now ubiquitous in most characterization labs. However, traditional microscopy operations are still limited largely by a human-centric click-and-go paradigm utilizing vendor-provided software, which limits the scope, utility, efficiency, effectiveness, and at times reproducibility of microscopy experiments. Here, in this work, a coupled software–hardware platform is developed that consists of a software package termed AEcroscopy (short for Automated Experiments in Microscopy), along with a field-programmable-gate-array device with LabView-built customized acquisition scripts, which overcome these limitations and provide the necessary abstractions toward full automation of microscopy platforms. The platform works across multiple vendor devices on scanning probe microscopes and electron microscopes. It enables customized scan trajectories, processing functions that can be triggered locally or remotely on processing servers, user-defined excitation waveforms, standardization of data models, and completely seamless operation through simple Python commands to enable a plethora of microscopy experiments to be performed in a reproducible, automated manner. This platform can be readily coupled with existing machine-learning libraries and simulations, to provide automated decision-making and active theory-experiment optimization to turn microscopes from characterization tools to instruments capable of autonomous model refinement and physics discovery.

47 OTHER INSTRUMENTATION↗

Atomic-scale vacancy engineering unlocks basal-plane catalytic activity in metallic WSe 2 for reversible oxygen electrocatalysis

Two-dimensional metallic transition metal dichalcogenides offer high electrical conductivity and large surface areas for electrocatalysis, yet their inherent basal planes are catalytically inert. Here, we present an atomic-scale vacancy engineering strategy to activate the basal surfaces of metallic WSe 2 for reversible oxygen electrocatalysis. This approach, based on intentionally designed substitutional metal doping, promotes the spontaneous formation of selenium vacancies while preserving the metallic 1 T′ phase, thereby creating highly reactive and oxygen-affinitive sites. Density functional theory calculations reveal that these vacancy-mediated metal complexes dramatically lower the energy barriers for initial oxygen adsorption, enabling dissociative oxygen adsorption. Operando and ex-situ spectroscopic analyses confirm that vacancy-mediated metal complexes transform into dynamic Se/W-oxide intermediates under operating conditions. Se/W-oxides on the surface experimentally and theoretically prove electrocatalytic activity and reversibility. Applying this strategy in lithium–oxygen batteries, the basal-plane activated WSe 2 shows high discharge capacities (9868 mA h g −1 , corresponding to 3947 mA h g$^{-1}_{cathode}$), impressive cycle retention over 550 cycles at 1000 mA h g −1 , and outstanding rate–capability over a wide current–density range (100–3000 mA g −1 ) during 256 cycles.

2D materials↗

Origin for electrochemically driven phase transformation in the oxygen electrode for a solid oxide cell

The next generation of fuel cells, electrolyzers, and batteries requires higher power, faster kinetics, and larger energy density, which necessitate the use of compositionally complex oxides to achieve multifunctionalities and activity. These compositionally complex oxides may change their phases and structures during an electrochemical process—a so-called “electrochemically driven phase transformation.” The origin for such a phase change has remained obscure. The aim of this paper is to present an experimental study and a theoretical analysis of phase evolution in praseodymium nickelates. Nickelate-based electrodes show up to 60 times greater phase transformation during operation when compared with thermally annealed ones. Theoretical analysis suggests that the presence of a reduced oxygen partial pressure at the interface between the oxygen electrode and the electrolyte is the origin for the phase change in an oxygen electrode. Guided by the theory, the addition of the electronic conduction in the interface layer leads to the significant suppression of phase change while improving cell performance and performance stability.

25 ENERGY STORAGE↗

Probing celestial energy and charge correlations through real-time quantum simulations: Insights from the Schwinger model

Motivated by recent developments in the application of light-ray operators (LROs) in high energy physics, we propose a new strategy to study correlation functions of LROs through real-time quantum simulations. We argue that quantum simulators provide an ideal laboratory to explore the properties LROs in lower-dimensional quantum field theories. This is exemplified in the 1 + 1 -d Schwinger model, employing tensor network methods, focusing on the calculation of energy and charge correlators. Despite some challenges in extracting the necessary correlation functions from the lattice, the methodology used can be extended to real quantum devices. Published by the American Physical Society 2025

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

High-luminosity meV-resolution single-shot hard X-ray spectrograph for cavity-based X-ray free-electron lasers

Cavity-based X-ray free-electron lasers (CBXFELs) represent a possible realization of fully coherent hard X-ray sources having high spectral brilliance along with a narrow spectral bandwidth of ∼1–50 meV, a high repetition pulse rate of ∼1 MHz, and good stability. A diagnostic tool is required to measure CBXFEL spectra with meV resolution and high luminosity on a shot-to-shot basis. We have designed a high-luminosity single-shot hard X-ray spectrograph that images 9.831 keV X-rays in a ∼200 meV spectral window with a spectral resolution of a few meV. The spectrograph is designed around angular dispersion of X-rays in Bragg diffraction from crystals. It operates close to design specifications, exhibiting a linear dispersion rate of ∼1.4 µm meV −1 and a ∼200 meV window of high-fidelity spectral imaging. The experimentally demonstrated spectral resolution is ∼20 meV; this resolution is twice as low as expected from theory primarily because the spectrograph is highly sensitive to crystal angular instabilities. The experiment was performed at the bending magnet X-ray optics testing beamline 1-BM at the Advanced Photon Source.

Bragg diffraction↗

Computing Bottleneck Structures at Scale for High-Precision Network Performance Analysis

The Theory of Bottleneck Structures is a recently-developed framework for studying the performance of data networks. It describes how local perturbations in one part of the network propagate and interact with others. This framework is a powerful analytical tool that allows network operators to make accurate predictions about network behavior and thereby optimize performance. Previous work implemented a software package for bottleneck structure analysis, but applied it only to toy examples. In this work, we introduce the first software package capable of scaling bottleneck structure analysis to production-size networks. Here, we benchmark our system using logs from ESnet, the Department of Energy's high-performance data network that connects research institutions in the U.S. Using the previously published tool as a baseline, we demonstrate that our system achieves vastly improved performance, constructing the bottleneck structure graphs in 0.21 s and calculating link derivatives in 0.09 s on average. We also study the asymptotic complexity of our core algorithms, demonstrating good scaling properties and strong agreement with theoretical bounds. These results indicate that our new software package can maintain its fast performance when applied to even larger networks. They also show that our software is efficient enough to analyze rapidly changing networks in real time. Overall, we demonstrate the feasibility of applying bottleneck structure analysis to solve practical problems in large, real-world data networks.

benchmark↗

Grid Topology Discovery Algorithm Evaluation of Suitability for Utility Deployment (CRADA 606 Final Report)

This work presents the results of a field-informed demonstration aimed at evaluating the practical suitability of a topology discovery algorithm for utility environments. We demonstrated an algorithm that uses a graph-theory-informed state estimation approach for model selection. In collaboration with Survalent and Peninsula Light Co., the algorithm was applied to real feeder models and field measurements from supervisory control and data acquisition (SCADA) and advanced metering infrastructure (AMI) systems to identify the operational topology of a power distribution system. The demonstration assessed the algorithm’s performance under realistic data conditions, including sparse and noisy measurements, and examined its ability to identify the most likely network configurations. The results confirmed that the approach can effectively narrow down feasible topologies, providing operators with improved situational awareness of network status. Key lessons learned emphasize the need for systematic data validation and strategic sensor placement to enhance observability. These insights inform future deployment strategies and guide refinements for broader adoption in utility operations.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Lorentz Symmetry Group, Retardation, Intergalactic Mass Depletion and Mechanisms Leading to Galactic Rotation Curves

The general theory of relativity (GR) is symmetric under smooth coordinate transformations, also known as diffeomorphisms. The general coordinate transformation group has a linear subgroup denoted as the Lorentz group of symmetry, which is also maintained in the weak field approximation to GR. The dominant operator in the weak field equation of GR is thus the d’Alembert (wave) operator, which has a retarded potential solution. Galaxies are huge physical systems with dimensions of many tens of thousands of light years. Thus, any change at the galactic center will be noticed at the rim only tens of thousands of years later. Those retardation effects are neglected in the present day galactic modelling used to calculate rotational velocities of matter in the rims of the galaxy and surrounding gas. The significant differences between the predictions of Newtonian instantaneous action at a distance and observed velocities are usually explained by either assuming dark matter or by modifying the laws of gravity (MOND). In this paper, we will show that, by taking general relativity seriously without neglecting retardation effects, one can explain the radial velocities of galactic matter in the M33 galaxy without postulating dark matter. It should be stressed that the current approach does not require that velocities v are high; in fact, the vast majority of galactic bodies (stars, gas) are substantially subluminal—in other words, the ratio of $\frac{v}{c} \ll 1$. Typical velocities in galaxies are 100 km/s, which makes this ratio 0.001 or smaller. However, one should consider the fact that every gravitational system, even if it is made of subluminal bodies, has a retardation distance, beyond which the retardation effect cannot be neglected. Every natural system, such as stars and galaxies and even galactic clusters, exchanges mass with its environment, for example, the sun loses mass through solar wind and galaxies accrete gas from the intergalactic medium. This means that all natural gravitational systems have a finite retardation distance. The question is thus quantitative: how large is the retardation distance? For the M33 galaxy, the velocity curve indicates that the retardation effects cannot be neglected beyond a certain distance, which was calculated to be roughly 14,000 light years; similar analysis for other galaxies of different types has shown similar results. We demonstrate, using a detailed model, that this does not require a high velocity of gas or stars in or out of the galaxy and is perfectly consistent with the current observational knowledge of galactic and extra galactic material content and dynamics

79 ASTRONOMY AND ASTROPHYSICS↗

Efficient Mixed-Precision Matrix Factorization of the Inverse Overlap Matrix in Electronic Structure Calculations with AI-Hardware and GPUs

In recent years, a new kind of accelerated hardware has gained popularity in the artificial intelligence (AI) community which enables extremely high-performance tensor contractions in reduced precision for deep neural network calculations. In this article, we exploit Nvidia Tensor cores, a prototypical example of such AI-hardware, to develop a mixed precision approach for computing a dense matrix factorization of the inverse overlap matrix in electronic structure theory, S –1 . This factorization of S –1 , written as ZZT = S –1 , is used to transform the general matrix eigenvalue problem into a standard matrix eigenvalue problem. Here we present a mixed precision iterative refinement algorithm where Z is given recursively using matrix–matrix multiplications and can be computed with high performance on Tensor cores. To understand the performance and accuracy of Tensor cores, comparisons are made to GPU-only implementations in single and double precision. Additionally, we propose a nonparametric stopping criteria which is robust in the face of lower precision floating point operations. The algorithm is particularly useful when we have a good initial guess to Z, for example, from previous time steps in quantum-mechanical molecular dynamics simulations or from a previous iteration in a geometry optimization.

36 MATERIALS SCIENCE↗

Kondo Lattice Model of Magic-Angle Twisted-Bilayer Graphene: Hund’s Rule, Local-Moment Fluctuations, and Low-Energy Effective Theory

For this work, we apply a generalized Schrieffer-Wolff transformation to the extended Anderson-like topological heavy fermion (THF) model for the magic-angle (θ=1.05°) twisted bilayer graphene (MATBLG) [Phys. Rev. Lett. 129, 047601 (2022)], to obtain its Kondo lattice limit. In this limit localized $\mathcal{f}$ electrons on a triangular lattice interact with topological conduction $\mathcal{c}$ electrons. By solving the exact limit of the THF model, we show that the integer fillings ν=0, ±1, ±2 are controlled by the heavy $\mathcal{f}$ electrons, while ν=±3 is at the border of a phase transition between two $\mathcal{f}$-electron fillings. For ν=0, ±1, ±2, we then calculate the Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions between the $\mathcal{f}$ moments in the full model and analytically prove the SU(4) Hund’s rule for the ground state which maintains that two $\mathcal{f}$ electrons fill the same valley-spin flavor. Our (ferromagnetic interactions in the) spin model dramatically differ from the usual Heisenberg antiferromagnetic interactions expected at strong coupling. We show the ground state in some limits can be found exactly by employing a positive semidefinite “bond-operators” method. We then compute the excitation spectrum of the $\mathcal{f}$ moments in the ordered ground state, prove the stability of the ground state favored by RKKY interactions, and discuss the properties of the Goldstone modes, the (reason for the accidental) degeneracy of (some of) the excitation modes, and the physics of their phase stiffness. We develop a low-energy effective theory for the $\mathcal{f}$ moments and obtain analytic expressions for the dispersion of the collective modes. We discuss the relevance of our results to the spin-entropy experiments in TBG.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

A practical approach to determine minimal quantum gate durations using amplitude-bounded quantum controls

Here, we present an iterative scheme to estimate the minimal duration in which a quantum gate can be realized while satisfying hardware constraints on the control pulse amplitudes. The scheme performs a sequence of unconstrained numerical optimal control cycles that each minimize the gate fidelity for a given gate duration alongside an additional penalty term for the control pulse amplitudes. After each cycle, the gate duration is adjusted based on the inverse of the resulting maximum control pulse amplitudes by re-scaling the dynamics to a new duration where control pulses satisfy the amplitude constraints. Those scaled controls then serve as an initial guess for the next unconstrained optimal control cycle, using the adjusted gate duration. We provide multiple numerical examples that each demonstrate fast convergence of the scheme toward a gate duration that is close to the quantum speed limit, given the control pulse amplitude bound. The proposed technique is agnostic to the underlying system and control Hamiltonian models, as well as the target unitary gate operation, making the time-scaling iteration an easy to implement and practically useful scheme for reducing the durations of quantum gate operations.

97 MATHEMATICS AND COMPUTING↗

Local SU(2) × U(1) quark flavor symmetry in the RS bulk

We propose a model of quark flavor based on an additional SU(2) × U(1) local symmetry in a warped extra dimensional bulk. In contrast to other works, we break the additional gauge symmetry in the bulk via two complex scalars which acquire bulk vevs, rather than relying on brane-localized symmetry breaking. A gauge-covariant Kaluza-Klein decomposition of a theory with a bulk spontaneously broken gauge symmetry is performed, and exact expressions for the bulk profiles of all physical particles in such systems are given. The SM quark masses and mixings are then recreated using gauge-covariant bulk quark mass terms and Yukawa-like couplings to the new bulk scalars. A numerical sampling of points in the model parameter space that recreate the quark masses and mixings is performed at a KK scale of M KK = 5 TeV. We then compute the ΔF = 2 4-quark operators arising from our new flavor gauge bosons and scalars, and those arising from Kaluza-Klein modes of SM gauge bosons. By decoupling one of our bulk scalar fields to all quark fields except the right-handed up-like sector, we find that it is possible to greatly suppress tree-level contributions to the highly constrained Kaon mixing parameters. Instead, the dominant constraints on the model emerge from neutral Bd and D meson mixing. These constraints are explored with our numerical sampling of the model parameter space, and the specific contribution of the new flavor gauge bosons and scalars is discussed. We find that for a significant range of realistic flavor gauge couplings, the new gauge bosons compete with the normally dominant gluon flavor-changing currents, but flavor-changing operators emerging from the bulk scalar fields are highly suppressed. Finally, we briefly comment on flavor constraints that are independent of the flavor gauge sector arising from the Z$\overline{b}$ L b L coupling and rare top decays.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Enhancing Photostability of Sn-Pb Perovskite Solar Cells by an Alkylammonium Pseudo-Halogen Additive

High-performance tin-lead perovskite solar cells (PSCs) are needed for all-perovskite-tandem solar cells. However, iodide related fast photodegradation severely limits the operational stability of Sn-Pb perovskites despite the demonstrated high efficiency and thermal stability. Herein, this work employs an alkylammonium pseudo-halogen additive to enhance the power conversion efficiency (PCE) and photostability of methylammonium (MA)-free, Sn-Pb PSCs. Density functional theory (DFT) calculations reveal that the pseudo-halogen tetrafluoroborate (BF 4 - ) has strong binding capacity with metal ions (Sn 2+ /Pb 2+ ) in the Sn-Pb perovskite lattice, which lowers iodine vacancy formation. Upon combining BF 4 - with an octylammonium (OA + ) cation, the PCE of the device with a built-in light-scattering layer is boosted to 23.7%, which represents a new record for Sn-Pb PSCs. The improved efficiency benefits from the suppressed defect density. Under continuous 1 sun illumination, the OABF 4 embodied PSCs show slower generation of interstitial iodides and iodine, which greatly improves the device photostability under open-circuit condition. Moreover, the device based on OABF 4 retains 88% of the initial PCE for 1000 h under the maximum-power-point tracking (MPPT) without cooling.

14 SOLAR ENERGY↗

Gravitational duals to the grand canonical ensemble abhor Cauchy horizons

The gravitational dual to the grand canonical ensemble of a large N holographic theory is a charged black hole. These spacetimes - for example Reissner- Nordström-AdS - can have Cauchy horizons that render the classical gravitational dynamics of the black hole interior incomplete. We show that a (spatially uniform) deformation of the CFT by a neutral scalar operator generically leads to a black hole with no inner horizon. There is instead a spacelike Kasner singularity in the interior. For relevant deformations, Cauchy horizons never form. For certain irrelevant deformations, Cauchy horizons can exist at one specific temperature. We show that the scalar field triggers a rapid collapse of the Einstein-Rosen bridge at the would-be Cauchy horizon. Finally, we make some observations on the interior of charged dilatonic black holes where the Kasner exponent at the singularity exhibits an attractor mechanism in the low temperature limit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Deciphering Reaction Mechanisms of Molecular Proton Reduction Catalysts with Cyclic Voltammetry: Kinetic vs Thermodynamic Control

The kinetics and thermodynamics of elementary reaction steps involved in the catalytic reduction of protons to hydrogen define the reaction landscape for catalysis. The mechanisms can differ in the order of the elementary proton transfer, electron transfer, and bond-forming steps and can be further differentiated by the sites at which protons and electrons localize. Access to fully elucidated mechanistic, kinetic, and thermochemical details of molecular catalysts is crucial to facilitate the development of new catalysts that operate with optimal efficiency, selectivity, and durability. The mechanism by which a catalyst operates, as well as the kinetics and thermodynamics associated with the individual steps, can often be accessed through electroanalytical studies. Here, this Account details the application of cyclic voltammetry to interrogate reaction mechanisms and quantify the kinetics and thermodynamics of elementary reaction steps for a series of molecular catalysts that mediate electrochemical proton reduction. I distinguish the limiting scenarios wherein a catalyst operates under kinetic control vs thermodynamic control, with a focus on detecting how cyclic voltammetry features shift with proton source strength and concentration, as well as scan rate. For systems that operate under kinetic control, catalytic currents are observed at, or slightly positive toward, the formal potential for the redox process that triggers catalysis. Under thermodynamic control, catalytic responses shift as a function of the proton source pKa and effective pH of the solution. After drawing this distinction, we introduce the appropriate voltammetry experiments and accompanying analytical expressions for extracting key metrics from the data. To illustrate analytical strategies to quantify elementary reaction steps of catalysts operating under kinetic control, I describe our studies of proton reduction catalysts Co(dmgBF 2 ) 2 (CH 3 CN) 2 (dmgBF 2 = difluoroboryl-dimethylglyoxime) and [Ni(P 2 Ph N 2 Ph ) 2 ] 2+ (P 2 Ph N 2 Ph = 1,5-phenyl-3,7-phenyl-1,5-diaza-3,7-diphosphacyclooctane). Here, peak shift analysis, foot-of-the-wave analysis, and plateau current analysis are applied to data sets wherein voltammetric response are recorded as a function of catalyst concentration, proton source concentration, proton source strength, and scan rate to quantify rate constants for elementary proton transfer and bond-forming steps in a catalytic cycle. Further, the case study of [Ni(P 2 Ph N 2 Ph ) 2 ] 2+ illustrates how complementary spectroscopic methods can bolster the mechanistic assignment. Collectively, these two studies showcase how detailed mechanistic studies inform on rate-limiting elementary steps in catalysis and other key processes underpinning catalysis. Second, I present analytical strategies to interrogate catalysts operating under thermodynamic control, centered on the case study of [Ni II (P 2 Ph N 2 Bn ) 2 ] 2+ (P 2 Ph N 2 Bn = 1,5-dibenzyl-3,7-diphenyl-1,5-diaza-3,7-diphosphacyclooctane). Here, the application of nonaqueous Pourbaix theory to extract thermodynamic information is introduced, and the construction of a coupled Pourbaix diagram is detailed. This study identifies ligand-based protonation as the key process that places catalysis under thermodynamic control and influences the reaction mechanism. Together, the work detailed in this Account showcases the utility of electroanalytical methods to disentangle complex reaction mechanisms and extract key thermochemical and kinetic parameters for elementary steps of catalysis. Through detailed presentation of the key analytical expressions that underpin these analyses, this Account seeks to facilitate the adoption of cyclic voltammetry by the community to fully extract kinetic, thermochemical, and mechanistic information on electrochemical small-molecule activation.

catalysts↗

Kinetic simulations of collision-less plasmas in open magnetic geometries

Laboratory plasmas in open magnetic geometries can be found in many different applications such as (a) scrape-of-layer (SOL) and divertor regions in toroidal confinement fusion devices, (b) linear divertor simulators, (c) plasma-based thrusters and (d) magnetic mirrors etc. A common feature of these plasma systems is the need to resolve, in addition to velocity space, at least one physical dimension (e.g. along flux lines) to capture the relevant physics. In general, this requires a kinetic treatment. Fully kinetic particle-in-cell (PIC) simulations can be applied but at the expense of large computational effort. A common way to resolve this is to use a hybrid approach: kinetic ions and fluid electrons. In the present work, the development of a hybrid PIC computational tool suitable for open magnetic geometries is described which includes (a) the effect of non-uniform magnetic fields, (b) finite fully-absorbing boundaries for the particles and (c) volumetric particle sources. Analytical expressions for the momentum transport in the paraxial limit are presented with their underlying assumptions and are used to validate the results from the PIC simulations. A general method is described to construct discrete particle distribution functions in a state of mirror-equilibrium. This method is used to obtain the initial state for the PIC simulation. Collisionless simulations in a mirror geometry are performed. The results show that the effect of magnetic compression is correctly described and momentum is conserved. The self-consistent electric field is calculated and is shown to modify the ion velocity distribution function in a manner consistent with analytic theory. Based on this analysis, the ion distribution function is understood in terms of a loss-cone distribution and an isotropic Maxwell-Boltzmann distribution driven by a volumetric plasma source. Finally, the inclusion of a Monte Carlo based Fokker-Planck collision operator is discussed in the context of future work.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗