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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Impact of cyber attacks on distributed compressive sensing based state estimation in power distribution grids

Modern power distribution grids suffer from multiple vulnerabilities due to the tight integration between the physical system and the cyber infrastructure. Sophisticated and malicious cyber attacks continue to adversely impact the grid operation leading to performance degradation, service interruption, and grid failure. State estimation plays an essential role in grid monitoring and advancing cyber-attack situational awareness. In this regard, this paper first proposes a distributed compressive sensing (CS) state estimation approach for an unobservable distribution grid. Further, the proposed distributed CS approach divides the distribution grid into sub-areas to perform local state estimation. Then an alternating direction method of multipliers (ADMM) based iterative information exchange among neighboring areas is employed to complete the estimation process. In this estimation process, the impact of loss of measurement data, false data injection (FDI), replay, and neighborhood cyber-attacks is analyzed. Extensive simulations are performed on the IEEE 37-bus and IEEE 123-bus standard networks to demonstrate the algorithm’s robustness to the aforementioned cyber-attacks. A quantitative analysis of computational complexity and simulation time of the distributed CS based approach is also presented.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Hydraulic fracturing to enhance injectivity and storage capacity of CO 2 storage reservoirs: Benefits and risks

Several potential CO 2 storage reservoirs have been found to have insufficient porosity and permeability to support cost effective commercial-scale injection. As a result, the use of hydraulic fracturing to enhance injectivity and storage capacity of CO 2 storage reservoirs was explored. Previous modeling studies indicate that fracturing can increase storage capacity by modest to significant amounts (10%–35%), depending on model assumptions. Simulations completed as part of this study confirm that for a range of horizontal well lengths, number of fractures, fracture geometries, and fracture properties, injectivity is improved and capacity increases by 13%–71% over the base case unfractured vertical well. Intuitively, increasing the well length and number of fractures had a corresponding impact on increased capacity. Here, fracture area (i.e., the fracture height multiplied by its width) was an important parameter for increasing capacity but the specific geometry (e.g., the ratio of height-to-width) was unimportant. The most important aspect that affected capacity was the ability of a fracture to connect high permeability horizontal zones in the reservoir. This would allow a single well to access both layers, thereby maximizing total storage capacity of the reservoir while likely leading to an overall increase of the CO 2 footprint, which is an important consideration for Class VI UIC permitting. The results of this work demonstrate that hydraulic fracturing is an attractive option to consider when faced with an underperforming geologic carbon storage site that is at risk of causing a project to fail.

03 NATURAL GAS↗
DOE OSTI2023

Accuracy and precision of ESI-Orbitrap-IRMS observations of hours to tens of hours via reservoir injection

Here, orbitrap isotope ratio mass spectrometry (Orbitrap-IRMS) has recently been applied to high-precision, natural-abundance isotope ratio measurements of a diverse range of compounds, including amino acids, oxyanions, fatty acids, and metals. These measurements can characterize many isotope ratios simultaneously at high (≈1.0‰) precision. In a successful experiment, observed precision will track the shot-noise limit and be limited by experimental time. Some isotope ratios, for example those involving 17 O in organic compounds or multiply-substituted (‘clumped’) isotopologues, require experimental times of hours to tens of hours to achieve desired precision, while current sample introduction techniques focus on observations on the order of seconds to tens of minutes. In this study, we characterize Orbitrap-IRMS performance for three long duration measurements (individual acquisitions ≥1 h and as long as 24 h) using an automated reservoir injection system coupled to a Q Exactive HF Orbitrap with an electrospray ionization (ESI) source. First, we characterize long-term intra-measurement stability through a 24-h long measurement of acetone. We report the following isotope ratios and precisions (as acquisition errors, errors on the observed ratio within this measurement (σ AE )): 13 C/ 12 C (σ AE = 0.07‰), 17 O/ 16 O (σ AE = 1.1‰), 18 O/ 16 O (σ AE = 0.3‰), and 13 C 13 C/ 12 C (σ AE = 0.65‰). The σ AE of each tracks the shot noise limit throughout and is limited by the challenging conditions (high resolution and low numbers of ions per scan) required for 17 O/ 16 O measurement in the presence of 13 C via Orbitrap. Second, we characterize inter-measurement stability via a sequence of seven 75-min analyses of perchlorate. We observe the following ratios and acquisition errors: 37 Cl/ 35 Cl (σ AE = 0.09‰); 17 O/ 16 O (σ AE = 1.6‰); 18 O/ 16 O (σ AE = 0.7‰), 37 Cl 17 O/ 35 Cl 16 O (σ AE = 2.7‰), and 37 Cl 18 O/ 35 Cl 16 O (σ AE = 1.2‰). However, we find that inter-measurement drift between acquisitions limits our accuracy and precision for standardized measurements (i.e., error on reported δ values) to ≈1‰ for the 37 Cl/ 35 Cl measurement. Hence, the benefits of low σ AE may not be fully realized. Third, we demonstrate accuracy via sample/standard comparisons of a methionine sample with 13 C enrichment of ≈20‰ relative to a known standard. Using a sequence of seven 60-min analyses, we recover the following isotope ratios and standardized precisions (i.e., error on reported δ values, denoted propagated acquisition errors, σ PAE ): 33 S/ 32 S (σ PAE = 1.0‰), 34 S/ 32 S (σ PAE = 0.7‰), 15 N/ 14 N (σ PAE = 2.1‰), 2 H/ 1 H (σ PAE = 3.2‰), 13 C/ 12 C (σ PAE = 0.4‰), 18 O/ 16 O (σ PAE = 1.6‰), & 13 C 13 C/ 12 C (σ PAE = 2.8‰) with confirmation of accurate results for the known 13 C/ 12 C and 13 C 13 C/ 12 C enrichments. Together, our results demonstrate the viability of Orbitrap-IRMS for long duration measurements of diverse sample types via an automated reservoir injection system. Inter-measurement stability remains a challenge; we expect our methods to be most applicable to extended measurements of hard-to-observe properties, such as 17 O in organics and clumped isotopologues.

58 GEOSCIENCES↗
DOE OSTI2021

A consistent and conservative volume distribution algorithm and its applications to multiphase flows using Phase-Field models

In the present study, the multiphase volume distribution problem, where there can be an arbitrary number of phases, is addressed using a consistent and conservative volume distribution algorithm. The proposed algorithm satisfies the summation constraint, the conservation constraint, and the consistency of reduction. The first application of the volume distribution algorithm is to determine the Lagrange multipliers in multiphase Phase-Field models that enforce the mass conservation, and a multiphase conservative Allen-Cahn model that satisfies the consistency of reduction is developed. A corresponding consistent and conservative numerical scheme is developed for the model. The multiphase conservative Allen-Cahn model has a better ability than the multiphase Cahn-Hilliard model to preserve under-resolved structures. The second application is to develop a numerical procedure, called the boundedness mapping, to map the order parameters, obtained numerically from a multiphase model, into their physical interval, and at the same time to preserve the physical properties of the order parameters. Along with the consistent and conservative schemes for the multiphase Phase-Field models, the numerical solutions of the order parameters are reduction consistent, conservative, and bounded, which are theoretically analyzed and numerically validated. Then, the multiphase Phase-Field models are coupled with the momentum equation by satisfying the consistency of mass conservation and the consistency of mass and momentum transport, thanks to the consistent formulation. Finally, it is demonstrated that the proposed model and scheme converge to the sharp-interface solution and are capable of capturing the complicated multiphase dynamics even when there is a large density and/or viscosity ratio.

42 ENGINEERING↗
DOE OSTI2022

Implementing contact angle boundary conditions for second-order Phase-Field models of wall-bounded multiphase flows

In the present work, a general formulation is proposed to implement the contact angle boundary conditions for the second-order Phase-Field models, which is applicable to N-phase (N ≥ 2) moving contact line problems. To remedy the issue of mass change due to the contact angle boundary condition, a source term or Lagrange multiplier is added to the original second-order Phase-Field models, which is determined by the consistent and conservative volume distribution algorithm so that the summation of the order parameters and the consistency of reduction are not influenced. To physically couple the proposed formulation to the hydrodynamics, especially for large-density-ratio problems, the consistent formulation is employed. The reduction-consistent conservative Allen-Cahn models are chosen as examples to illustrate the application of the proposed formulation. The numerical scheme that preserves the consistency and conservation of the proposed formulation is employed to demonstrate its effectiveness. Results produced by the proposed formulation are in good agreement with the exact and/or asymptotic solutions. The proposed method captures complex dynamics of moving contact line problems having large density ratios.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

WeakIdent: Weak formulation for identifying differential equation using narrow-fit and trimming

Data-driven identification of differential equations is an interesting but challenging problem, especially when the given data are corrupted by noise. When the governing differential equation is a linear combination of various differential terms, the identification problem can be formulated as solving a linear system, with the feature matrix consisting of linear and nonlinear terms multiplied by a coefficient vector. This product is equal to the time derivative term, and thus generates dynamical behaviors. The goal is to identify the correct terms that form the equation to capture the dynamics of the given data. We propose a general and robust framework to recover differential equations using a weak formulation with two new mechanisms, narrow-fit and trimming, for both ordinary and partial differential equations (ODEs and PDEs). The weak formulation facilitates an efficient and robust way to handle noise, and two new mechanisms, narrow-fit and trimming, improve the coefficient support and value recoveries respectively. For each sparsity level, Subspace Pursuit is utilized to find an initial set of support from the large dictionary. Then, we focus on highly dynamic regions (rows of the feature matrix), and error normalize the feature matrix in the narrow-fit step. The support is further updated via trimming the terms that contribute the least. Finally, the support set of features with the smallest Cross-Validation error is chosen as the result. A comprehensive set of numerical experiments are presented for both systems of ODEs and PDEs with various noise levels. The proposed method gives a robust recovery of the coefficients, and a significant denoising effect which can handle up to 100% noise-to-signal ratio for some equations. We compare the proposed method with several state-of-the-art algorithms for the recovery of differential equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A sharp interface Lagrangian-Eulerian method for flexible-body fluid-structure interaction

This paper introduces a sharp-interface approach to simulating fluid-structure interaction (FSI) involving flexible bodies described by general nonlinear material models and across a broad range of mass density ratios. This new flexible-body immersed Lagrangian-Eulerian (ILE) scheme extends our prior work on integrating partitioned and immersed approaches to rigid-body FSI. Our numerical approach incorporates the geometrical and domain solution flexibility of the immersed boundary (IB) method with an accuracy comparable to body-fitted approaches that sharply resolve flows and stresses up to the fluid-structure interface. Unlike many IB methods, our ILE formulation uses distinct momentum equations for the fluid and solid subregions with a Dirichlet-Neumann coupling strategy that connects fluid and solid subproblems through simple interface conditions. As in earlier work, we use approximate Lagrange multiplier forces to treat the kinematic interface conditions along the fluid-structure interface. This penalty approach simplifies the linear solvers needed by our formulation by introducing two representations of the fluid-structure interface, one that moves with the fluid and another that moves with the structure, that are connected by stiff springs. This approach also enables the use of multi-rate time stepping, which allows us to use different time step sizes for the fluid and structure subproblems. Our fluid solver relies on an immersed interface method (IIM) for discrete surfaces to impose stress jump conditions along complex interfaces while enabling the use of fast structured-grid solvers for the incompressible Navier-Stokes equations. The dynamics of the volumetric structural mesh are determined using a standard finite element approach to large-deformation nonlinear elasticity via a nearly incompressible solid mechanics formulation. This formulation also readily accommodates compressible structures with a constant total volume, and it can handle fully compressible solid structures for cases in which at least part of the solid boundary does not contact the incompressible fluid. Selected grid convergence studies demonstrate second-order convergence in volume conservation and in the pointwise discrepancies between corresponding positions of the two interface representations as well as between first and second-order convergence in the structural displacements. The time stepping scheme is also demonstrated to yield second-order convergence. To assess and validate the robustness and accuracy of the new algorithm, comparisons are made with computational and experimental FSI benchmarks. Test cases include both smooth and sharp geometries in various flow conditions. Furthermore, we also demonstrate the capabilities of this methodology by applying it to model the transport and capture of a geometrically realistic, deformable blood clot in an inferior vena cava filter.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Risk assessment of wellbore leakage during underground hydrogen storage

The expansion of renewable energy sources would require large-scale energy storage options to overcome the intermittent nature of these sources. Underground hydrogen storage (UHS) in depleted hydrocarbon reservoirs offers a scalable and practical energy storage solution. These reservoirs are chosen for their availability and large capacity, but the unique properties of hydrogen raise concerns about potential leakage pathways, particularly through wellbores. In this study, we develop and apply, for the first time, reduced-order models (ROMs) specifically designed for efficient leakage risk prediction in UHS systems operating in depleted hydrocarbon reservoirs. Using 3,000 high-fidelity simulation scenarios, we examine the influence of 11 key parameters, including reservoir and aquifer depths, wellbore permeability and porosity, initial saturations of water, oil and gas fractions (hydrogen, light, intermediate, and heavy hydrocarbons), reservoir pressure multiplier, and the aquifer-to-reservoir volume ratio, to simulate leakage behavior over a 1,000-year timescale. We train ROMs using a two-step classification-regression approach, achieving R 2 values exceeding 99 % across all targets. These ROMs effectively capture the leakage evolution and identify critical controls of leakage, guiding the design of mitigation strategies. Results indicate that gas leakage occurs in about 27 % of scenarios as early as five years post-operation, reaching volumes of up to 106 ft3. Oil leakage is less frequent (~17 %) and typically begins decades later. Our findings also show that hydrogen often migrates first, owing to its smaller molecular size and higher buoyancy, followed by heavier hydrocarbons. Over time, these heavier components contribute significantly to the total leaked volume, reinforcing the need for targeted monitoring and remediation strategies. Our analysis highlights that deeper storage reservoirs, shallower aquifers, and low-permeability wellbores significantly reduce leakage risks. In conclusion, this work offers a robust framework for risk-informed UHS deployment, supporting energy security through reliable large-scale hydrogen storage while safeguarding environmental integrity.

08 HYDROGEN↗
DOE OSTI2022

Superatomic chemistry

Superatoms are atomic clusters with tailored size and composition that mimic the chemistry of atoms in the periodic table. However, unlike the atoms whose chemistry is governed by their valence electron orbitals, the chemistry of superatoms is governed by their highest occupied molecular orbitals. In addition, due to their large size and non-spherical geometry, superatoms can promote unusual reactions and serve as the building blocks of cluster assembled materials with properties very different from conventional materials. This perspective highlights the unique role of superatoms in chemical and material sciences by focusing on superhalogens, which not only possess electron affinities larger than those of halogens but also can be stable when multiply charged. We discuss how these unique features of superhalogens enable noble gas atoms like argon to form chemical bonds at room temperature and zinc to exhibit an oxidation state of +3. Here, the advantages of using superhalogens in the synthesis of water-resistant materials for solar cells, halogen-free electrolytes for solid-state batteries, and multiferroic materials are also discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Energy based fracture initiation criterion for strain-crystallizing rubber-like materials with pre-existing cracks

Fracture prediction is indispensable for polymers, like rubbers, which have a broad range of applications mainly due to their high extensibility. The phenomenon known as strain-induced crystallization further contributes to the fracture toughness of certain rubbers. Here in this study, a criterion based on internal bond energy, incorporating the effects of crystallization, is proposed to predict fracture initiation in rubber-like materials with pre-existing cracks. First, a multi-scale mechanical model is developed for characterizing the behavior of rubber when subjected to both uniaxial and biaxial deformation states. At the microscale, both the amorphous and crystalline chain segments are modeled as elastic in order to consider the energy contribution by the molecular bond distortions. This internal energy is considered along with the entropic and crystalline free energy for each chain. In the chain model, the effects of loading condition and the relative orientation of a chain on its crystallinity are taken into account. At the macroscopic scale, an existing crystallinity distribution function is adapted and a mixed finite element formulation with an augmented Lagrangian multiplier is utilized to impose the incompressibility constraint. A non-affine maximal advance path constraint based homogenization model is utilized for bridging the two scales. Its potential to account for anisotropy in the stretched network compels the model to be preferable due to its physical significance, for the purpose of fracture modeling. The rigidity of the crystallites is accounted for by proposing a crystallite distortion energy in addition to the critical bond dissociation energy, for fracture initiation to occur. The model is validated by comparison with existing experimental results for both crystallizing and non-crystallizing rubbers. In addition to its potential to predict the material behavior when subjected to uniaxial and biaxial loading, the capability of the model to quantitatively estimate the effect of crystallization on fracture initiation is also verified.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Link statistics of dislocation network during strain hardening

Dislocations are line defects in crystals that multiply and self-organize into a complex network during strain hardening. The length of dislocation links, connecting neighboring nodes within this network, contains crucial information about the evolving dislocation microstructure. By analyzing data from Discrete Dislocation Dynamics (DDD) simulations in face-centered cubic (fcc) Cu, we characterize the statistical distribution of link lengths of dislocation networks during strain hardening on individual slip systems. Here, our analysis reveals that link lengths on active slip systems follow a double-exponential distribution, while those on inactive slip systems conform to a single-exponential distribution. The distinctive long tail observed in the double-exponential distribution is attributed to the stress-induced bowing out of long links on active slip systems, a feature that disappears upon removal of the applied stress. We further demonstrate that both observed link length distributions can be explained by extending a one-dimensional Poisson process to include different growth functions. Specifically, the double-exponential distribution emerges when the growth rate for links exceeding a critical length becomes super-linear, which aligns with the physical phenomenon of long links bowing out under stress. This work advances our understanding of dislocation microstructure evolution during strain hardening and elucidates the underlying physical mechanisms governing its formation.

Crystal plasticity↗
DOE OSTI2026

Distributed Tomographic Reconstruction with Quantization

Conventional tomographic reconstruction typically depends on centralized servers for both data storage and computation, leading to concerns about memory limitations and data privacy. Distributed reconstruction algorithms mitigate these issues by partitioning data across multiple nodes, reducing server load and enhancing privacy. However, these algorithms often encounter challenges related to memory constraints and communication overhead between nodes. In this paper, we introduce a decentralized Alternating Directions Method of Multipliers (ADMM) with configurable quantization. By distributing local objectives across nodes, our approach is highly scalable and can efficiently reconstruct images while adapting to available resources. To overcome communication bottlenecks, we propose two quantization techniques based on K-means clustering and JPEG compression. Numerical experiments with benchmark images illustrate the tradeoffs between communication efficiency, memory use, and reconstruction accuracy.

Miao, Runxuan↗
DOE OSTI2024

A safe reinforcement learning algorithm for supervisory control of power plants

Traditional control theory-based methods require tailored engineering for each system and constant fine-tuning. In power plant control, one often needs to obtain a precise representation of the system dynamics and carefully design the control scheme accordingly. Model-free Reinforcement learning (RL) has emerged as a promising solution for control tasks due to its ability to learn from trial-and-error interactions with the environment. It eliminates the need for explicitly modeling the environment’s dynamics, which is potentially inaccurate. However, the direct imposition of state constraints in power plant control raises challenges for standard RL methods. To address this, we propose a chance-constrained RL algorithm based on Proximal Policy Optimization for supervisory control. Our method employs Lagrangian relaxation to convert the constrained optimization problem into an unconstrained objective, where trainable Lagrange multipliers enforce the state constraints. In conclusion, our approach achieves the smallest distance of violation and violation rate in a load-follow maneuver for an advanced Nuclear Power Plant design.

constrained optimization↗
DOE OSTI2020

Low-cost, constrained-motion dynamometer for milling force measurement

This paper describes the design and testing of a low-cost dynamometer for milling force measurement. The monolithic design is based on constrained-motion/flexure-based kinematics, where force is inferred from displacement measured using a low-cost optical interrupter (i.e., a knife edge that partially interrupts the beam in an emitter-detector pair). The time-dependent displacement of the dynamometer’s moving platform caused by the milling force is converted to the frequency domain, multiplied by the inverse of the single degree of freedom frequency response, and converted back to the time domain to obtain the time dependent cutting force. Lastly, comparisons with commercially available, piezoelectric-based force measurement are provided.

47 OTHER INSTRUMENTATION↗
DOE OSTI2025

Accurate and rapid acoustic damage characterization in complex structures using sparse sensor networks and deep learning models

Damage diagnosis in critical components is essential for ensuring the safety and reliability of operations across industries, spanning manufacturing, aerospace, and energy. Traditional acoustic nondestructive testing methods primarily focus on detecting defects through the direct scattering of single-mode incident waves from the damage, which limit their applicability to simple structures and small inspection areas. Our earlier research demonstrated that machine learning algorithms combined with sparse sensor networks can identify critical defect signatures even from multiply scattered, multi-mode acoustic signals, indicating the potential for improved defect inspection in complex, real-world structures. In this work, we demonstrate the successful implementation of this approach in a fixed sensor configuration to rapidly and accurately detect simulated defects in a geometrically complex, real-world structure, a brake rotor hub. Three different types of defects were physically simulated on the surface of the hub, and the collected data were used to train an autoencoder-based deep learning model. Two models were tested, one using single measurements and the other using multiple measurements taking advantage of the spatial distribution of the sensor network. After training, the multi-measurement model achieved 100 % accuracy in identifying, classifying, and locating unseen, unique damages. This work illustrates the potential of the proposed method for a wide range of industrial applications.

36 MATERIALS SCIENCE↗
DOE OSTI2023

AdjointBackMapV2: Precise reconstruction of arbitrary CNN unit’s activation via adjoint operators

Adjoint operators have been found to be effective in the exploration of CNN’s inner workings (Wan and Choe, 2022). However, the previous no-bias assumption restricted its generalization. We overcome the restriction via embedding input images into an extended normed space that includes bias in all CNN layers as part of the extended space and propose an adjoint-operator-based algorithm that maps high-level weights back to the extended input space for reconstructing an effective hypersurface. Such hypersurface can be computed for an arbitrary unit in the CNN, and here we prove that this reconstructed hypersurface, when multiplied by the original input (through an inner product), will precisely replicate the output value of each unit. We show experimental results based on the CIFAR-10 and CIFAR-100 data sets where the proposed approach achieves near 0 activation value reconstruction error.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Performance of prototype GE1/1 chambers for the CMS muon spectrometer upgrade

The high-luminosity phase of the Large Hadron Collider (HL-LHC) will result in ten times higher particle background than measured during the first phase of LHC operation. In order to fully exploit the highly-demanding operating conditions during HL-LHC, the Compact Muon Solenoid (CMS) Collaboration will use Gas Electron Multiplier (GEM) detector technology. The technology will be integrated into the innermost region of the forward muon spectrometer of CMS as an additional muon station called GE1/1. The primary purpose of this auxiliary station is to help in muon reconstruction and to control level-1 muon trigger rates in the pseudo-rapidity region 1.6 ≤ |η| ≤ 2.2. The new station will contain trapezoidal-shaped GEM detectors called GE1/1 chambers. The design of these chambers is finalized, and the installation is in progress during the Long Shutdown phase two (LS-2) that started in 2019. Several full-size prototypes were built and operated successfully in various test beams at CERN. Here, we describe performance measurements such as gain, efficiency, and time resolution of these prototype chambers, developed after years of R&D, and summarize their behavior in different gas compositions as a function of the applied voltage.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

Analysis of the EMCCD point-source response using x-rays

Electron Multiplying Charge Coupled Devices, EMCCD are used as x-ray detectors. The NSLS-II Soft Inelastic x-ray Scattering (SIX) beam line has two EMCCDs for x-ray detection in the spectrometer arm. The spectrometer with high resolving power disperses x-rays vertically. The x-ray vertical position on the sensor plane is related to its energy. This allows for very accurate x-ray energy measurements through x-ray coordinates. X-rays interact with silicon and create a number of electron-hole pairs proportional to the x-ray energy. Electrons drift and diffuse toward pixel gates and are collected there. The diffused electrons form a charge cloud distributed over several neighboring pixels. This charge sharing enables coordinate measurements with accuracy better than the pixel pitch. The charge distribution shape has to be taken into account to achieve ultimate accuracy in coordinate measurements. In this paper, we present a method of the charge distribution shape analysis and demonstrate its applications. The drift and diffusion of electrons ftom the point of generation to pixel gates results in the bell-shaped electron cloud usually approximated by Gaussian shape. The number of electrons collected under a pixel is proportional to the shape function integral. These electron packets get transferred to the sense node of the output amplifier. The transfer process could introduce distortions to the original charge distribution. For example, during transfers, electrons in the packet could be exposed to traps if they are present in the sensor. The trapping and later the release processes distort the apparent shape of the charge distribution. Therefore, deviations of the charge distribution shape ftom the originally symmetrical form can indicate the presence of trap centers in the sensor and can be used for sensor diagnostics.

47 OTHER INSTRUMENTATION↗