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NASA NTRS1996

An AWE Implementation for Electromagnetic Analysis

Although full wave electromagnetic systems are large and cumbersome to solve, typically only a few parameters, such as input impedance, S parameters, and far field pattern, are needed by the designer or analyst. A reduced order modeling of these parameters is therefore an important consideration in minimizing the the CPU requirements. The Asymptotic Waveform Evaluation (AWE) method is one approach to construct a reduced order model of the input impedance or other useful electromagnetic parameters. We demonstrate its application and validity when used in conjunction with the finite element method to simulate full wave electromagnetic problems.

Gong, Jian↗

DOE OSTI2021

Learning effective physical laws for generating cosmological hydrodynamics with Lagrangian deep learning

The goal of generative models is to learn the intricate relations between the data to create new simulated data, but current approaches fail in very high dimensions. When the true data-generating process is based on physical processes, these impose symmetries and constraints, and the generative model can be created by learning an effective description of the underlying physics, which enables scaling of the generative model to very high dimensions. In this work, we propose Lagrangian deep learning (LDL) for this purpose, applying it to learn outputs of cosmological hydrodynamical simulations. The model uses layers of Lagrangian displacements of particles describing the observables to learn the effective physical laws. The displacements are modeled as the gradient of an effective potential, which explicitly satisfies the translational and rotational invariance. The total number of learned parameters is only of order 10, and they can be viewed as effective theory parameters. Further, we combine N-body solver fast particle mesh (FastPM) with LDL and apply it to a wide range of cosmological outputs, from the dark matter to the stellar maps, gas density, and temperature. The computational cost of LDL is nearly four orders of magnitude lower than that of the full hydrodynamical simulations, yet it outperforms them at the same resolution. We achieve this with only of order 10 layers from the initial conditions to the final output, in contrast to typical cosmological simulations with thousands of time steps. This opens up the possibility of analyzing cosmological observations entirely within this framework, without the need for large dark-matter simulations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Construction of quasisymmetric stellarators using a direct coordinate approach

In this work, optimized stellarator configurations and their analytical properties are obtained using a near-axis expansion approach. Such configurations are associated with good confinement as the guiding center particle trajectories and neoclassical transport are isomorphic to those in a tokamak. This makes them appealing as fusion reactor candidates. Using a direct coordinate approach, where the magnetic field and flux surface functions are found explicitly in terms of the position vector at successive orders in the distance to the axis, the set of ordinary differential equations for first and second order quasisymmetry is derived. Examples of quasi-axisymmetric shapes are constructed using a pseudospectral numerical method. Finally, the direct coordinate approach is used to independently verify two hypotheses commonly associated with quasisymmetric magnetic fields, namely that the number of equations exceeds the number of parameters at third order in the expansion and that the near-axis expansion does not prohibit exact quasisymmetry from being achieved on a single flux surface.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Enabling Dynamic Probabilistic Risk Assessment of Physical Security Using EMRALD and MAAP (Presentation)

The optimization of physical security in nuclear power plants requires sophisticated methodologies that integrate operator actions and plant behavior through advanced simulation tools. Idaho National Laboratory has developed the Modeling and Analysis for Safety and Security using the Dynamic EMRALD Framework (MASS-DEF) methodology, an approach that integrates force-on-force simulations, dynamic probabilistic risk assessment, and thermal hydraulics modeling to enhance security planning while reducing costs. A reduced order model for thermal hydraulic simulations performed by the Modular Accident Analysis Program (MAAP) was developed to evaluate reactor core behavior during attack scenarios. MAAP simulations are computationally intensive and must be run in a secure environment, complicating analysis and validation. By pre-computed scenario outcomes for a small number of modified parameters, the reduced order model significantly decreases the computational cost and enables offsite review of the results.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRSDate not supplied

Predicting Maximum Temperatures of a Li-ion Battery on a Simulated Flight Profile using a Model-based Prognostics

One of the challenges in using Li-ion packs in aeronautics is their safety, and thermal runaway (TR) is a major concern. The current engineering solutions to prevent a Li-ion pack from a catastrophic TR require additional mass and volume to isolate cells. The excess mass could be reduced by improving detection and, thus, preventing a TR event. One of the possible early warning indicators of a TR is crossing a threshold temperature. We have developed an approach, based on the Unscented Kalman Filter (UKF), to predict the likelihood of reaching the threshold temperature for simulated flight profiles. The current battery prognostics algorithms for aerospace predict state-of-charge (SOC) and end-of-life (EOL) [1]. We extended this two-level algorithm to predict the maximum temperature during discharge. The amount of heat generated in a cell depends on factors such as cell chemistry, cell packaging, total cycles, operating temperature, and abuse history [2]. Our semi-empirical thermal model depends on three phenomenological parameters which account for those factors. In addition, a two-parameter reduced-order model is developed to predict the temperature rise for short bursts of “random-walk” (RW) discharge current sequence, which simulates a flight's current-loading profile. The performance of these models on different datasets and types of current loading will be presented. To predict the maximal temperatures for future cycles we must estimate the evolution of thermal parameters as the batteries age. It is found that the parameters of the 3-parametric thermal model cannot be estimated only from the RW data. To address the issue, we will present two alternative approaches: i) expanding the datasets to include discharge profiles beyond RWs; ii) model reduction to a two-parametric model. The two approaches will be illustrated by an application to the cycling data from a commercial LG 18650 cell. References: 1. M. Daigle, C.S. Kulkarni, End-of-discharge and End-of-life Prediction in Lithium-ion Batteries with Electrochemistry-based Aging Models, in: AIAA Infotech @ Aerospace, American Institute of Aeronautics and Astronautics, San Diego, California, USA, 2016. 2. M. Börner, et. al, Correlation of aging and thermal stability of commercial 18650-type lithium ion batteries, Journal of Power Sources. 342 (2017) 382–392.

Thermal runaway↗

DOE OSTI2024

Transport coefficient sensitivities in a semi-analytic model for magnetized liner inertial fusion

Performance of magnetized liner inertial fusion (MagLIF) experiments is highly dependent on transport processes including magnetized heat flows and magnetic flux losses. Magnetohydrodynamic simulations used to model these experiments require a choice of model for the transport coefficients, which are the constants of proportionality relating driving terms, such as temperature gradients and currents, to the associated heat and magnetic field transport. The coefficients have been the subject of repeated recalculation using various methods throughout the years. Using a semi-analytic MagLIF model, we compare models for the transport coefficients. The choice of model modifies magnetic-flux losses caused by the Nernst thermoelectric effect and thermal conduction losses. We present simulated results from parameter scans conducted in order to compare the effects of the different models on parameters of interest in MagLIF. In some regions of parameter space, discrepancies of up to 38% are found in integrated quantities like the fusion yield. These results may serve as a guide for experimental validation of the various models, particularly as laser preheat energies and initial axial field strengths are increased on MagLIF experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2004

Synthesizing 3D Surfaces from Parameterized Strip Charts

We believe 3D information visualization has the power to unlock new levels of productivity in the monitoring and control of complex processes. Our goal is to provide visual methods to allow for rapid human insight into systems consisting of thousands to millions of parameters. We explore this hypothesis in two complex domains: NASA program management and NASA International Space Station (ISS) spacecraft computer operations. We seek to extend a common form of visualization called the strip chart from 2D to 3D. A strip chart can display the time series progression of a parameter and allows for trends and events to be identified. Strip charts can be overlayed when multiple parameters need to visualized in order to correlate their events. When many parameters are involved, the direct overlaying of strip charts can become confusing and may not fully utilize the graphing area to convey the relationships between the parameters. We provide a solution to this problem by generating 3D surfaces from parameterized strip charts. The 3D surface utilizes significantly more screen area to illustrate the differences in the parameters and the overlayed strip charts, and it can rapidly be scanned by humans to gain insight. The selection of the third dimension must be a parallel or parameterized homogenous resource in the target domain, defined using a finite, ordered, enumerated type, and not a heterogeneous type. We demonstrate our concepts with examples from the NASA program management domain (assessing the state of many plans) and the computers of the ISS (assessing the state of many computers). We identify 2D strip charts in each domain and show how to construct the corresponding 3D surfaces. The user can navigate the surface, zooming in on regions of interest, setting a mark and drilling down to source documents from which the data points have been derived. We close by discussing design issues, related work, and implementation challenges.

Robinson, Peter I.↗

NASA NTRS1990

A first-order Lyapunov robustness method for linear systems with uncertain parameters

A method for stability-robustness analysis based on a quadratic Liapunov function that varies linearly with uncertainty parameters is derived. Linear time-invariant systems with structured uncertainties are discussed. The Liapunov function is optimized numerically to maximize the robustness region in parameter space. Numerical results are given for four examples in which the first-order method is compared to previous Liapunov methods. While the zero-order method is slightly better than the first-order method for one example, the first-order method is clearly superior in the other three (more realistic) examples. The first-order method is especially superior for the active control of flexible structures, where robustness with respect to (1) unmodeled coupling between modeled modes and (2) unmodeled modes is important. For such applications, the first-order method is much better at detecting the increased robustness associated with increased separation between frequencies.

Leal, M. A.↗

DOE OSTI2026

Enabling Dynamic Probabilistic Risk Assessment of Physical Security Using EMRALD and MAAP

The optimization of physical security in nuclear power plants requires sophisticated methodologies that integrate operator actions and plant behavior through advanced simulation tools. To address this, Idaho National Laboratory [JL2.1]has developed the Modeling and Analysis for Safety and Security using the Dynamic EMRALD Framework (MASS-DEF) methodology, an approach that integrates force-on-force simulations, dynamic probabilistic risk assessment, and thermal-hydraulics modeling [JL3.1]to enhance security planning while reducing costs. We developed a tool that produces reduced order models using thermal hydraulic simulations from the Modular Accident Analysis Program (MAAP) [1]. These models can quickly evaluate reactor core behavior during attack simulations, and in so doing, address two barriers of traditional methods: (1) MAAP simulations are computationally intensive, and (2) attack scenarios must be run in a secure environment, which complicates analysis and validation. By precomputing scenario outcomes for a small number of modified parameters, the reduced order model significantly decreases the computational cost and enables offsite review of the results.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

Many-Exciton Quantum Dynamics in a Ruddlesden–Popper Tin Iodide

We present a study on the many-body exciton interactions in a Ruddlesden–Popper tin halide, namely, (PEA) 2 SnI 4 (PEA = phenylethylammonium), using coherent two-dimensional electronic spectroscopy. The optical dephasing times of the third-order polarization observed in these systems are determined by exciton many-body interactions and lattice fluctuations. We investigate the excitation-induced dephasing (EID) and observe a significant reduction of the dephasing time with increasing excitation density as compared to its lead counterpart (PEA) 2 PbI 4 , which we have previously reported in a separate publication [J. Chem. Phys. 2020, 153, 164706]. Surprisingly, we find that the EID interaction parameter is four orders of magnitude higher in (PEA) 2 SnI 4 than that in (PEA) 2 PbI 4 . This increase in the EID rate may be due to exciton localization arising from a more statically disordered lattice in the tin derivative. This is supported by the observation of multiple closely spaced exciton states and the broadening of the linewidth with increasing population time (spectral diffusion), which suggests a static disordered structure relative to the highly dynamic lead-halide. Additionally, we find that the exciton nonlinear coherent lineshape shows evidence of a biexcitonic state with low binding energy (<10 meV) not observed in the lead system. We model the lineshapes based on a stochastic scattering theory that accounts for the interaction with a nonstationary population of dark background excitations. Our study provides evidence of differences in the exciton quantum dynamics between tin- and lead-based Ruddlesden–Popper metal halides (RPMHs) and links them to the exciton–exciton interaction strength and the static disorder aspect of the crystalline structure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Diagonalizing the Born–Oppenheimer Hamiltonian via Moyal perturbation theory, nonadiabatic corrections, and translational degrees of freedom

This article describes a method for calculating higher order or nonadiabatic corrections in Born–Oppenheimer theory and its interaction with the translational degrees of freedom. The method uses the Wigner–Weyl correspondence to map nuclear operators into functions on the classical phase space and the Moyal star product to represent operator multiplication on those functions. These are explained in the body of the paper. The result is a power series in κ 2 , where κ = (m/M)1/4 is the usual Born–Oppenheimer parameter. The lowest order term is the usual Born–Oppenheimer approximation, while higher order terms are nonadiabatic corrections. These are needed in calculations of electronic currents, momenta, and densities. The separation of nuclear and electronic degrees of freedom takes place in the context of the exact symmetries (for an isolated molecule) of translations and rotations, and these, especially translations, are explicitly incorporated into our discussion. This article presents an independent derivation of the Moyal expansion in molecular Born–Oppenheimer theory. Here, we show how electronic currents and momenta can be calculated within the framework of Moyal perturbation theory; we derive the transformation laws of the electronic Hamiltonian, the electronic eigenstates, and the derivative couplings under translations; we discuss in detail the rectilinear motion of the molecular center of mass in the Born–Oppenheimer representation; and we show how the elimination of the translational components of the derivative couplings leads to a unitary transformation that has the effect of exactly separating the translational degrees of freedom.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1994

Constraints on molecular gas in cooling flows and powerful radio galaxies

We searched for molecular gas in a heterogeneous sample of five radio-loud galaxies (three of which are inferred to be in cooling flow clusters) using the Swedish-European Southern Observatory (Swedish-ESO) Submillimeter Telescope. We do not detect CO in emission in any of the cluster sources at a 3 sigma level of typically 15 mK. White et al. (1991) have suggested column densities of N(sub H) approximately 10(exp 21)/sq cm in these clusters with a spatial covering factor of order unity and a total mass of M approximately 10(exp 12) solar mass. Our limits are inconsistent with these column densities and spatial covering factor unless the molecular gas is very cold (kinetic temperature close to 2.7 K) or there only a few clouds along each line of sight. We estimate minimum temperatures in the range approximately 20-30 K. We find that clouds of atomic and molecular hydrogen require strict fine-tuning of parameter space in order to satisfy the requirements for the large column densities N(sub H) approximately 10(exp 21)/sq cm, unit covering factor, and a small number of clouds along the line of sight. Currently the only way molecular gas can be responsible for the X-ray absorption and still be consistent with our observations is if (1) there is of order one cloud along the line of sight and (2) the optical depth in C-12 1 to 0 is less than 10. In addition, we present a Very Large Array (VLA) image of NGC 4696 which suggests this object is a member of the class of 'amorphous cooling flow radio sources.' The C-12 1 to 0 line is detected in emission in PKS 0634-206, a classical double radio galaxy which is rich in extended optical emission line gas. The estimated molecular gas mass is M(sub mol) approximately 3 x 10(exp 9) solar mass and is much larger than that of the ionized component detected in hydrogen alpha suggesting that the emission-line nebula is radiation bounded.

O'Dea, Christopher P.↗

DOE OSTI2024

Quantification and assessment of the atmospheric boundary layer height measured during the AWAKEN experiment by a scanning LiDAR

The atmospheric boundary layer (ABL) height plays a key role in many atmospheric processes as one of the dominant flow length scales. However, a systematic quantification of the ABL height over the entire range of scales (i.e., with periods ranging from one minute to one year) is still lacking in literature. In this work, the ABL height is quantified based on high-resolution measurements collected by a scanning pulsed Doppler LiDAR during the recent American WAKE experimeNt (AWAKEN) campaign. The high availability of ABL height estimates (≈2200 collected over one year and each of them based on 10-min averaged statistics) allows to robustly assess five different ABL height models, i.e., one for convective thermal conditions and four for stable conditions. Thermal condition is quantified by a stability parameter spanning three orders of magnitude and probed by near-ground 3D sonic anemometry. The free-atmosphere stability, quantified by the Brunt–Väisälä frequency, is both calculated from simultaneous radiosonde measurements and obtained from the best fit of two of the chosen ABL height models. Good agreement is found between the data and three of the chosen models, quantified by mean absolute errors on the ABL height between 281 and 585 m. Furthermore, the seasonal variability of the convective ABL height model parameters (−15% to +23% with respect to the year baseline) agrees with the variability of buoyancy-generated turbulence caused by the variation in solar radiation throughout the year.

17 WIND ENERGY↗

DOE OSTI2021

Evaluating proxies for the drivers of natural gas productivity using machine-learning models

We report the extensive development of unconventional reservoirs using horizontal drilling and multistage hydraulic fracturing has generated large volumes of reservoir characterization and production data. The analysis of this abundant data using statistical methods and advanced machine-learning (ML) techniques can provide data-driven insights into well performance. Most predictive modeling studies have focused on the impact that different well completion and stimulation strategies have on well production but have not fully exploited the available in situ rock property data to determine its role in reservoir productivity. We have used machine-learning techniques to rank rock mechanical properties, microseismic attributes, and stimulation parameters in the order of their significance for predicting natural gas production from an unconventional reservoir. The data for this study came from a hydraulically fractured well in the Marcellus Shale in Monongalia County, West Virginia. The data classes included measurements aggregated by well completion stage that included (1) gas production, (2) well-log-derived measurements including bulk density, elastic moduli, shear impedance, compressional impedance, brittleness, and gamma measurements, (3) microseismic attributes, (4) long-period long-duration (LPLD) event counts, (5) fracture counts, and (6) stimulation parameters that included the fluid injection volume and average pumping pressure. To identify observable proxies for the drivers of gas production, we evaluated five commonly used ML approaches including multivariate adaptive regression spline, Gaussian mixture model, random forest, gradient boosting, and neural network. We selected five variables including LPLD event count, seismogenic b-value, hydraulic diffusivity, cumulative moment, and fluid volume as the features most likely to impact gas productivity at the stage level in the study area. The data-driven selection of these parameters for their importance in determining gas production can help reservoir engineers design more effective hydraulic-fracture treatments in the Marcellus Shale and other similar unconventional reservoirs. Plain language summary: We use machine-learning methods and data-driven selection of reservoir parameters to rank and better understand their importance in determining gas production, which can help reservoir engineers design more effective hydraulic-fracture treatments in the Marcellus Shale and other similar unconventional reservoirs.

58 GEOSCIENCES↗

NASA NTRS2008

Simulated Reentry Heating by Torching

The two first order reentry heating parameters are peak heating flux (W/cm2) and peak heat load (kJ/cm2). Peak heating flux (and deceleration, gs) is higher for a ballistic reentry and peak heat load is higher for a lifting reentry. Manned vehicle reentries are generally lifting reentries at nominal 1-5 gs so that personnel will not be crushed by high deceleration force. A few off-nominal manned reentries have experienced 8 or more gs with corresponding high heating flux (but below nominal heat load). The Shuttle Orbiter reentries provide about an order of magnitude difference in peak heating flux at mid-bottom (TPS tiles, approximately 6 W/cm2 or 5 BTU/ft2- sec) and leading edge (RCC, approximately 60 W/cm2 or 50 BTU/ft2- sec). Orion lunar return and Mars sample lander are of the same order of magnitude as orbiter leading edge peak heat loads. Flight temperature measurements are available for some orbiter TPS tile and RCC locations. Return-to-Flight on-orbit tile-repair-candidate-material-heating performance was evaluated by matching propane torch heating of candidate-materials temperatures at several depths to orbiter TPS tile flight-temperatures. Char and ash characteristics, heat expansion, and temperature histories at several depths of the cure-in-place ablator were some of the TPS repair material performance characteristics measured. The final char surface was above the initial surface for the primary candidate (silicone based) material, in contrast to a receded surface for the Apollo-type ablative heat shield material. Candidate TPS materials for Orion CEV (LEO and lunar return), and for Mars sample lander are now being evaluated. Torching of a candidate ablator material, PICA, was performed to match the ablation experienced by the STARDUST PICA heat shield. Torching showed that the carbon fiberform skeleton in a sample of PICA was inhomogeneous in that sample, and allowed measurements (of the clumps and voids) of the inhomogeneity. Additional reentry heating-performance characterizations of high temperature insulation materials were performed.

Harvey, Gale A.↗

NASA NTRS2008

Simulated Reentry Heating by Torching

The two first order reentry heating parameters are peak heating flux (W/square cm) and peak heat load (kJ/square cm). Peak heating flux (and deceleration, gs) is higher for a ballistic reentry and peak heat load is higher for a lifting reentry. Manned vehicle reentries are generally lifting reentries at nominal 1-5 gs so that personnel will not be crushed by high deceleration force. A few off-nominal manned reentries have experienced 8 or more gs with corresponding high heating flux (but below nominal heat load). The Shuttle Orbiter reentries provide about an order of magnitude difference in peak heating flux at mid-bottom (TPS tiles, approximately 6 W/square cm or 5 BTU/square ft - sec) and leading edge (RCC, approximately 60 W/square cm or 50 BTU/square ft- sec). Orion lunar return and Mars sample lander are of the same order of magnitude as orbiter leading edge peak heat loads. Flight temperature measurements are available for some orbiter TPS tile and RCC locations. Return-to-Flight on-orbit tile-repair-candidate-material-heating performance was evaluated by matching propane torch heating of candidate-materials temperatures at several depths to orbiter TPS tile flight-temperatures. Char and ash characteristics, heat expansion, and temperature histories at several depths of the cure-in-place ablator were some of the TPS repair material performance characteristics measured. The final char surface was above the initial surface for the primary candidate (silicone based) material, in contrast to a receded surface for the Apollo-type ablative heat shield material. Candidate TPS materials for Orion CEV (LEO and lunar return), and for Mars sample lander (MSL) are now being evaluated. Torching of a candidate ablator material, PICA, was performed to match the ablation experienced by the STARDUST PICA heat shield. Torching showed that the carbon fiberform skeleton in a sample of PICA was inhomogeneous in that sample, and allowed measurements (of the clumps and voids) of the inhomogeneity. Additional reentry heating-performance characterizations of high temperature insulation materials were performed.

Harvey, Gale A.↗

DOE OSTI2026

A Robust Methodology to Elucidate Kinetics of Room Temperature Electrochemical Propane Adsorption on Platinum

Electrocatalytic activation of alkanes can further decarbonize chemical manufacturing by leveraging affordable renewable electricity and readily available shale gas reserves in the United States. Earlier works have identified the unique role of Pt in adsorbing and activating alkanes, like propane, at room temperature in acidic, aqueous electrolytes, revealing spontaneous formation of deeply dehydrogenated propane-derived surface species with an intact C 3 - backbone. Although an adsorption mechanism was hypothesized, it has not been explicitly investigated to date, preventing the quantification of kinetic rate parameters. A robust methodology to investigate and benchmark propane adsorption kinetics on Pt is critical for the rational design of electrocatalysts that exhibit higher selectivity toward desired partially oxidized products. Herein, we analyze an oxidative current transience that appears during the adsorption of propane on Pt in aqueous electrochemical conditions and develop a methodology that elucidates the adsorption mechanism and enables quantification of rate parameters such as order dependences and apparent activation barriers. This method yields an expected first-order dependence with respect to propane concentration at low coverage and reveals a second-order dependence with respect to the concentration of surface active sites. Additionally, the apparent activation barrier for propane adsorption was calculated using an Arrhenius analysis of the current transience under temperature control. The experimentally measured activation barrier of 35 kJ mol –1 is in excellent agreement with the theoretical barrier calculated by density functional theory (DFT). The kinetic analysis was extended, via the use of transition state theory, to extract entropy and enthalpy of activation, yielding consistent results with the proposed two-step adsorption mechanism and DFT calculations. These results demonstrate reliable quantification of kinetic parameters for electrocatalytic activation of C–H bonds in alkanes that can be employed for rational catalyst development for a versatile range of electrocatalytic conditions.

alkane activation↗

NASA NTRS1999

A Multipole Expansion Method for Analyzing Lightning Field Changes

Changes in the surface electric field are frequently used to infer the locations and magnitudes of lightning-caused changes in thundercloud charge distributions. The traditional procedure is to assume that the charges that are effectively deposited by the flash can be modeled either as a single point charge (the Q model) or a point dipole (the P model). The Q model has four unknown parameters and provides a good description of many cloud-to-ground (CG) flashes. The P model has six unknown parameters and describes many intracloud (IC) discharges. In this paper we introduce a new analysis method that assumes that the change in the cloud charge can be described by a truncated multipole expansion, i.e., there are both monopole and dipole terms in the unknown source distribution, and both terms are applied simultaneously. This method can be used to analyze CG flashes that are accompanied by large changes in the cloud dipole moment and complex IC discharges. If there is enough information content in the measurements, the model can also be generalized to include quadrupole and higher order terms. The parameters of the charge moments are determined using a dme-dimensional grid search in combination with a linear inversion, and because of this, local minima in the error function and the associated solution ambiguities are avoided. The multipole method has been tested on computer-simulated sources and on natural lightning at the NASA Kennedy Space Center and U.S. Air Force Eastern Range.

Koshak, William J.↗