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DOE OSTI2025

Efficient Measurement of Length Distribution of 1D Nanoparticles in Solution via Optical Polarimetry

The efficient measurement of the length distribution of nanotubes, nanowires, and other one-dimensional (1D) nanoparticles in solution is important to enable their incorporation into materials and devices and to optimize their processing for properties of interest, such as thermal/electrical conductivity or mechanical strength, in suspensions and composites. We report an electric-field (E-field)-assisted optical-polarimetry technique to measure the length distribution of ensembles of high-aspect-ratio particles in dilute suspension. The degree of alignment of polarizable 1D particles suspended in a fluid under Brownian motion explicitly depends on the E-field strength and the particle length. We show that it is possible to extract the length distribution of 1D nanoparticles suspended in an insulating fluid by applying a range of E-fields and using optical polarimetry to measure the corresponding alignment order parameter. Notably, the method is relatively insensitive to the diameter of the 1D particles, which can be poorly known or vary within a sample. The technique is validated with silver nanowires and carbon nanotubes of known lengths, as well as polymer-depletion-length-separated single-wall carbon nanotube samples with length distributions independently measured with analytical ultracentrifugation. Finally, we demonstrate the ability of the optical-polarimetry technique to quantify changes in the length distribution of ultranarrow, sub-nanometer-diameter single-wall carbon nanotubes under different types and durations of ultrasonication. Within its range of applicability (polarizable 1D nanoparticles in the 0.5 to 15 μm length range, constrained by the voltage stability of the media and the suspended particles), the E-field-assisted optical-polarimetry method is a particularly efficient and accurate method to measure the length distribution of nanowires and nanotubes in suspension.

1D nanoparticles↗

DOE OSTI2024

Nationwide cost and capacity estimates for sedimentary basin geothermal power and implications for geologic CO 2 storage

Sedimentary basins are naturally porous and permeable subsurface formations that underlie approximately half of the United States. In addition to being targets for geologic CO 2 storage, these resources could supply geothermal power: sedimentary basin geothermal heat can be extracted with water or CO 2 and used to generate electricity. The geothermal power potential of these basins and the accompanying implication for geologic CO 2 storage are, however, understudied. Here, we use the Sequestration of CO 2 Tool (SCO2T PRO ) and the generalizable GEOthermal techno-economic simulator (genGEO) to address this gap by a) estimating the cost and capacity of sedimentary basin geothermal power plants across the United States and b) comparing those results to nationwide CO 2 sequestration cost and storage potential estimates. We find that across the United States, using CO 2 as a geothermal heat extraction fluid reduces the cost of sedimentary basin power compared to using water, and some of the lowest cost capacity occurs in locations not typically considered for their geothermal resources (e.g., Louisiana, South Dakota). Additionally, using CO 2 effectively doubles the sedimentary basin geothermal resource base, equating to hundreds of gigawatts of new capacity, by enabling electricity generation in geologies that are otherwise (with water) too impermeable, too thin, too cold, or not deep enough. We find there is competition for the best sedimentary basin resources between water- and CO 2 -based power, but no overlap between the lowest-cost resources for CO 2 storage and CO 2 -based power. In this way, our results suggest that deploying CO 2 -based power may increase the cost of water based systems (by using the best resources) and the cost of CO 2 storage (by storing CO 2 in locations that otherwise may not be targeted). As such, our findings demonstrate that determining the best role for sedimentary basins within the energy transition may require balancing tradeoffs between competing priorities.

CPG↗

NASA NTRS1980

Use of an electrical resistance hygrometer to measure human sweat rates

The application of the resistance hygrometer as a tool to measure the localized sweat rate from the human body in both the active and passive sweat regions was studied. It was found that the physiological function of the skin membrane and fluid carrier transport phenomena from the outer skin have an indistinguishable effect on the observed findings from the instrument. The problems associated with the resistance hygrometer technique are identified and the usage of the instrument in the physiological experimentation from the engineering standpoint is evaluated.

Suga, T.↗

NASA NTRS2006

Seals/Secondary Fluid Flows Workshop 1997; Volume II: HSR Engine Special Session

The High Speed Civil Transport (HSCT) will be the largest engine ever built and operated at maximum conditions for long periods of time. It is being developed collaboratively with NASA, FAA, Boeing-McDonnell Douglas, Pratt & Whitney, and General Electric. This document provides an initial step toward defining high speed research (HSR) sealing needs. The overview for HSR seals includes defining objectives, summarizing sealing and material requirements, presenting relevant seal cross-sections, and identifying technology needs. Overview presentations are given for the inlet, turbomachinery, combustor and nozzle. The HSCT and HSR seal issues center on durability and efficiency of rotating equipment seals, structural seals and high speed bearing and sump seals. Tighter clearances, propulsion system size and thermal requirements challenge component designers.

Hendricks, Robert C.↗

DOE OSTI2014

Electrical impedance tomography spectroscopy method for characterising particles in solid-liquid phase

Electrical impedance tomography (EIT) is one of the process tomography techniques to provide an on-line non-invasive imaging for multiphase flow measurement. With EIT measurements, the images of impedance real part, impedance imaginary part, phase angle, and magnitude can be obtained. However, most of the applications of EIT in the process industries rely on the conductivity difference between two phases in fluids to obtain the concentration profiles. It is not common to use the imaginary part or phase angle due to the dominant change in conductivity or complication in the use of other impedance information. In a solid-liquid two phases system involving nano- or submicro-particles, characterisation of particles (e.g. particle size and concentration) have to rely on the measurement of impedance phase angle or imaginary part. Particles in a solution usually have an electrical double layer associated with their surfaces and can form an induced electrical dipole moment due to the polarization of the electrical double layer under the influence of an alternating electric field. Similar to EIT, electrical impedance spectroscopy (EIS) measurement can record the electrical impedance data, including impedance real part, imaginary part and phase angle (θ), which are caused by the polarization of the electrical double layer. These impedance data are related to the particle characteristics e.g. particle size, particle and ionic concentrations in the aqueous medium, therefore EIS method provides a capability for characterising the particles in suspensions. Electrical impedance tomography based on EIS measurement or namely, electrical impedance tomography spectroscopy (EITS) could image the spatial distribution of particle characteristics. In this paper, a new method, including test set-up and data analysis, for characterisation of particles in suspensions are developed through the experimental approach. The experimental results on tomographic imaging of colloidal particles based on EIS measurement using a sensor of 8 electrodes are reported. Results have demonstrated the potential as well as revealed the challenge in the use of EIS and EITS for characterisation of particle in suspension.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2015

Use of Encapsulated Zinc Particles in a Eutectic Chloride Salt to Enhance Thermal Energy Storage Capacity for Concentrated Solar Power

Concentrated Solar Power (CSP) is considered as a viable large-scale renewable energy source to produce electricity. However, current costs to produce electricity from CSP are not cost competitive as compared to the traditional energy generation technologies based on fossil fuels and nuclear. It is envisioned that development of high efficiency and high heat capacity thermal storage fluids will increase system efficiency, reduce structural storage volume, and hence, contribute to reducing costs. Particularly, with respect to CSP, current high temperature energy storage fluids, such as molten salts, are relatively limited in terms of their thermal energy storage capacity and thermal conductivity. The current work explores possibility of boosting the thermal storage capacity of molten salts through latent heat of added phase change materials. We studied the advantage Of adding coated Zn micron-sized particles to alkali chloride salt eutectic for enhanced thermal energy storage. Zinc particles (0.6 mu m and 5 mu m) obtained from commercial source were coated with an organo-phosphorus shell to improve chemical stability and to prevent individual particles from coalescing with one another during melt/freeze cycles. Thermal cycling tests (200 melt/freeze cycles) showed that coated Zn particles have good thermal stability and are chemically inert to alkali chloride salt eutectic in both N-2 and in air atmospheres. Elemental mapping of the cross-sectional view of coated Zn particles from the composite after thermal cycles showed no signs of oxidation, agglomeration or other type of particle degradation. The measured enhancement in volumetric thermal storage capacity of the composite with just similar to 10 vol% of coated Zn particles over the base chloride salt eutectic varies from 15% to 34% depending on cycling temperature range (Delta T = 50 degrees C -100 degrees C. (C) 2015 Elsevier Ltd. All rights reserved.

encapsulation↗

DOE OSTI2020

Wettability of ultra-small pores of carbon electrodes by size-asymmetric ionic fluids

Recently, we studied the phase behavior of ionic fluids under confinement using the classical density functional theory within the framework of the restricted primitive model. Additionally, the theoretical results indicate that narrowing the pore size may lead to a drastic reduction in the electric double layer capacitance, while increasing the surface electrical potential would improve the ionic accessibility of micropores. In this work, we extend the theoretical investigation to systems containing size-asymmetric electrolytes that may exhibit a vapor-liquid like phase transition in the bulk phase. The effects of pore size and surface electric potential on the phase diagram and microscopic structures of the confined electrolytes were studied over a broad range of parameters. We found that decreasing the pore size or increasing the surface potential could destabilize the liquid phase in micropores, and capillary evaporation could occur regardless of the size asymmetry between cations and anions. Compared to that in a symmetric ionic system, the vapor-liquid phase separation is more likely to take place as the size asymmetry becomes more pronounced. The phase transition would alter the “accessibility” of ions to micropores and lead to coexisting micropores with different surface charge densities as identified by Monte Carlo simulation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2016

Capacitively coupled hydrogen plasmas sustained by tailored voltage waveforms: excitation dynamics and ion flux asymmetry

Parallel plate capacitively coupled plasmas in hydrogen at relatively high pressure (~1 Torr) are excited with tailored voltage waveforms containing up to five frequencies. Predictions of a hybrid model combining a particle-in-cell simulation with Monte Carlo collisions and a fluid model are compared to phase resolved optical emission spectroscopy measurements, yielding information on the dynamics of the excitation rate in these discharges. When the discharge is excited with amplitude asymmetric waveforms, the discharge becomes electrically asymmetric, with different ion energies at each of the two electrodes. Unexpectedly, large differences in the $\text{H}_{2}^{+}$ fluxes to each of the two electrodes are caused by the different $\text{H}_{3}^{+}$ energies. When the discharge is excited with slope asymmetric waveforms, only weak electrical asymmetry of the discharge is observed. In this case, electron power absorption due to fast sheath expansion at one electrode is balanced by electron power absorption at the opposite electrode due to a strong electric field reversal.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2016

General Line Ampacity State Solver

INL’s General Line Ampacity State Solver (GLASS) is a high performance software platform that enables advanced grid system operations and planning efforts to be computed in real time. It enables the combination of advanced sensors and sensor networks, communication and data transfer channels, secure and reliable data management, and real-time processing through a flexible system architecture, with the ability to support and integrate with any utility enterprise system. GLASS is designed to help resolve the problems associated with thermally limited transmission and distribution networks, namely bare overhead power transmission lines. GLASS enables the methodology of Concurrent Cooling (Dynamic Line Rating) by reducing the need of using a cost-prohibited number of weather stations (reduce the number of weather stations per mile of overhead power line) to achieve the resolution necessary for individual electric transmission line span capacity calculations. GLASS achieves this by coupling real-time grid operations data and infrastructure architecture information with real-time field deployed weather station measurements and pre-computed Computational Fluid Dynamics (CFD)-based wind modeling interpolation parameters (look-up tables). GLASS uses mathematical models based on the IEEE 738 standard and builds off of the provided iterative solution using modern software paradigms and programming styles to provide a more robust and modular software system. GLASS also interfaces in real-time with utility companies using known transmission line spans and structures. GLASS provides real-time ampacity calculations based on recent weather station data as well as transmission line specifications. GLASS also allows the user to interact graphically with internal databases, which include information such as transmission line conductor types and thermal rating limits, weather station names and locations, specific transmission line span and structure locations, as well as recent ampacity calculations.

Gentle, Jake↗

NASA NTRS1965

Pickup device reads pressures from ports in rotating mechanisms

Indexing pickup monitors fluid pressures from ports at various angles on high or low speed rotating mechanisms in operation. By a simple axial movement of a takeoff connector, angle changing takes place. This device can be adapted for electric current monitoring.

Janas, B.↗

NASA NTRS1998

Application of a Modified Gas Chromatograph to Analyze Space Experiment Combustion Gases on Space Shuttle Mission STS-94

A space experiment designed to study the behavior of combustion without the gravitational effects of buoyancy was launched aboard the Space Shuttle Columbia on July 1, 1997. The space experiment, designated as Combustion Module-1 (CM-1), was one of several manifested on the Microgravity Sciences Laboratory - 1 (MSL-1) mission. The launch, designated STS-94, had the Spacelab Module as the payload, in which the MSL-1 experiments were conducted by the Shuttle crewmembers. CM-1 was designed to accommodate two different combustion experiments during MSL-1. One experiment, the Structure of Flame Balls at Low Lewis-number experiment (SOFBALL), required gas chromatography analysis to verify the composition of the known, premixed gases prior to combustion, and to determine the remaining reactant and the products resulting from the combustion process in microgravity. A commercial, off-the-shelf, dual-channel micro gas chromatograph was procured and modified to interface with the CM-1 Fluids Supply Package and the CM-1 Combustion Chamber, to accommodate two different carrier gases, each flowing through its own independent column module, to withstand the launch environment of the Space Shuttle, to accept Spacelab electrical power, and to meet the Spacelab flight requirements for electromagnetic interference (EMI) and offgassing. The GC data was down linked to the Marshall Space Flight Center for near-real time analysis, and stored on-orbit for post-flight analysis. The gas chromatograph operated successfully during the entire SOFBALL experiment and collected 309 runs. Because of the constraints imposed upon the gas chromatograph by the CM-1 hardware, system and operations, it was unable to measure the gases to the required accuracy. Future improvements to the system for a re-flight of the SOFBALL experiment are expected to enable the gas chromatograph to meet all the requirements.

Coho, William K.↗

NASA NTRS1995

Coupled Aerodynamic-Thermal-Structural (CATS) Analysis

Coupled Aerodynamic-Thermal-Structural (CATS) Analysis is a focused effort within the Numerical Propulsion System Simulation (NPSS) program to streamline multidisciplinary analysis of aeropropulsion components and assemblies. Multidisciplinary analysis of axial-flow compressor performance has been selected for the initial focus of this project. CATS will permit more accurate compressor system analysis by enabling users to include thermal and mechanical effects as an integral part of the aerodynamic analysis of the compressor primary flowpath. Thus, critical details, such as the variation of blade tip clearances and the deformation of the flowpath geometry, can be more accurately modeled and included in the aerodynamic analyses. The benefits of this coupled analysis capability are (1) performance and stall line predictions are improved by the inclusion of tip clearances and hot geometries, (2) design alternatives can be readily analyzed, and (3) higher fidelity analysis by researchers in various disciplines is possible. The goals for this project are a 10-percent improvement in stall margin predictions and a 2:1 speed-up in multidisciplinary analysis times. Working cooperatively with Pratt & Whitney, the Lewis CATS team defined the engineering processes and identified the software products necessary for streamlining these processes. The basic approach is to integrate the aerodynamic, thermal, and structural computational analyses by using data management and Non-Uniform Rational B-Splines (NURBS) based data mapping. Five software products have been defined for this task: (1) a primary flowpath data mapper, (2) a two-dimensional data mapper, (3) a database interface, (4) a blade structural pre- and post-processor, and (5) a computational fluid dynamics code for aerothermal analysis of the drum rotor. Thus far (1) a cooperative agreement has been established with Pratt & Whitney, (2) a Primary Flowpath Data Mapper has been prototyped and delivered to General Electric Aircraft Engines and Pratt & Whitney for evaluation, (3) a collaborative effort has been initiated with the National Institute of Standards and Testing to develop a Standard Data Access Interface, and (4) a blade tip clearance capability has been implemented into the Structural Airfoil Blade Engineering Routine (SABER) program. We plan to continue to develop the data mappers and data management tools. As progress is made, additional efforts will be made to apply these tools to propulsion system applications.

Source record↗

NASA NTRS2010

Performance Testing of a Prototypic Annular Linear Induction Pump for Fission Surface Power

Results of performance testing of an annular linear induction pump are presented. The pump electromagnetically pumps liquid metal (NaK) through a circuit specially designed to allow for quantification of the performance. Testing was conducted over a range of conditions, including frequencies of 33, 36, 39, and 60 Hz, liquid metal temperatures from 25 to 525 C, and input voltages from 5 to 120 V. Pump performance spanned a range of flow rates from roughly 0.16 to 5.7 L/s (2.5 to 90 gpm), and pressure head <1 to 90 kPa (<0.145 to 13 psi). The maximum efficiency measured during testing was slightly greater than 6%. The efficiency was fairly insensitive to input frequency from 33 to 39 Hz, and was markedly lower at 60 Hz. In addition, the efficiency decreased as the NaK temperature was raised. While the pump was powered, the fluid responded immediately to changes in the input power level, but when power was removed altogether, there was a brief slow-down period before the fluid would come to rest. The performance of the pump operating on a variable frequency drive providing 60 Hz power compared favorably with the same pump operating on 60 Hz power drawn directly from the electrical grid.

Polzin, K. A.↗

DOE OSTI2023

Cobalt-substituted perovskite compounds for solid oxide electrochemical cells

Oxygen electrodes are provided, comprising a perovskite compound having Formula (I), Sr(Ti 1-x Fe x-y Co y )O 3-δ wherein 0.90 ≥ x ≥ 0.40 and 0.02 ≥ y ≥ 0.30. Electrochemical devices comprising such oxygen electrodes are also provided, comprising a counter electrode in electrical communication with the oxygen electrode, and a solid oxide electrolyte between the oxygen electrode and the counter electrode. Methods of using such electrochemical devices are also provided, comprising exposing the oxygen electrode to a fluid comprising O 2 under conditions to induce the reaction O 2 +4e − →2O 2− , or to a fluid comprising O 2− under conditions to induce the reaction 2O 2− →O 2 +4e − .

Zhang, Shan-Lin↗

DOE OSTI2023

Closed Loop Geothermal Working Group: GeoCLUSTER App, Subsurface Simulation Results, and Publications

To better understand the heat production, electricity generation performance, and economic viability of closed-loop geothermal systems in hot-dry rock, the Closed-Loop Geothermal Working Group -- a consortium of several national labs and academic institutions has tabulated time-dependent numerical solutions and levelized cost results of two popular closed-loop heat exchanger designs (u-tube and co-axial). The heat exchanger designs were evaluated for two working fluids (water and supercritical CO2) while varying seven continuous independent parameters of interest (mass flow rate, vertical depth, horizontal extent, borehole diameter, formation gradient, formation conductivity, and injection temperature). The corresponding numerical solutions (approximately 1.2 million per heat exchanger design) are stored as multi-dimensional HDF5 datasets and can be queried at off-grid points using multi-dimensional linear interpolation. A Python script was developed to query this database and estimate time-dependent electricity generation using an organic Rankine cycle (for water) or direct turbine expansion cycle (for CO2) and perform a cost assessment. This document aims to give an overview of the HDF5 database file and highlights how to read, visualize, and query quantities of interest (e.g., levelized cost of electricity, levelized cost of heat) using the accompanying Python scripts. Details regarding the capital, operation, and maintenance and levelized cost calculation using the techno-economic analysis script are provided. This data submission will contain results from the Closed Loop Geothermal Working Group study that are within the public domain, including publications, simulation results, databases, and computer codes. GeoCLUSTER is a Python-based web application created using Dash, an open-source framework built on top of Flask that streamlines the building of data dashboards. GeoCLUSTER provides users with a collection of interactive methods for streamlining the exploration and visualization of an HDF5 dataset. The GeoCluster app and database are contained in the compressed file geocluster_vx.zip, where the "x" refers to the version number. For example, geocluster_v1.zip is Version 1 of the app. This zip file also contains installation instructions. **To use the GeoCLUSTER app in the cloud, click the link to "GeoCLUSTER on AWS" in the Resources section below. To use the GeoCLUSTER app locally, download the geocluster_vx.zip to your computer and uncompress this file. When uncompressed this file comprises two directories and the geocluster_installation.pdf file. The geo-data app contains the HDF5 database in condensed format, and the GeoCLUSTER directory contains the GeoCLUSTER app in the subdirectory dash_app, as app.py. The geocluster_installation.pdf file provides instructions on installing Python, the needed Python modules, and then executing the app.

15 GEOTHERMAL ENERGY↗

DOE OSTI2023

Tabulated Database of Closed-Loop Geothermal Systems Performance for Cloud-Based Technical and Economic Modeling of Heat Production and Electricity Generation: Preprint

To better understand the heat production, electricity generation performance and economic viability of closed loop geothermal systems in hot-dry-rock, the Closed Loop Geothermal Group, a consortium of several national labs and academic institutions has tabulated time-dependent numerical solutions and levelized cost results of two popular closed loop heat exchanger designs (u-tube and co-axial). The heat exchanger designs were evaluated for two working fluids (water and super-critical CO2) while varying seven continuous independent parameters of interest (i.e., mass flow rate, vertical depth, horizontal extent, borehole diameter, formation gradient, formation conductivity, and injection temperature). The corresponding numerical solutions (approximately 1.2 million per heat exchanger design) are stored as multi-dimensional HDF5 datasets and can be queried at off-grid points using multi-dimensional linear interpolation. A Python script was developed to query this database and estimate time-dependent electricity generation using an Organic Rankine cycle (for water) or direct turbine expansion cycle (for CO2) and perform a cost assessment. This document aims to give an overview of the HDF5 database file and highlights how to read, visualize, and query quantities of interest (e.g., levelized cost of electricity, levelized cost of heat) using the accompanying python scripts. Details regarding the capital, operation, and maintenance and levelized cost calculation using the TEA (techno-economic analysis) script are provided.

co-axial↗

NASA NTRS1994

A time-dependent gyro-kinetic model of thermal ion upflows in the high-latitude F region

Ample evidence supports the significance of the high-latitude ionospheric contribution to magnetospheric plasma. Assuming flux conservation along a flux tube, the upward field-aligned ion flows observed in the magnetosphere require high-latitude ionospheric field-aligned ion upflows of the order of 10(exp 8) to 10(exp 9)/sq cm/s. Since radar and satellite observations of high-latitude F region flows at times exceed this flux requirement by an order of magnitude, the thermal ionospheric upflows are not simply the ionospheric response to a magnetospheric flux requirement. Several ionospheric ion upflow mechanisms have been proposed, but simulations based on fluid theory do not reproduce all the observed features of ionospheric ion upflows. Certain asymmetries in the statistical morphology of high-latitude F region ion upflows suggest that the ion upflows may be generated by ion-neutral frictional heating. We developed a single-component (O(+)), time-dependent gyro-kinetic model of the high-latitude F region response to frictional heating in which the neutral exobase is a discontinuous boundary between fully collisional and collisionless plasmas. The concept of a discontinuous neutreal exobase and the assumption of a constant and uniform polarization electric field reduce the ion velocity distribution function, from which we can compute the ion density, parallel velocity, parallel and perpendicular temperature, and parallel flux. Using our model, we simulated the response of a convecting flux tube between 500 km and 2500 km to various frictional heating inputs; the results were both qualitatively and quantitatively different from fluid model results, which may indicate an inadequacy of the fluid theory approach. The gyro-kinetic frictional heating model responses to the various simulations were qualitatively similar: (1) initial perturbations of all the modeled parameters propagated rapidly up the flux tube, (2) transient values of the ion parallel velocity, temperature, and flux exceeded 3 km/s, 2 x 10(exp 4) K, and 10(exp 9)/sq cm/s, respectively, (3) a second transient regime developed wherein the parallel temperature drops to very low values (a few hundred Kelvins), and (4) well after heating ceased, large parallel temperatures and large downward parallel velocities and fluxes developed as the flux tube slowly returned to diffusive equilibrium. The ion velocity distributions during the simulation are often non-Maxwellian and are sometimes composed of two distinct ion populations.

Loranc, M.↗

DOE OSTI2015

Dynamic model based on voltage transfer curve for pattern formation in dielectric barrier glow discharge

Simulation work is very important for understanding the formation of self-organized discharge patterns. Previous works have witnessed different models derived from other systems for simulation of discharge pattern, but most of these models are complicated and time-consuming. In this paper, we introduce a convenient phenomenological dynamic model based on the basic dynamic process of glow discharge and the voltage transfer curve (VTC) to study the dielectric barrier glow discharge (DBGD) pattern. VTC is an important characteristic of DBGD, which plots the change of wall voltage after a discharge as a function of the initial total gap voltage. In the modeling, the combined effect of the discharge conditions is included in VTC, and the activation-inhibition effect is expressed by a spatial interaction term. Besides, the model reduces the dimensionality of the system by just considering the integration effect of current flow. All these greatly facilitate the construction of this model. Numerical simulations turn out to be in good accordance with our previous fluid modeling and experimental result.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗